Wednesday, 31 December 2014

On This Day in Math - December 31

The Difficult Problem, by N P Bogdonav-Belsky
The problem for mental solution, appropriate for today is \( \frac{10^2+11^2+12^2+13^2+14^2}{365}\)

For other great mathematicians or philosophers, he [Gauss] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.
~W.W.R. Ball

A Holy day for a mathematician: Silvester or Sylvester (also spelled szilveszter, sylvester or sylwester) is the day of the Feast of Pope Sylvester I, a saint who served as Pope of the Catholic Church from 314 to 335 The feast day is held on the anniversary of Sylvester's death, 31 December, a date that, since the adoption of the Gregorian calendar, has coincided with New Year's Eve. Because of this coincidence, several countries, primarily in Europe, use a variant of Silvester's name as the preferred name for the holiday; these countries include Austria, Bosnia and Herzegovina, Croatia, Czech Republic, France, Germany, Hungary, Israel, Italy, Liechtenstein, Luxembourg, Poland, Slovakia, Switzerland, and Slovenia.

The 365th (and usually last) day of the year; 365 is a centered square number, and thus the sum of two consecutive squares (132 + 142 ) and also one more than four times a triangular number. (Students could explore which triangular number and which square numbers produce 365.)
365 is the sum of two squares in two ways,  132 + 142 and  192 + 22 *Lord Karl Voldevive@Karl4MarioMugan

There are 10 days during the year that are the sum of three squares.  This is the last one.
 365 = 10²+11²+12²  *jim wilder @wilderlab  

365 is a palindrome in base 2; 101101101
it's 555 in base 8, and 16d in hexdecimal (base 16)


EVENTS
1719 When the first Astronomer Royal, John Flamsteed died on this day (see below) he was serving as Rector of Burstow (just east of Gatwick), and had been for thirty-five years. For some reason, no marker was placed on the grave, and 170 years later, it was not clear where the famous astronomer was buried. Finally, in 1888, another astronomer from Greenwich Observatory, Edwin Dunkin searched, and found, the burial site mentioned in his wife's will. Today there are several markers in the church at Barstow, including the one below indicating his resting place in the Chancel.
Several other images of the church, and markers for Flamsteed, are at the site from which I obtained this note. *Blogs Greenwich http://blogs.greenwich.co.uk/rob-powell/the-grave-of-john-flamsteed/
Stephen Craven - http://www.geograph.org.uk/photo/2786257

1831  Gauss writes to his close friend, Wilhelm Olbers regarding an essay published by Laplace, "The essay...  is quite unworthy of this great geometer. I find two different, very gross blunders in it.  I had always imagined that among geometers of the first rank the calculation was always only the dress in which they present that which they created not by calculation, but by mediation about the subject itself. ". *Carl Friedrich Gauss: Titan of Science by Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

1915 The Mathematical Association of America was founded in Columbus, Ohio. Starting with 1045 charter members, the Association now has some 34,000 members who are interested in the improvement of mathematical instruction at the collegiate level. *VFR

1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. *TIS

1961 This was the last day of the year 1961, a Stobogrammatic number. If you rotate the number by 180o it still looks the same. Then name seems to have been created for the Jan 1961 issue of The Mathematics Magazine by J. M. Howell of Los Angeles City College. The last day of the year is a significant date since it is the last time someone will be living in such a year for a very long time. *Mathematics Magazine

1987 The last minute (UT) of the last hour of the last day of the year 1987 carried an extra second, a leap second. This was to coordinate the slowdown in rotation of the Earth on its axis, or Solar Time, with the more precise atomic time. The one-second insertion was made at 6:59:59 P.M. at the Naval Observatory in Washington D.C. Just exactly when the proverbial man-in-the¬street choose to insert this second was his own business, but in New York’s Times Square it was done with much hoopla at midnight. *U.S. Naval Observatory's “Stargazing Notes for December 1987.” *VFR


1999 Millenium memorial puzzle at Luppitt. It is made of fine grained granite, which is an exceptionally hard stone. It was unveiled on 31st December 2000 - Just in time for the true Millennium. The puzzles on the site, as described at the puzzle's website:

The puzzles include a wordsearch concealing over 30 local placenames, a three way anamorphic illusion, a completely new idea based on the Tinner's Rabbits, an ancient maze from a French church, a modern Railway Maze (specially designed by Professor Sir Roger Penrose), a Word Anagram, a Letter misplacement puzzle, a traditional Word square puzzle, cryptarithms, hidden mice, and other curiosities and puzzles.


