## Sunday, 26 February 2017

### On This Day in Math - February 26

Euler calculated without effort,
just as men breathe,
as eagles sustain themselves in the air.
~Francois Arago

The 57th day of the year; 57(base ten) is written with all ones in base seven. It is the last day this year that can be written in base seven with all ones.(What is the last day of the year that can be written with all ones in base two,... base three?)

57 is the maximum number of regions inside a circle formed by chords connecting 7 points on the circle. Students might ask themselves why this is the same as the first five numbers in the sixth row of Pascal's triangle.

57 is the number of permutations of the numbers 1 to 6 in which exactly 1 element is greater than the previous element (called a permutations with 1 "ascents").

57 is the maximum number of possible interior regions formed by 8 intersecting circles.

The number of ways of coloring the faces of a cube with 3 different colors is 57. For coloring a cube with n colors, the number of possible colorings is given by

57, is sometimes known as Grothendieck's prime.  The explanation is given in Amir D. Aczel's last book, Finding Zero.  Grothendieck had used primes as a framework on which to build some more general result when:

EVENTS
1616 Galileo is warned to abandon Copernican views. On February 19, 1616, the Inquisition had asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe after Nicollo Lorin had accused Galileo of Heretical remarks in a letter to his former student, Benedetto Castelli. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders. *Wik A transcript filed by the 1633 Inquisition indicates he was also enjoined from either speaking or writing about his theory. Yet Galileo remained in conflict with the Church. He was eventually interrogated by the Inquisition in Apr 1633. On 22 Jun 1633, Galileo was sentenced to prison indefinitely, with seven of ten cardinals presiding at his trial affirming the sentencing order. Upon signing a formal recantation, the Pope allowed him to live instead under house-arrest. From Dec 1633 to the end of his life on 8 Jan 1641, he remained in his villa at Florence.*TIS In 1992, the Vatican officially declared that Galileo had been the victim of an error.

1665 A letter from Christiaan Huygens to his father, Constantyn Huygens describes the discovery of synchronization between two pendulum clocks in his room.
While I was forced to stay in bed for a few days and made observations on my two clocks of the new workshop, I noticed a wonderful effect that nobody could have thought of before. The two clocks, while hanging [on the wall] side by side with a distance of one or two feet between, kept in pace relative to each other with a precision so high that the two pendulums always swung together, and never varied. While I admired this for some time, I finally found that this happened due to a sort of sympathy: when I made the pendulums swing at differing paces, I found that half an hour later, they always returned to synchronism and kept it constantly afterwards, as long as I let them go.

1849 Prince Albert visited the RI  for the 1st time to hear a lecture by Faraday. *Royal Institution ‏@ri_science Image

1855 Carl F. Gauss' body lay in state under the dome in the rotunda of the observatory in Gottingen two days after his death.  At nine o'clock a group of 12 students of science and mathematics, including Dedikind, carried the coffin out of the observatory and to his final resting place in St. Alben's Church Cemetery. After the casket was lowered it was covered with  covered with palms and laurel .

1885 “The Burroughs Company brought out their ﬁrst adding machine and announced that it would sell for $27.75$ plus $1.39$ shipping charges, for a total of whatever that came to.” *Tom Koch, 366 Dumb Days in History by Tom Koch

1962 A new teaching method based on “how and why things happen in mathematics rather than on traditional memorization of rules” is announced by the Educational Research Council of Greater Cleveland. This became the Cleveland Program of the New Math.*VFR

In 1896, Henri Becquerel stored a wrapped photographic plate in a closed desk drawer, and a phosphorescent uranium compound laid on top, awaiting a bright day to test his idea that sunlight would make the phosphorescent uranium emit rays. It remained there several days. Thus by sheer accident, he created a new experiment, for when he developed the photographic plate on 1 Mar 1896, he found a fogged image in the shape of the rocks. The material was spontaneously generating and emitting energetic rays totally without the external sunlight source. This was a landmark event. The new form of penetrating radiation was the discovery of the effect of radioactivity. He had in fact reported an earlier, related experiment to the French Academy on 24 Feb 1896, though at that time he thought phosphorescence was the cause.*TIS

1935 The first test of the ideas presented in Robert Watson-Watt's earlier memo, "Detection and location of aircraft by radio methods", were conducted on this date in a field near in Upper Stowe, about three miles south of Weedon Bec in Northhamptonshire. The tests were successful and on several occasions a clear signal was seen on the oscilloscopes hidden in the back of  an ambulance  from a Handley Page Heyford bomber being flown around the site by Bobby Blucke, who would later become Air Vice-Marshal Blucke. The tests were so secret that only three people were allowed to witness them, Watson-Watt, his colleague Arnold Wilkins, and a single member of the Air Ministry, A. P. Rowe *Wik

1996 Silicon Graphics Inc. buys Cray Research for $767 million, becoming the leading supplier of high-speed computing machines in the U.S. Over a forty year career, Cray founder Seymour Cray consistently produced most of the fastest computers in the world-- innovative, powerful supercomputers used in defense, meteorological, and scientific investigations. *CHM 2012 New world record distance for paper airplane throw: Joe Ayoob, a former Cal Quarterback, throws a John Collins paper airplane design, (which was named Suzanne), officially breaking the world record by 19 feet, 6 inches. The new world record was 226 feet, 10 inches. The previous record is 207 feet and 4 inches set by Stephen Kreiger in 2003. *ESPN BIRTHS 1585 Federico Cesi (26 Feb OR 13 Mar 1585 (sources differ, but Thony Christie did some research to suggest the Feb date is the correct one); 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847. 1664 Nicolas Fatio de Duillier (alternative names are Facio or Faccio;) (26 February 1664 – 12 May 1753) was a Swiss mathematician known for his work on the zodiacal light problem, for his very close (some have suggested "romantic" ) relationship with Isaac Newton, for his role in the Newton v. Leibniz calculus controversy , and for originating the "push" or "shadow" theory of gravitation. [Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra-mundane corpuscles) impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together.] He also developed and patented a method of perforating jewels for use in clocks. When Leibniz sent a set of problems for solution to England he mentioned Newton and failed to mention Faccio among those probably capable of solving them. Faccio retorted by sneering at Leibniz as the ‘second inventor’ of the calculus in a tract entitled ‘Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia,’ 4to, London, 1699. Finally he stirred up the whole Royal Society to take a part in the dispute (Brewster, Memoirs of Sir I. Newton, 2nd edit. ii. 1–5). In 1707, Fatio came under the influence of a fanatical religious sect, the Camisards, which ruined Fatio's reputation. He left England and took part in pilgrim journeys across Europe. After his return only a few scientific documents by him appeared. He died in 1753 in Maddersfield near Worcester, England. After his death his Geneva compatriot Georges-Louis Le Sage tried to purchase the scientific papers of Fatio. These papers together with Le Sage's are now in the Library of the University of Geneva. Eventually he retired to Worcester, where he formed some congenial friendships, and busied himself with scientific pursuits, alchemy, and the mysteries of the cabbala. In 1732 he endeavoured, but it is thought unsuccessfully, to obtain through the influence of John Conduitt [q. v.], Newton's nephew, some reward for having saved the life of the Prince of Orange. He assisted Conduitt in planning the design, and writing the inscription for Newton's monument in Westminster Abbey. *Wik 1786 Dominique François Jean Arago (26 Feb 1786, 2 Oct 1853) was a French physicist and astronomer who discovered the chromosphere of the sun (the lower atmosphere, primarily composed of hydrogen gas), and for his accurate estimates of the diameters of the planets. Arago found that a rotating copper disk deflects a magnetic needle held above it showing the production of magnetism by rotation of a nonmagnetic conductor. He devised an experiment that proved the wave theory of light, showed that light waves move more slowly through a dense medium than through air and contributed to the discovery of the laws of light polarization. Arago entered politics in 1848 as Minister of War and Marine and was responsible for abolishing slavery in the French colonies. *TIS A really great blog about Arago, With the catchy title, "François Arago: the most interesting physicist in the world!" is posted here. Read this introduction, and you will not be able to resist: When he was seven years old, he tried to stab a Spanish solider with a lance When he was eighteen, he talked a friend out of assassinating Napoleon He once angered an archbishop so much that the holy man punched him in the face He has negotiated with bandits, been chased by a mob, broken out of prison He is: François Arago, the most interesting physicist in the world 1799 Benoit Clapeyron (26 Feb 1799, 28 Jan 1864) French engineer who expressed Sadi Carnot's ideas on heat analytically, with the help of graphical representations. While investigating the operation of steam engines, Clapeyron found there was a relationship (1834) between the heat of vaporization of a fluid, its temperature and the increase in its volume upon vaporization. Made more general by Clausius, it is now known as the Clausius-Clapeyron formula. It provided the basis of the second law of thermodynamics. In engineering, Clayeyron designed and built locomotives and metal bridges. He also served on a committee investigating the construction of the Suez Canal and on a committee which considered how steam engines could be used in the navy.*TIS 1842 Nicolas Camille Flammarion (26 Feb 1842; 3 Jun 1925 at age 83) was a French astronomer who studied double and multiple stars, the moon and Mars. He is best known as the author of popular, lavishly illustrated, books on astronomy, including Popular Astronomy (1880) and The Atmosphere (1871). In 1873, Flammarion (wrongly) attributed the red color of Mars to vegetation when he wrote “May we attribute to the color of the herbage and plants which no doubt clothe the plains of Mars, the characteristic hue of that planet...” He supported the idea of canals on Mars, and intelligent life, perhaps more advanced than earth's. Flammarion reported changes in one of the craters of the moon, which he attributed to growth of vegetation. He also wrote novels, and late in life he turned to psychic research. *TIS 1843 Karl Friedrich Geiser (26 Feb 1843 in Langenthal, Bern, Switzerland, 7 May 1934 in Küsnacht, Zürich, Switzerland) Swiss mathematician who worked in algebraic geometry and minimal sufaces. He organised the first International Mathematical Congress in Zurich.*SAU 1864 John Evershed (26 Feb 1864, 17 Nov 1956) English astronomer who discovered (1909) the Evershed effect - the horizontal motion of gases outward from the centres of sunspots. While photographing solar prominences and sunspot spectra, he noticed that many of the Fraunhofer lines in the sunspot spectra were shifted to the red. By showing that these were Doppler shifts, he proved the motion of the source gases. This discovery came to be known as the Evershed effect. He also gave his name to a spectroheliograph, the Evershed spectroscope.*TIS 1946 Ahmed Hassan Zewail (February 26, 1946 – August 2, 2016) was an Egyptian-American scientist, known as the "father of femtochemistry". He was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry and became the first Egyptian and the first Arab to win a Nobel Prize in a scientific field. He was the Linus Pauling Chair Professor of Chemistry, Professor of Physics, and the director of the Physical Biology Center for Ultrafast Science and Technology at the California Institute of Technology. Zewail died aged 70 on the evening of August 2, 2016, after a long battle with cancer. *Wik DEATHS 1638 Claude-Gaspar Bachet de M´eziriac (9 Oct 1581, 26 Feb 1638), noted for his work in number theory and mathematical recreations. He published the Greek text of Diophantus’s Arithmetica in 1621. He asked the ﬁrst ferrying problem: Three jealous husbands and their wives wish to cross a river in a boat that will only hold two persons, in such a manner as to never leave a woman in the company of a man unless her husband is present. (With four couples this is impossible.)*VFR (I admit that I don't know how this differs from the similar river crossings problems of Alcuin in the 800's, Help someone?)His books on mathematical puzzles formed the basis for almost all later books on mathematical recreations.*SAU 1693 Sir Charles Scarborough MP FRS FRCP (19 December 1615 – 26 February 1693) was an English physician and mathematician. He was born in St. Martin's-in-the-Fields, London in 1615, the son of Edmund Scarburgh, and was sent to St. Paul's School, whence he proceeded to Caius College, Cambridge, and educated at St Paul's School, Gonville and Caius College, Cambridge (BA, 1637, MA, 1640) and Merton College, Oxford (MD, 1646). While at Oxford he was a student of William Harvey, and the two would become close friends. Scarborough was also tutor to Christopher Wren, who was for a time his assistant. Following the Restoration in 1660, Scarborough was appointed physician to Charles II, who knighted him in 1669; Scarborough attended the king on his deathbed, and was later physician to James II and William and Mary. During the reign of James II, Scarborough served (from 1685 to 1687) as Member of Parliament for Camelford in Cornwall. Scarborough was an original fellow of the Royal Society and a fellow of the Royal College of Physicians, author of a treatise on anatomy, Syllabus Musculorum, which was used for many years as a textbook, and a translator and commentator of the first six books of Euclid's Elements (published in 1705). He also was the subject of a poem by Abraham Cowley, An Ode to Dr Scarborough. Scarborough died in London in 1693. He was buried at Cranford, Middlesex, where there is a monument to him in the parish church erected by his widow. *Wik 1878 Pietro Angelo Secchi (18 Jun 1818, 26 Feb 1878 at age 59) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall.*TIS 1985 Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was the joint winner, with Leonid Kantorovich, of the 1975 Nobel Memorial Prize in Economic Sciences. Koopmans' early works on the Hartree–Fock theory are associated with the Koopmans' theorem, which is very well known in quantum chemistry. Koopmans was awarded his Nobel prize (jointly with Leonid Kantorovich) for his contributions to the field of resource allocation, specifically the theory of optimal use of resources. The work for which the prize was awarded focused on activity analysis, the study of interactions between the inputs and outputs of production, and their relationship to economic efficiency and prices.*SAU Credits : *CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell ## Saturday, 25 February 2017 ### On This Day in Math - February 25  Cathedral Church of St Paul the Apostle *Wik People must understand that science is inherently neither a potential for good nor for evil. It is a potential to be harnessed by man to do his bidding. ~Glenn T. Seaborg The 56th day of the year; There are 56 normalized 5x5 Latin Squares (First row and column have 1,2,3,4,5; and no number appears twice in a row or column. There are a much smaller number of 4x4 squares, try them first) 56 is the sum of the first six triangular numbers (56= 1 + 3 + 6 + 10 + 15 + 21) and thus the sixth tetrahedral number. It is also the sum of six consecutive primes. 3 + 5 + 7 + 11 + 13 + 17 56 letters are required to write the famous prime number 6700417 in English. The number was one of the factors of $F(5)=2^{2^5}+1$ Fermat had conjectured that all such "Fermat Numbers" were prime. In 1732, Euler showed that F(5) was the product or 641 times 6700417. Euler never stated that both numbers were prime, and historians still disagree about whether he knew, or even suspected, that it was. Fifty-Six is a city in Stone County, Arkansas, United States. As of the 2010 census, the city had a total population of 173, an increase of 10 persons from 2000. When founding the community in 1918, locals submitted the name "Newcomb" for the settlement. This request was rejected, and the federal government internally named the community for its school district number (56) The Aubrey holes are a ring of fifty-six Chalk pits at Stonehenge, named after the seventeenth-century antiquarian John Aubrey. They date to the earliest phases of Stonehenge in the late fourth and early third millennium BC. Their purpose is still unknown. *Wik EVENTS 1598 John Dee demonstrates the solar eclipse by viewing an image through a pinhole. Two versions from Ashmole and Aubrey give different details of who was present. Dee's Diary only contains the notation, "the eclips. A clowdy day, but great darkness about 9 1/2 maine " *Benjamin Wooley, The Queen's Conjuror 1606 Henry Briggs sends a Letter to Mr. Clarke, of Gravesend, dated from Gresham College, with which he sends him the description of a ruler, called Bedwell's ruler, with directions how to use it. (it seems from the letter to be a ruler for measuring the volume of timber. If you have information on where I could see a picture or other image of the device, please advise) *Augustus De Morgan, Correspondence of scientific men of the seventeenth century 1672 (NS) John Wallis collects his work on tangents in a letter to Oldenburg for publication in the Philosophical Transactions. According to a letter from Collins to James Gregory, "I mentioned Slusius (René-François de Sluse) his intent to publish his method de maximis et minimis et tangentibus, which Dr. Wallis hearing of hath sent up his owne Notations about the same, which should have been printed in the last Transactions, but is deferred to the next one newly come out." *John Wallis, Philip Beeley, Christoph J. Scriba, Correspondence of John Wallis (1616-1703) 1939 Appropriately, it was an astronomer who coined the term photography, but the question is, which one. Some credit Johann Heinrich von Madler for combining “photo” (from the Greek word for “light”) and “graphy” (“to write”). *APS.org Madler's claim rests on a paper supposedly written on 25 February 1839 in the German newspaper Vossische Zeitung. Many still credit Sir John Herschel both for coining the word and for introducing it to the public. His uses of it in private correspondence prior to 25 February 1839 and at his Royal Society lecture on the subject in London on 14 March 1839 have long been amply documented and accepted as settled facts. *Wik 1870 Hermann Amandus Schwarz sent his friend Georg Cantor a letter containing the ﬁrst rigorous proof of the theorem that if the derivative of a function vanishes then the function is constant. See H. Meschkowski, Ways of Thought of Great Mathematicians, pp. 87–89 for an English translation of the letter. *VFR 1959 The APT Language is Demonstrated: The Automatically Programmed Tools language is demonstrated. APT is an English-like language that tells tools how to work and is mainly used in computer-assisted manufacturing. NEW YORKER: Cambridge, Mass. - Feb. 25: The Air Force announced today that it has a machine that can receive instructions in English - figure out how to make whatever is wanted- and teach other machines how to make it. An Air Force general said it will enable the United States to build a war machine that nobody would want to tackle. Today it made an ashtray. *CHM 1976 Romania issued a stamp picturing the mathematician Anton Davidoglu (1876–1958). [Scott #2613] *VFR BIRTHS 1670 Maria Winckelmann (Maria Margarethe Winckelmann Kirch (25 Feb 1670 in Panitzsch, near Leipzig, Germany - 29 Dec 1720 in Berlin, Germany) was a German astronomer who helped her husband with his observations. She was the first woman to discover a comet.