1999 Professor Andrew Wiles is knighted. The Princeton mathematician found fame in October 1994 when he succeeded in proving Fermat's Last Theorem. This was an amazing achievement that had eluded some of the greatest minds since Pierre Fermat conjured up his theory in the 1630s. His work has received every major honour and he had the pleasure in 1999 of seeing some of his former pupils crack another of mathematics' great puzzles: The Shimura-Taniyama-Weil conjecture. *BBC

1999 Alan Sugar, the man who founded Amstrad some 30 years ago and now runs Tottenham Hotspur football club,(Sugar sold his interest in the Spurs in 2007 according to a comment from Luke Robinson, below) has been knighted.
So too has Maurice Wilkes, who developed the world's first practical stored-program computer in 1949.
"I'm tickled pink by the news," said Mr Sugar, whose company launched the world's first mass-market word processor built with low-cost components from the Far East.
At the height of its success, Amstrad was worth £1.5bn on the FTSE-100 index. Mr Sugar eventually broke Amstrad up, spinning off Viglen Technology, its personal computer business, of which he is now chairman.
Maurice Wilkes led the Cambridge University team that developed the Edsac - Electronic Delay Storage Automatic Calculator. It was a huge contraption that could carry out just 650 instructions per second. Nevertheless, it went down in history as the first truly programmable computer. *BBC

BIRTHS
1789 Benoît "Claudius" Crozet (December 31, 1789; Villefranche, France – January 29, 1864) was an educator and civil engineer.
After serving in the French military, in 1816, he immigrated to the United States. He taught at the U.S. Military Academy at West Point, New York, and helped found the Virginia Military Institute at Lexington, Virginia. He was Principal Engineer for the Virginia Board of Public Works and oversaw the planning and construction of canals, turnpikes, bridges and railroads in Virginia, including the area which is now West Virginia. He became widely known as the "Pathfinder of the Blue Ridge."
On June 7, 1816, in Paris, Crozet married Agathe Decamp.
Late in fall of 1816, Crozet and his bride headed for the United States. Almost immediately after arriving, Crozet began work as a professor of engineering at the U.S. Military Academy at West Point, New York.
While at West Point, Crozet is credited by some as being the first to use the chalkboard as an instructional tool. (Professor Ricky, a math historian at USMA has written, "old records show that it was introduced at West Point by Mr. George Baron, a civilian teacher, who in the autumn of 1801 gave to Cadet Swift 'a specimen of his mode of teaching at the blackboard' ").He also designed several of the buildings at West Point. Thomas Jefferson referred to Claudius Crozet as "by far the best mathematician in the United States." He also published A Treatise on Descriptive Geometry while at West Point, a copy of which was sent to Jefferson. Jefferson's response on Nov 23, 1821 began, "I thank you, Sir, for your kind attention in sending me a copy of your valuable treatise on Descriptive geometry." He continued the messsage with praise for the work, and the instructor both. The dining hall at the Virginia Military Institute is named in his honor. It has been affectionately nicknamed "Club Crozet" by the Cadets. * Wik & Natl. Archives

1864 Robert Grant Aitken (31 Dec 1864; 29 Oct 1951) American astronomer who specialized in the study of double stars, of which he discovered more than 3,000. He worked at the Lick Observatory from 1895 to 1935, becoming director from 1930. Aitken made systematic surveys of binary stars, measuring their positions visually. His massive New General Catalogue of Double Stars within 120 degrees of the North Pole allowed orbit determinations which increased astronomers' knowledge of stellar masses. He also measured positions of comets and planetary satellites and computed orbits. He wrote an important book on binary stars, and he lectured and wrote widely for the public.*TIS

1896 Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a mathematician specializing in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.
Among his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov-Arnold-Moser), which lies at the foundations of chaos theory.
Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field.
Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus greater than 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through.
André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. In the early 1970s Weil gave a series of seminars on the history of number theory prior to the 20th century and he remarked that Siegel once told him that when the first person discovered the simplest case of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of the history of mathematics and put his studies to good use in such works as the Riemann-Siegel formula.*Wik