*SAU "German astronomer Maria Kirch (1670 – 1720). Kirch was original educated by her father and her uncle who believed that girls should receive the same education as boys. From them she learnt mathematics and astronomy going on to study with and work together with the amateur astronomer Christoph Arnold. Through Arnold she got to know the astronomer Gottfried Kirch and despite the fact that he was 30 years older than her they married. Kirch was official astronomer of the Berlin Royal Academy of Science and he and Maria ran the Academy’s observatory together for many years. In 1702 she became the first woman to discover a comet but the credit for the discovery was given to her husband. When Gottfried died in 1710 Maria applied for his position arguing correctly that she had done half of the work in the past. Despite her having published independently and having an excellent reputation as well as the active support of Leibniz the Academy refused to award her the post. She worked in various other observatories until 1717 when her son was appointed to his fathers post, Maria once again becoming the assistant. Despite having more than proved her equality to any male astronomer Maria never really received the recognition she deserved." From Thony Christie's Renaissance Mathematicus blog on Daughters of Urania. 1827 Henry William Watson (25 Feb 1827 in Marylebone, London, England - 11 Jan 1903 in Berkswell (near Coventry), England) was an English mathematician who wrote some influential text-books on electricity and magnetism. *SAU 1902 Kenjiro Shoda (February 25, 1902 – March 3, 1977 *SAU gives March 20 for death) was a Japanese mathematician. He was interested in group theory, and went to Berlin to work with Issai Schur. After one year in Berlin, Shoda went to Göttingen to study with Emmy Noether. Noether's school brought a mathematical growth to him. In 1929 he returned to Japan. Soon afterwards, he began to write Abstract Algebra, his mathematical textbook in Japanese for advanced learners. It was published in 1932 and soon recognised as a significant work for mathematics in Japan. It became a standard textbook and was reprinted many times.*Wik 1922 Ernst Gabor Straus (February 25, 1922 – July 12, 1983) was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions. His extensive list of co-authors includes Albert Einstein and Paul Erdős as well as other notable researchers including Richard Bellman, Béla Bollobás, Sarvadaman Chowla, Ronald Graham, László Lovász, Carl Pomerance, and George Szekeres. It is due to his collaboration with Straus that Einstein has Erdős number 2. *Wik 1926 Masatoşi Gündüz İkeda (25 February 1926, Tokyo. - 9 February 2003, Ankara), was a Turkish mathematician of Japanese ancestry, known for his contributions to the field of algebraic number theory. *Wik DEATHS 1723 Sir Christopher Wren (20 Oct 1632; 25 Feb 1723) Architect, astronomer, and geometrician who was the greatest English architect of his time (Some may suggest Hooke as an equal) whose famous masterpiece is St. Paul's Cathedral, among many other buildings after London's Great Fire of 1666. Wren learned scientific skills as an assistant to an eminent anatomist. Through astronomy, he developed skills in working models, diagrams and charting that proved useful when he entered architecture. He inventing a "weather clock" similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique. He was president of the Royal Society 1680-82. His scientific work was highly regarded by Sir Isaac Newton as stated in the Principia. *TIS Thony Christie points out that, "Most people don’t realise that as well as being Britain’s most famous 17th century architect, Wren was also a highly respected mathematician. In fact Isaac Newton named him along with John Wallace and William Oughtred as one of the three best English mathematicians of the 17th century. As a young man he was an active astronomer and was a highly vocal supporter of the then still relatively young elliptical astronomy of Johannes Kepler." (I love the message on his tomb in the Crypt of St. Pauls: Si monumentum requiris circumspice ...."Reader, if you seek his monument, look about you." Lisa Jardine's book is excellent 1775 William Small (13 October 1734; Carmyllie, Angus, Scotland – 25 February 1775; Birmingham, England). He attended Dundee Grammar School, and Marischal College, Aberdeen where he received an MA in 1755. In 1758, he was appointed Professor of Natural Philosophy at the College of William and Mary in Virginia, then one of Britain’s American colonies. Small is known for being Thomas Jefferson's professor at William and Mary, and for having an influence on the young Jefferson. Small introduced him to members of Virginia society who were to have an important role in Jefferson's life, including George Wythe a leading jurist in the colonies and Francis Fauquier, the Governor of Virginia. Recalling his years as a student, Thomas Jefferson described Small as: "a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and a large and liberal mind... from his conversation I got my first views of the expansion of science and of the system of things in which we are placed." In 1764 Small returned to Britain, with a letter of introduction to Matthew Boulton from Benjamin Franklin. Through this connection Small was elected to the Lunar Society, a prestigious club of scientists and industrialists. In 1765 he received his MD and established a medical practice in Birmingham, and shared a house with John Ash, a leading physician in the city. Small was Boulton's doctor and became a close friend of Erasmus Darwin, Thomas Day, James Keir, James Watt, Anna Seward and others connected with the Lunar Society. He was one of the best-liked members of the society and an active contributor to their debates. Small died in Birmingham on 25 February 1775 from malaria contracted during his stay in Virginia. He is buried in St. Philips Church Yard, Birmingham. The William Small Physical Laboratory, which houses the Physics department at the College of William & Mary, is named in his honor. *Wik 1786 Thomas Wright (22 September 1711 – 25 February 1786) was an English astronomer, mathematician, instrument maker, architect and garden designer. He was the first to describe the shape of the Milky Way and speculate that faint nebulae were distant galaxies.*Wik 1947 Louis Carl Heinrich Friedrich Paschen (22 Jan 1865; 25 Feb 1947) was a German physicist who was an outstanding experimental spectroscopist. In 1895, in a detailed study of the spectral series of helium, an element then newly discovered on earth, he showed the identical match with the spectral lines of helium as originally found in the solar spectrum by Janssen and Lockyer nearly 40 years earlier. He is remembered for the Paschen Series of spectral lines of hydrogen which he elucidated in 1908. *TIS 1950 Nikolai Nikolaevich Luzin, (also spelled Lusin) (9 December 1883, Irkutsk – 28 January 1950, Moscow), was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.*Wik 1972 Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war. Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars. *Wik His Mathematical Snapshots is a delight to read, but get the ﬁrst English edition if you can—there are lots of surprises there. *VFR "When Steinhaus failed to attend an important meeting of the Committee of the Polish Academy of Sciences in 1960, he received a letter chiding him for "not having justified his absence." He immediately wired the President of the Academy that "as long as there are members who have not yet justified their presence, I do not need to justify my absence." [ Told by Mark Kac in "Hugo Steinhaus -- A Remembrance and a Tribute," Amer. Math. Monthly 81 (June-July 1974) 578. ] * http://komplexify.com 1988 Kurt Mahler (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a mathematician and Fellow of the Royal Society. Mahler proved that the Prouhet–Thue–Morse constant and the Champernowne constant 0.1234567891011121314151617181920... are transcendental numbers. He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D. from Johann Wolfgang Goethe University of Frankfurt am Main in 1927. He left Germany with the rise of Hitler and accepted an invitation by Louis Mordell to go to Manchester. He became a British citizen in 1946. He was elected a member of the Royal Society in 1948 and a member of the Australian Academy of Science in 1965. He was awarded the London Mathematical Society's Senior Berwick Prize in 1950, the De Morgan Medal, 1971, and the Thomas Ranken Lyle Medal, 1977. *Wik 1999 Glenn Theodore Seaborg (April 19, 1912,Ishpeming, Michigan – February 25, 1999) was an American scientist who won the 1951 Nobel Prize in Chemistry for "discoveries in the chemistry of the transuranium elements", contributed to the discovery and isolation of ten elements, and developed the actinide concept, which led to the current arrangement of the actinoid series in the periodic table of the elements. He spent most of his career as an educator and research scientist at the University of California, Berkeley where he became the second Chancellor in its history and served as a University Professor. Seaborg advised ten presidents from Harry S. Truman to Bill Clinton on nuclear policy and was the chairman of the United States Atomic Energy Commission from 1961 to 1971 where he pushed for commercial nuclear energy and peaceful applications of nuclear science. The element seaborgium was named after Seaborg by Albert Ghiorso, E. Kenneth Hulet, and others, who also credited Seaborg as a co-discoverer. It was so named while Seaborg was still alive, which proved controversial. He influenced the naming of so many elements that with the announcement of seaborgium, it was noted in Discover magazine's review of the year in science that he could receive a letter addressed in chemical elements: seaborgium, lawrencium (for the Lawrence Berkeley Laboratory where he worked), berkelium, californium, americium (Once when being aggressively cross-examined during testimony on nuclear energy for a senate committee, the Senator asked, “How much do you really know about Plutonium.” Seaborg quietly answered, “Sir, I discovered it.” , Which he did as part of the team at the Manhattan Project. *Wik Credits : *CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell ## Friday, 24 February 2017 ### On This Day in Math -February 24  3D Lichtenberg Figures *Wik Information is the resolution of uncertainty. ~Claude Shannon The 55th day of the year; 55 is the largest triangular number that appears in the Fibonacci Sequence. (Is there a largest square number?) 55 is also a Kaprekar Number: 55² = 3025 and 30 + 25 = 55 (Thanks to Jim Wilder) And speaking of 52, Everyone knows that 32 + 42 = 52, but did you know that 332 + 442 = 552 But after that, there could be no more.... right? I mean, that's just too improbable, so why is he stil l going on like this? You don't think......Nah. 55 is the only year day that is both a non-trivial base ten palindrome and also a palindrome in base four. EVENTS 1582 Pope Gregory XIII promulgated his calendar reform in the papal bull Inter gravissimus (Of the gravest concern). It took effect (in Italy and some other Catholic countries) October 5, 1582 (Julian Thursday, 4 October 1582, being followed by Gregorian Friday, 15 October 1582) 1616 Inquisition qualifiers deny teaching of Heliocentric view . On February 19, 1616, the Inquisition had asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders. *Wik 1755 William Hogarth’s satirical print, “An Election Entertainment,” was published. It contains a Tory sign bearing the inscription “Give us our eleven days.” This refers to the fact that eleven dates were removed from the calendar when England converted to the Gregorian calendar on September 14, 1752. *VFR Image here 1772 Lagrange, in a letter to d’Alembert, called higher mathematics “decadent.” *Grabiner, Origins of Cauchy’s Rigorous Calculus, pp. 25, 185 1842 Sylvester resigned his position at the University of Virginia (after only four months), after a dispute with a student who was reading a newspaper in class. Persistent rumors that he killed the student are unfounded. *VFR 1881 Cambridge University in England allowed women to officially take university examinations and to have their names posted along with those of the male students. Previously some women were given special permission to take the Tripos Exam. One of these was Charlotte Agnes Scott, who did quite well on the exam. At the award ceremony “The man read out the names and when he came to ‘eighth,’ before he could say the name, all the undergraduates called out ‘Scott of Girton,’ and cheered tremendously, shouting her name over and over again with tremendous cheers and wavings of hats.” [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, 194-195] *VFR 1896 Henri Becquerel read a report to the French Academy of Sciences of his investigation of the phosphorescent rays of some “double sulfate of uranium and potassium” crystals. He reported that he placed the crystals on the outside of a photographic plate wrapped in sheets of very thick black paper and exposed the whole to the sun for several hours. When he developed the photographic plate, he saw a black silhouette of the substance exposed on the negative. When he placed a coin or metal screen between the uranium crystals and the wrapped plate, he saw images of those objects on the negative. He did not yet know yet that the sun is not necessary to initiate the rays, nor did he yet realize that he had accidentally discovered radioactivity. He would learn more from a further accidental discovery on 26 Feb 1896.*TIS 1920 As part of the National Education Association’s annual meeting, 127 mathematics teachers from 20 states met in Cleveland, Ohio, for the “purpose of organizing a National Council of Mathematics Teachers.” *VFR 1931, the Fields Medal was established to recognize outstanding contributions to mathematics. It was conceived since there was no Nobel Prize for mathematicians. Although John Charles Fields probably thought of the medal at some earlier time, the first recorded mention of it was made on 24 Feb 1931 in minutes of a committee meeting. He was chairman of the Committee of the International Congress which had been set up by the University of Toronto to organize the 1924 Congress in Toronto. After the event, Fields proposed that income of$2,500 remaining from that convention would be designated for two medals to be awarded at future International Mathematical Congresses. In 1936, the first awards were made in Oslo.*TIS

In 1968, Nature carried the announcement of the discovery of a pulsar (a pulsating radio source). The first pulsar was discovered by a graduate student, Jocelyn Bell, on 28 Nov 1967, then working under the direction of Prof. Anthony Hewish. The star emitted radio pulses with clock-like precision. It was observed at the Mullard Radio Astronomy Observatory, Cambridge University, England. A special radio telescope, was used with 2,048 antennae arrayed across 4.4 acres. Pulsars prompted studies in quantum-degenerate fluids, relativistic gravity and interstellar magnetic fields. *TIS [Before the nature of the signal was determined, the researchers, Bell and her Ph.D supervisor Antony Hewish, somewhat seriously considered the possibility of extraterrestrial life, "We did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. It is an interesting problem - if one thinks one may have detected life elsewhere in the universe how does one announce the results responsibly? Who does one tell first?" The observation was given the half-humorous designation Little green men 1, until researchers Thomas Gold and Fred Hoyle correctly identified these signals as rapidly rotating neutron stars with strong magnetic fields.] Read the details in her own words here.

2009 Comet Lulin, a non-periodic comet, makes its closest approach to Earth, peaking in brightness between magnitude +4 and magnitude +6. *Wik

BIRTHS
1663 Thomas Newcomen (24 Feb 1663 (Newcomen was baptised OTD unfortunately there is no mention of his birth date in the baptism record); 5 Aug 1729 at age 66) English engineer and inventor of the the world's first successful atmospheric steam engine. His invention of c.1711 came into use by 1725 to pump water out of coal mines or raise water to power water-wheels. On each stroke, steam filled a cylinder closed by a piston, then a spray of water chilled and condensed the steam in the cylinder creating a vacuum, then atmospheric pressure pushed the piston down. A crossbeam transferred the motion of the piston to operating the pump. This was wasteful of fuel needed to reheat the cylinder for the next stroke. Despite being slow and inefficient, Newcomen's engine was relied on for the first 60 years of the new steam age it began, perhaps the single most important invention of the Industrial Revolution. *TIS

1709 Jacques de Vaucanson (24 Feb 1709; 21 Nov 1782 at age 73) French inventor of automata - robot devices of later significance for modern industry. In 1737-38, he produced a transverse flute player, a pipe and tabor player, and a mechanical duck, which was especially noteworthy, not only imitating the motions of a live duck, but also the motions of drinking, eating, and "digesting." He made improvements in the mechanization of silk weaving, but his most important invention was ignored for several decades - that of automating the loom by means of perforated cards that guided hooks connected to the warp yarns. (Later reconstructed and improved by J.-M. Jacquard, it became one of the most important inventions of the Industrial Revolution.) He also invented many machine tools of permanent importance. *TIS