1929 Jeremy Bernstein (31 Dec 1929, ) American physicist, educator, and writer widely known for the clarity of his writing for the lay reader on the major issues of modern physics. He was a staff writer for the New Yorker for over 30 years until 1993. He has held appointments at the Institute for Advanced Study, Brookhaven National Laboratory, CERN, Oxford, the University of Islamabad, and the Ecole Polytechnique. Berstein has written over 50 technical papers as well as his books popularizing science including Albert Einstein; Cranks, Quarks, and the Cosmos and A Theory for Everything. His passion for science was launched after he entered Harvard University, thereafter combining it with a talent as a writer. *TIS

1930 Jaime Alfonso Escalante Gutierrez (December 31, 1930 — March 30, 2010) was a Bolivian educator well-known for teaching students calculus from 1974 to 1991 at Garfield High School, East Los Angeles, California. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.*Wik

1945 Leonard Max Adleman (December 31, 1945, ) is an American theoretical computer scientist and professor of computer science and molecular biology at the University of Southern California. He is known for being a co-inventor of the RSA (Rivest-Shamir-Adleman) cryptosystem in 1977, and of DNA computing. RSA is in widespread use in security applications. *Wik

1952 Vaughan Frederick Randal Jones (31 Dec 1952, ) is a New Zealand mathematician who was awarded the Fields Medal in 1990 for his study of functional analysis and knot theory. In 1984, Jones discovered a relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space. It was a complete surprise because his invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years.*TIS


DEATHS
1610 Ludolph van Ceulen, a German mathematician who is famed for his calculation of π to 35 places. In Germany π used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius​, translated Archimedes' approximation to π for Van Ceulen. This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to π using Archimedes' method with regular polygons with many sides.*SAU He has Pi on his memorial stone.

1679 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver's rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS

1719 John Flamsteed (19 Aug 1646; 31 Dec 1719)English astronomer who established the Greenwich Observatory. Science Historian/blogger Thony Christie writes:

" Observational astronomy only produced three significant star catalogues in the two thousand years leading up to the 18th century. The first, the Greek catalogue from Hipparchus and Ptolemaeus published by Ptolemaeus in the 2nd century CE, which contained just over 1000 stars mapped with an accuracy that was astounding for the conditions under which it was produced. The second, containing somewhat more that 700 stars plus another 300 borrowed from the Ptolemaeus catalogue, was produced by the Danish astronomer Tycho Brahe in the last quarter of the 16th century, with an accuracy many factors better than his Greek predecessors. Both of these catalogues were produced with naked eye observations. The first catalogue to be produced using telescopic sights on the measuring instruments was that of John Flamsteed published posthumously in 1725, which contains more than 3000 stars measured to a much higher degree of accuracy than that of Tycho."

He then goes on to correct some misconceptions about Flamsteed's life that are commonly repeated, (he did NOT take part in talking Charles II into creating the observatory) and gives a nice description of a complex man. *Renaissance Mathematicus

1894 Thomas Jan Stieltjes, who did pioneering work on the integral. *VFR Thomas Stieltjes worked on almost all branches of analysis, continued fractions and number theory. *SAU

1913 Seth Carlo Chandler, Jr. (17 Sep 1846, 31 Dec 1913) was an American astronomer best known for his discovery (1884-85) of the Chandler Wobble, a complex movement in the Earth's axis of rotation (now referred to as polar motion) that causes latitude to vary with a period of 14 months. His interests were much wider than this single subject, however, and he made substantial contributions to such diverse areas of astronomy as cataloging and monitoring variable stars, the independent discovery of the nova T Coronae, improving the estimate of the constant of aberration, and computing the orbital parameters of minor planets and comets. His publications totaled more than 200. *TIS

1962 Charles G Darwin was the grandson of the famous biologist and graduated from Cambridge. He lectured on Physics at Manchester and after service in World War I and a period back at Cambridge he became Professor of Physics at Edinburgh. He left eventually to become head of a Cambridge college. He worked in Quantum Mechanics and had controversial views on Eugenics. *SAU

1982 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*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

Tuesday, 30 December 2014

On This Day in Math - December 30







It requires a very unusual mind to undertake the analysis of the obvious.

~Alfred North Whitehead

The 364th day of the year; 364 is the total number of gifts in the Twelve