1804 Heinrich Friedrich Emil Lenz (24 Feb 1804, 10 Feb 1865 at age 61) was the Russian physicist who framed Lenz's Law to describe the direction of flow of electric current generated by a wire moving through a magnetic field. Lenz worked on electrical conduction and electromagnetism. In 1833 he reported investigations into the way electrical resistance changes with temperature, showing that an increase in temperature increases the resistance (for a metal). He is best-known for Lenz's law, which he discovered in 1834 while investigating magnetic induction. It states that the current induced by a change flows so as to oppose the effect producing the change. Lenz's law is a consequence of the, more general, law of conservation of energy. *TIS

1868 James Ireland Craig (24 Feb 1868 in Buckhaven, Fife, Scotland - 26 Jan 1952 in Cairo, Egypt) graduated from Edinburgh and Cambridge. He taught at Eton and Winchester and then went to work on the Nile Survey for the Egyptian government. He made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.*SAU

1878 Felix Bernstein born. In 1895 or 1896, while still a Gymnasium student, he volunteered to read the proofs of a paper of Georg Cantor on set theory. In the process of doing this the idea came to him one morning while shaving of how to prove what is now called the Cantor/Bernstein theorem: If each of two sets is equivalent to a subset of the other, then they are equivalent. *VFR He also worked on transfinite ordinal numbers.*SAU

1909 Max Black​ (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *Wik

1920 K C Sreedharan Pillai (1920–1985) was an Indian statistician who was known for his works on multivariate analysis and probability distributions. Pillai was honoured by being elected a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He was an elected member of the International Statistical Institute. *Wik Perhaps his best known contribution is the widely used multivariate analysis of variance test which bears his name.*SAU

1946 Gregori Aleksandrovich Margulis (24 Feb 1946 - )Russian mathematician who was awarded the Fields Medal in 1978 for his contributions to the theory of Lie groups, though he was not allowed by the Soviet government to travel to Finland to receive the award. In 1990 Margulis immigrated to the United States. Margulis' work was largely involved in solving a number of problems in the theory of Lie groups. In particular, Margulis proved a long-standing conjecture by Atle Selberg concerning discrete subgroups of semisimple Lie groups. The techniques he used in his work were drawn from combinatorics, ergodic theory, dynamical systems, and differential geometry.*TIS The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis *Wik

1955 Steven Paul Jobs (24 Feb 1955; 5 Oct 2011 at age 56) U S inventor and entrepreneur who, in 1976, co-founded Apple Inc. with Steve Wozniak to manufacture personal computers. During his life he was issued or applied for 338 patents as either inventor or co-inventor of not only applications in computers, portable electronic devices and user interfaces, but also a number of others in a range of technologies. From the outset, he was active in all aspects of the Apple company, designing, developing and marketing. After the initial success of the Apple II series of personal computers, the Macintosh superseded it with a mouse-driven graphical interface. Jobs kept Apple at the forefront of innovative, functional, user-friendly designs with new products including the iPad tablet and iPhone. Jobs was also involved with computer graphics movies through his purchase (1986) of the company that became Pixar *TIS

1967 Brian Paul Schmidt AC, FRS (February 24, 1967, ) is a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist at The Australian National University Mount Stromlo Observatory and Research School of Astronomy and Astrophysics and is known for his research in using supernovae as cosmological probes. He currently holds an Australia Research Council Federation Fellowship and was elected to the Royal Society in 2012.[2] Schmidt shared both the 2006 Shaw Prize in Astronomy and the 2011 Nobel Prize in Physics with Saul Perlmutter and Adam Riess for providing evidence that the expansion of the universe is accelerating. *Wik

DEATHS
1728 Charles René Reyneau (11 June 1656 in Brissac, Maine-et-Loire, France - 24 Feb 1728 in Paris, France) was a French mathematician who published an influential textbook on the newly invented calculus.*SAU (He) "undertook to reduce into one body, for the use of his scholars, the principal theories scattered here and there in Newton, Descartes, Leibnitz, Bernoulli, the Leipsic Acts, the Memoirs of the Paris Academy, and in other works; treasures which by being so widely dispersed, proved much less useful than they otherwise might have been. The fruit of this undertaking, was his “Analyse Demontree,” or Analysis Demonstrated, which he published in 1708. He gave it the name of “Analysis Demonstrated,” because he demonstrates in it several methods which had not been handled by the authors of them, with sufficient perspicuity and exactness. The book was so well approved, that it soon became a maxim, at least in France, that to follow him was the best, if not the only way, to make any extraordinary progress in the mathematics and he was considered as the first master, as the Euclid of the sublime geometry." (From the 1812 Chalmer's Biography, vol. 26, p. 151)

1799 Georg Christoph Lichtenberg (1 Jul 1742, 24 Feb 1799 at age 56). German physicist and satirical writer, best known for his aphorisms and his ridicule of metaphysical and romantic excesses. At Göttingen University, Lichtenberg did research in a wide variety of fields, including geophysics, volcanology, meteorology, chemistry, astronomy, and mathematics. His most important were his investigations into physics. Notably, he constructed a huge electrophorus and, in the course of experimentations, discovered in 1777 the basic principle of modern xerographic copying; the images that he reproduced are still called "Lichtenberg figures." These are radial patterns formed when sharp, pointed conducting bodies at high voltage get near enough to insulators to discharge electrically, or seen on persons struck by lightning. *TIS

1810 Henry Cavendish (10 Oct 1731; 24 Feb 1810) English chemist and physicist who conducted experiments with diverse interests in his private laboratory. Most notably, he determined the mass and density of the Earth. He investigated the properties of hydrogen and carbon dioxide, including comparing their density to that of air. Cavendish also showed that water was a compound and measured the specific heat of various substances. His manuscripts (published 1879) revealed discoveries he made in electrostatics before Coulomb, Ohm and Faraday - including deducing the inverse square law of electrostatic attraction and repulsion. He also found specific inductive capacity. His family name is attached to the Cavendish Laboratory (founded 1871, funded by a later family member) at Cambridge University. *TIS Cavendish was supposedly so shy that for his only portrait the artist painted his coat from a hook in the hall, then painted Cavendish body from memory. *"Shock and Awe", BBC broadcast on the history of electricity

1812 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36) He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS He studied geometric systems called ray systems, closely connected to Julius Plücker's line geometry. He conducted experiments to verify Christiaan Huygens' theories of light and rewrote the theory in analytical form. His discovery of the polarization of light by reflection was published in 1809 and his theory of double refraction of light in crystals, in 1810.
Malus attempted to identify the relationship between the polarising angle of reflection that he had discovered, and the refractive index of the reflecting material. While he deduced the correct relation for water, he was unable to do so for glasses due to the low quality of materials available to him (most glasses at that time showing a variation in refractive index between the surface and the interior of the glass). It was not until 1815 that Sir David Brewster was able to experiment with higher quality glasses and correctly formulate what is known as Brewster's law.
Malus is probably best remembered for Malus' law, giving the resultant intensity, when a polariser is placed in the path of an incident beam. His name is one of the 72 names inscribed on the Eiffel tower.*Wik

1844 Antoine-André-Louis Reynaud (12 Sept 1771, 24 Feb 1844) Reynaud published a number of extremely influential textbooks. He published a mathematics manual for surveyors as well as Traité d'algèbre, Trigonométrie rectiligne et sphérique, Théorèmes et problèmes de géométrie and Traité de statistique. His best known texts, however, were his editions of Bézout's Traité d'arithmétique which appeared in at least 26 versions containing much original work by Reynaud.
It appears that Reynaud became interested in algorithms when he was working with de Prony. At this time de Prony was very much involved in trying to get his logarithmic and trigonometric tables published and it seems to have made Reynaud think about analysing algorithms. Certainly Reynaud, although his results in this area were rather trivial, must get the credit for being one of the first people to give an explicit analysis of an algorithm, an area of mathematics which is of major importance today. *SAU

1856 Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. *Wik  A yahoo recording of the classic Tom Lehrer song about Lobachevsky is here with lyrics. Lehrer has stated there is no accusation of Lobachevsky plagiarizing anything, and his name was chosen for the rhythmic characteristics.

1871 Julius Ludwig Weisbach (10 August 1806 in Mittelschmiedeberg (now Mildenau Municipality), Erzgebirge, 24 February 1871, Freiberg) was a German mathematician and engineer. He studied with Carl Friedrich Gauss in Göttingen and with Friedrich Mohs in Vienna. He wrote an influential book for mechanical engineering students, called Lehrbuch der Ingenieur- und Maschinenmechanik, which has been expanded and reprinted on numerous occasions between 1845 and 1863. *Wik He wrote fourteen books and 59 papers he wrote on mechanics, hydraulics, surveying, and mathematics. It is in hydraulics that his work was most influential, with his books on the topic continuing to be of importance well into the 20th century. *SAU

1923 Edward Williams Morley (29 Jan 1838; 24 Feb 1923) American chemist who is best known for his collaboration with the physicist A.A. Michelson in an attempt to measure the relative motion of the Earth through a hypothetical ether (1887). He also studied the variations of atmospheric oxygen content. He specialized in accurate quantitative measurements, such as those of the vapor tension of mercury, thermal expansion of gases, or the combining weights of hydrogen and oxygen. Morley assisted Michelson in the latter's persuit of measurements of the greatest possible accuracy to detect a difference in the speed of light through an omnipresent ether. Yet the ether could not be detected and the physicists had seriously to consider that the ether did not exist, even questioning much orthodox physical theory. *TIS

1933 Eugenio Bertini (8 Nov 1846 in Forli, Italy - 24 Feb 1933 in Pisa, Italy) was an Italian mathematician who worked in projective and algebraic geometry. His work in algebraic geometry extended Cremona's work. He studied geometrical properties invariant under Cremona transformations and used the theory to resolve the singularities of a curve. A paper by Kleiman studies what the authors calls the two fundamental theorems of Bertini. These two fundamental theorems are among the ones most used in algebraic geometry. The first theorem is a statement about singular points of members of a pencil of hypersurfaces in an algebraic variety. The second theorem is about the irreducibility of a general member of a linear system of hypersurfaces. *SAU

2001 Claude Shannon (30 April 1916 in Petoskey, Michigan, USA - 24 Feb 2001 in Medford, Massachusetts, USA) founded the subject of information theory and he proposed a linear schematic model of a communications system. His Master's thesis was on A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. *SAU While working with John von Neumann on early computer designs, (John) Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948. Among several statues to Shannon, one is erected in his hometown of Gaylord, Michigan. The statue is located in Shannon Park in the center of downtown Gaylord, which was Shannon's boyhood home. Shannon Park is the former site of the Shannon Building, built and owned by Claude Shannon's father.

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Thursday, 23 February 2017

### On This Day in Math - February 23

 Gauss memorial in Brunswick

Pauca sed matura.
(Few, but ripe.)
~Carl F. Gauss, His motto. He would limit his publications to work he regarded as complete and perfect.

 Rubik's cube has 54 squares
The 54th day of the year; 54 is the smallest number that can be written as the sum of 3 squares in 3 ways.(Well, go on, find all three ways!)
There are 54 ways to draw six circles through all the points on a 6x6 lattice. *gotmath.com

54 is the fourth Leyland number, after mathematician Paul Leyland. Leyland numbers are numbers of the form $x^y + y^x$ where x,y are both integers greater than 1.

And the Sin(54o) is one-half the golden ratio.

EVENTS
 Drawing by Athanasius Kircher, 1684
1668/9 Cheerleaders Rejoice, The Megaphone is born.. A Letter from Newton on this date is extended by John Collins. In it he mentions "Another useful Instrument lately invented here, is Sir Samuell Morelands loud speaking Trumpett, of which he hath written a Booke or history with the title of Tuba Stentorophonica value one shilling, by which persons may discourse at about a Mile and a halfes distance, if not more". A very similar type of instrument had been thought of by Athanasius Kircher. Two years earlier he described a device that could be used for both broadcasting on one end and “overhearing” on the other. The term ‘megaphone’ was seemingly coined by Thomas Edison 200 years later. *Wik The image at right shows "war tubas" to detect sound of enemy aircraft in the 1920' and 30's before radar. This one shows Emperor Showa inspecting mobile Japanese tubas, but they were common in many countries. *Chris Wild, The strange history of listening before radar.

1826 Lobachevsky ﬁrst announced his principles of non-Euclidean geometry. This was done in a talk at his home University of Kazan. Unfortunately no record of the talk survives. *VFR

1855 At 1:05 a.m., Johann Carl Friedrich Gauss, Professor of Mathematics and Director of the Observatory at G¨ottingen, ceased breathing. His pocket watch, which he had carried with him most of his life, ceased ticking at almost exactly the same time. [Eves, Adieu, 43◦]*VFR

In 1896, the Tootsie Roll was introduced by Austrian immigrant Leo Hirshfield to the U.S. In a small store in New York City, he began producing his a chocolaty, chewy candy, which he named after a nickname of "Tootsie" for his five-year-old daughter, Clara. He was America's first candy maker to individually wrap penny candy. By 1905, production moved to a four-story factory in New York. During World War II, Tootsie Rolls were added to American soldiers' rations because of their ability to withstand severe weather conditions and give quick energy. Tootsie Rolls are made from a base of sugar, corn syrup, soy-bean oil, skim milk and cocoa. Current production is over 49 million pieces a day.*TIS Every year in Calculus as we were introducing Rolle's Thm, I would mention to my class the important contribution of his daughter, Tootsie.
Some nice "Tootsie Roll" math can be found at this blog from Christopher Danielson.

1912 Richard Courant gives his Inagural lecture, "On Existance Proofs in Mathematics,” at Gottingen. Existance proofs would run through his life’s works. A common joke years later, when he was not loved by all who knew him, was that Courant had proved by Counterexample, “Courant does not exist.” *Reid, Courant

1955 Germany issued a stamp for the centenary of the death of Gauss. [Scott #725] *VFR

In 1987, supernova 1987A in LMC was first seen. The brightest of the twentieth century, it was the first supernova visible with the naked eye since 1604. *TIS

2012 The near earth asteroid 2012 DA14 has an estimated diameter of about 44 meters and an estimated mass of about 120,000 metric tons. It was discovered on February 23, 2012, by the OAM Observatory, La Sagra in Spain (J75). Calculations show that on February 15, 2013, the distance between the asteroid and the Earth will be 0.07 LD (27,000 km; 17,000 mi) *Science Daily

BIRTHS
1583 Jean-Baptiste Morin (23 Feb 1583 in Villefranche, Beaujolais, France - 6 Nov 1656 in Paris, France) French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account.
Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu​ to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal.
Morin realised that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal.
Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realised as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645.*SAU

1723 Richard Price (23 February 1723 – 19 April 1791) was a British moral philosopher and preacher in the tradition of English Dissenters, and a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He fostered connections between a large number of people, including writers of the Constitution of the United States. He spent most of his adult life as minister of Newington Green Unitarian Church, where possibly the congregant he most influenced was early feminist Mary Wollstonecraft, who extended his ideas on the egalitarianism inherent in the spirit of the French Revolution to encompass women's rights as well. In addition to his work as a moral and political philosopher, he also wrote on issues of statistics and finance, and was inducted into the Royal Society for these contributions. Price was a friend of the mathematician and clergyman Thomas Bayes. He edited Bayes' most famous work "An Essay towards solving a Problem in the Doctrine of Chances" which contains Bayes' Theorem, one of the most fundamental theorems of probability theory, and arranged for its posthumous publication. Price wrote an introduction to Bayes' paper which provides some of the philosophical basis of Bayesian statistics.
Besides the above-mentioned, Price wrote an Essay on the Population of England (2nd ed., 1780) which directly influenced Thomas Robert Malthus.*Wik

1861 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU

1905 Prime Number Theorist Derrick Lehmer (February 23, 1905 – May 22, 1991) Derrick Lehmer, one of the world's best known prime number theorists, is born in Berkeley, California. Before World War II, Lehmer invented a number of electromechanical sieves for finding prime numbers and made many important contributions in prime number theory throughout his life. Prime numbers are of interest in themselves as mathematical curiosities but are also of great importance to cryptography. The Computer Museum History Center has three Lehmer sieves in its permanent collection. Lehmer died in 1991.*CHM Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing. *Wik

1922 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician,
in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics
described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository
series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7

1947 Robert Edward Bowen called Rufus by his friends, because of his striking red hair and beard (23 Feb 1947 in Vallejo, California, USA - 30 July 1978 in Santa Rosa, California, USA) Rufus Bowen worked on dynamical systems and died of a cerebral hemorrhage at the age of 31. *SAU

1951 Shigefumi Mori (23 Feb 1951 Nagoya, Japan, ) Japanese mathematician who has made important contributions to the field of algebraic geometry. His major work, in which he proved the existence of minimal models for all three-dimensional algebraic varieties (Jan 1988), has been dubbed Mori's Program. Within ten years since his first published paper, Mori had thereby completed what many said could never be done. In 1979, Mori published his first major results, a proof of the Hartshorne conjecture, which stated that a certain class of algebraic varieties are projective in nature. In other words, these varieties or sets of solutions to given polynomial equations could be described using projective geometry. He was awarded the Fields Medal in 1990 for his work in algebraic geometry.*TIS

DEATHS
1468 Johannes Gutenberg, printer, died. *VFR

1560 Gaspar Lax (1487 in Sarinena, Aragon, Spain - 23 Feb 1560 in Zaragoza, Spain) Lax published several good mathematics books based on works by Boethius, Euclid, Jordanus and Campanus. He was one of the Spanish school of "calculatores" who studied mechanics, being particularly involved with numerical examples, and using as their main tools the elements of proportion theory and infinitesimal arithmetic. This school seems to have originated with Lax and other students of Maior who studied in Paris, then returned to Spain. *SAU

1603 François Viète (1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a privy Councillor to both Henry III and Henry IV. A popular story about Viete as a codebreaker for Henry III is worth resharing: "While working for King Henry III, he discovered the key to a Spanish cipher of 500 characters, and so was able to read the secret correspondence of his enemies. Philipp II of Spain was so sure that his code was invulnerable that when he heard of this, he complained to the Pope that the French were using sorcery against him, contrary to good Christian morals."
Vieta's most significant contributions were in algebra. While letters had been used to describe an unknown quantity by earlier writers, Vieta was the first to also use letters for the parameters or constant coefficients in an equation. Vieta gave a solution of the problem of Apollonius, to construct a circle tangent to three given circles, and also made a study of solid" problems such as the trisection of the angle and the construction of the regular heptagon, which use a marked ruler in addition to the Euclidean tools of ruler and compass. (His method was similar to the Greek method called "neusis" {neuein "incline towards"} which had been used by early mathematicians such as Archimedes but gradually the technique dropped out of favor and use.)
Vieta calculated the value of $\pi$ to ten decimal places, using the method of Archimedes, and also gave an infinite product formula for $\pi$ one of the earliest occurrences of an infinite product.
*Robin Hartshorne

1844 Duncan Farquharson Gregory (13 April 1813 in Edinburgh, Scotland - 23 Feb 1844 in Edinburgh, Scotland) Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra.In this work Gregory built on the foundations of Peacock but went far further towards modern algebra. Gregory, in his turn, had a major influence on Boole and it was through his influence that Boole set out on his innovative research. *SAU

1855 Karl Friedrich Gauss (30 Apr 1777 in Brunswick, Germany , 23 Feb 1855 at age 77). His poorly educated mother couldn’t remember his birthdate, but could relate it to a movable religious feast. To conﬁrm the date of his birth Gauss developed a formula for the date of Easter. *VFR
He transformed nearly all areas of mathematics, for which his talent showed from a very early age. For his contributions to theory in magnetism and electricity, a unit of magnetic field has been named the gauss. He devised the method of least squares in statistics, and his Gaussian error curve remains well-known. He anticipated the SI system in his proposal that physical units should be based on a few absolute units such as length, mass and time. In astronomy, he calculated the orbits of the small planets Ceres and Pallas by a new method. He invented the heliotrope for trigonometric determination of the Earth's shape. With Weber, he developed an electromagnetic telegraph and two magnetometers. *TIS; He proved that the heptadecagon (17 gon) was constructable (see April 8) with straight-edge and compass. Because of difficulties engraving the 17gon on his memorial, a seventeen pointed star was used instead.
The Star is located below his foot on the right of the monument pedestal. Dave Renfro has provided me a complete and elementary proof of the construction.

1917 Jean-Gaston Darboux (14 Aug 1842, 23 Feb 1917 at age 74)French mathematician whose work on partial differential equations introduced a new method of integration (the Darboux integral) and contributed to infinitesimal geometry. He wrote a paper in 1870 on differential equations of the second order in which he presented the Darboux integral. In 1873, Darboux wrote a paper on cycloids and between 1887-96 he produced four volumes on infinitesimal geometry, including a discussion of one surface rolling on another surface. In particular he studied the geometrical configuration generated by points and lines which are fixed on the rolling surface. He also studied the problem of finding the shortest path between two points on a surface.*TIS

1961 Mary Ann Elizabeth Stephansen (10 March 1872 in Bergen, Norway - 23 Feb 1961 in Espeland, Norway)received her Ph.D. in mathematics from the University of Zurich in 1902. She was the first woman from Norway to receive a doctoral degree in any subject. Her thesis area was in partial differential equations. It was not until 1971 that another Norwegian woman obtained a doctorate in mathematics. Stephansen taught at the Norwegian Agricultural College from 1906 until her retirement in 1937. She began as an assistant in physics and mathematics, then was appointed to a newly created docent position in mathematics in 1921. She published four mathematical research papers on partial differential equations and difference equations.
A extensive biography of Elizabeth Stephansen is available as a pdf document at the web site of Professor Kari Hag. This also includes description of her mathematical work. *Agnes Scott College Web site

1963 Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century. He is known for his work in finite elasticity, thermoelasticity and for formulating the Signorini problem.
The Signorini problem is the first variational inequality problem, : it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions. The problem was posed by Antonio Signorini during a course taught at the Istituto Nazionale di Alta Matematica in 1959. The problem was taken up, in particular, by one of his students, Gaetano Fichera.
On the first days of January 1963, Fichera was able to give a complete proof of the existence and uniqueness of a solution for the problem with ambiguous boundary condition, which he called "Signorini problem" to honour his teacher. The preliminary note later published as Fichera 1963 was written up and submitted to Signorini exactly a week before his death: He was very satisfied to see a positive answer to his question. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Wednesday, 22 February 2017

### On This Day in Math - February 22

 Illustration from "On the forms of plane quartics", by Ruth Gentry

Suppose a contradiction were to be found in the axioms of set theory. Do you seriously believe that a bridge would fall down?
~Frank P. Ramsey

The 53rd day of the year; the month and day are both prime a total of 53 times in every leap year, but not today.

If you reverse the digits of 53 you get its hexadecimal representation; no other two digit number has this quality.

The sum of the first 53 primes is 5830, which is divisible by 53. It is the last year day for which n divides the sum of the first n primes.

53 is the smallest prime p such that 1p1 (ie, 1531) , 3p3, 7p7 and 9p9 are all prime.(Can you find the 2nd smallest?)

EVENTS
1535 On this day the contestants, Tartaglia and Fiore, were to deliver the answer to the 30 questions they were asking of their opponent to a notary. I assume the contest went on the same day, and it may not have taken long. Thony Christie at the Renaissance Mathematicus described it this way, "Tartaglia sat down and almost instantly gave the correct answers to Fiore’s entire list, who was completely unable to solve a single one of Tartaglia’s questions. This whitewash made Tartaglia a star amongst the reckoning masters." In Mario Livio's "The Equation That Couldn't be Solved" he says that Tartaglia finished all 30 of Fiore's questions in less than two hours. All 30 of Fiore's questions were of the form ax3 + bx = c, and Tartaglia had discovered a general solution for that type of cubic only eight days before the contest.

1630 Popcorn was introduced to the English colonists at their ﬁrst Thanksgiving dinner on this date (admit it, you thought it was in November) by Quadequina, brother of Massasoit. As his contribution to the dinner he offered a deerskin bag containing several bushels of “popped” corn. *Kane, Famous First Facts, p. 481 Popcorn is a type of corn with smaller kernels than regular corn, and when heated over a flame, it "pops" into the snack we know it as today. Native Americans were growing it for more than a thousand years before the arrival of European explorers. In 1964, scientists digging in southern Mexico found a small cob of popcorn discovered to be 7,000 years old. (don't you wonder if they tried to pop some of it?) Today, the United States grows nearly all of the world's popcorn. *TIS

1805 Francois Arago picked to head the completion of the measurement of the Paris Meridian. He was a 19yr old student at the Ecole Polytechnique. He was nominated by his professor, Dennis Poisson and appointed on Feb 2, 1805 to finish the work began by Mechain and Delambre. He would leave for Spain on Sept 3 of the following year *Amir D Aczel, Pendulum, pg 75-78

1876 The Johns Hopkins University Founded... commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed \$7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*Wik

1877 J. J. Sylvester, at a commencement address at Johns Hopkins, gave his view on the relation between teaching and research: “An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking ﬁsh, and it is certain that the more anyone gives himself up to the study of oratorial effect, the less he will ﬁnd himself in a fit state of mind to mathematicize.” See Midonick, The Treasury of Mathematics, p. 768. *VFR

1880 American Poet Sidney Lanier (1842–1922) read his “Ode to The Johns Hopkins University”, which indicated the original faculty was “Led by the soaring-genius’d Sylvester.” [Osiris, 1(1936), p. 112] *VFR

1926 At its fiftieth anniversary celebration, Johns Hopkins University awarded a long overdue doctorate to Christine Ladd-Franklin. Now a sprightly 79, she attended the ceremonies to collect her degree 44 years late. [New York Times, 23 February 1926, p. 12. Thanks to Judy Green. Also see Rossiter, Women Scientists in America, p. 46.] *VFR She applied to Johns Hopkins University as a graduate student, a university not traditionally open to women. A fellow contributor to the publication, Educational Times, who was familiar with her work, James J. Sylvester, noticed her name on a list of applicants and urged the university to admit her. In 1878, she was accepted on the terms that she would only attend his lectures.

1965 Rwanda, in central Africa, issued a series of stamps honoring the National University of Rwanda at Butare. Included in the picture is a radical sign, in fact, this is the only stamp which includes a radical sign, a symbol which originated in Germany. For the complicated history of this symbol, see Math Words,
[Scott #84, 88] *VFR

BIRTHS
1785 Jean-Charles-Athanase Peltier (22 Feb 1785; 27 Oct 1845 at age 60)
French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS

1796 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832. It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.

1817 Carl Borchardt (22 Feb 1817 in Berlin, Germany - 27 June 1880 in Rudersdorf (near Berlin), Germany) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1824 Pierre (-Jules-César) Janssen (22 Feb 1824, 23 Dec 1907) was a French astronomer who in 1868 devised a method for observing solar prominences without an eclipse (an idea reached independently by Englishman Joseph Norman Lockyer). Janssen observed the total Sun eclipse in India (1868). Using a spectroscope, he proved that the solar prominences are gaseous, and identified the chromosphere as a gaseous envelope of the Sun. He noted an unknown yellow spectral line in the Sun in 1868, and told Lockyer (who subsequently recognized it as a new element he named helium, from Greek "helios" for sun). Janssen was the first to note the granular appearance of the Sun, regularly photographed it, and published a substantial solar atlas with 6000 photographs (1904). *TIS

1849 Nikolay Yakovlevich Sonin (February 22, 1849 – February 27, 1915) was a Russian mathematician.
Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler–Maclaurin summation formula. Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.*Wik

1856 Micaiah John Muller Hill born. He worked in hydrodynamics, on the three-body problem, and has a diﬀerential equation named after him. *VFR He was Vice-Chancellor of the University of London from 1909 to 1911. His books on Euclids fifth and sixth books, and on the Theory of Proportion are available on the internet.

1857 Heinrich Rudolf Hertz (22 Feb 1857, 1 Jan 1894) was a German physicist who was the first to broadcast and receive radio waves. He studied under Kirchhoff and Helmholtz in Berlin, and became professor at Bonn in 1889. His main work was on electromagnetic waves (1887). Hertz generated electric waves by means of the oscillatory discharge of a condenser through a loop provided with a spark gap, and then detecting them with a similar type of circuit. Hertz's condenser was a pair of metal rods, placed end to end with a small gap for a spark between them. Hertz was also the first to discover the photoelectric effect. The unit of frequency - one cycle per second - is named after him. Hertz died of blood poisoning in 1894 at the age of 37. *TIS

1862 Ruth Gentry (February 22, 1862 - October 15, 1917) grew up in Indiana and received her A.B. degree at Indiana State Normal (now Indiana State University) in 1880. After ten years of teaching at preparatory schools, she earned a degree in mathematics from the University of Michigan in 1890. She spent the following year as a Fellow in Mathematics at Bryn Mawr, then became the first mathematician and the second recipient of the Association of College Alumnae European Fellowship, which she used in 1891-92 to attend lectures at the University of Berlin (but was not allowed to enroll for a degree). After a further semester attending mathematics lectures at the Sorbonne in Paris, Gentry returned to Bryn Mawr to become one of Charlotte Scott's first two graduate students. She received her Ph.D. in 1896 on the topic "On the Forms of Plane Quartic Curves." As she writes at the beginning of this thesis:
"Many papers dealing with curves of the fourth order, or Quartic Curves, are to be found in the various mathematical periodicals; but these leave the actual appearance of the curve as a whole so largely to the reader's imagination that it is here proposed to give a complete enumeration of the fundamental forms of Plane Quartic Curves as they appear when projected so as to cut the line infinity the least possible number of times, together with evidence that the forms presented can exist."
Gentry taught at Vassar College from 1896 until 1902, where she was the first mathematics faculty member to hold a Ph.D. degree. She was promoted to associate professor in 1900, but left Vassar two years later to become the associate principal and head of the mathematics department at a private school in Pittsburgh, Pennsylvania, a position she held until 1905. After that she spent some time as a volunteer nurse and traveled in the United States and Europe, but she became increasingly ill and died at the age of 55. She was a member of the American Mathematical Society from 1894 until her death in 1917 in Indianapolis, Indiana. *Agnes Scott College web page

1903 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

1928 BASIC co-inventor Thomas Kurtz is born. With John Kemeny, Kurtz developed the easy-to-learn programming language for his students at Dartmouth College in the early 1960s. He said: "If Fortran is the lingua franca ... BASIC is the lingua playpen." *CHM

DEATHS
1512 Amerigo Vespucci (9 Mar 1451, 22 Feb 1512 at age 60)Spanish astronomer whose name was given to the New World - America - because it was he and not Columbus, who realized and announced that Columbus had discovered a new continent. *TIS

1687 Francesco Lana de Terzi (Brescia, Lombardy 1631 – 22 February 1687 Brescia, Lombardy) was an Italian Jesuit, mathematician, naturalist and aeronautics pioneer. Having been professor of physics and mathematics at Brescia, he first sketched the concept for a vacuum airship and has been referred to as the Father of Aeronautics for his pioneering efforts, turning the aeronautics field into a science by establishing "a theory of aerial navigation verified by mathematical accuracy". He also developed the idea that developed into Braille. *Wik

1901 George Francis FitzGerald (3 Aug 1851 in Kill-o'-the Grange, Monkstown, Co. Dublin, Ireland - 21 Feb 1901 in Dublin, Ireland) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS

1941 Dayton Clarence Miller (13 Mar 1866, 22 Feb 1941 at age 74)American physicist. Author of The Science of Musical Sounds (1916). Miller's collection of nearly 1,650 flutes and other instruments, and other materials mostly related to the flute, is now at the Library of Congress. To provide a mechanical means of recording sound waves photographically, he invented the phonodeik (1908). He became expert in architectural ecoustics. During WW I, he was consulted concerning using his photodeik to help locate enemy guns. Miller spent considerable research effort on repeating the Michelson and Morley experiment, proposed by Maxwell, to detect a stationary aether. He spent some time working with Morley (1902-4), then more time at Mt. Wilson, recording results favoring the presence of the aether.*TIS

1975 Oskar Perron ( 7 May 1880 in Frankenthal, Pfalz, Germany - 22 Feb 1975 in Munich, Germany)was a German mathematician best known for the Perron paradox:
Suppose the largest natural number is N. Then if N is greater than 1 we have N2 greater than N contradicting the definition. His publications cover a wide range of mathematical topics. His work in analysis is certainly remembered through the Perron integral. However he also worked on differential equations, matrices and other topics in algebra, continued fractions, geometry and number theory. *SAU

1984 Maxwell Herman Alexander "Max" Newman, FRS (7 February 1897 – 22 February 1984) was a British mathematician and codebreaker. After WWII he continued to do research on combinatorial topology during a period when England was a major center of activity, notably Cambridge under the leadership of Christopher Zeeman. Newman made important contributions leading to an invitation to present his work at the 1962 International Congress of Mathematicians in Stockholm at the age of 65, and proved a Generalized Poincaré conjecture for topological manifolds in 1966. He died in Cambridge.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell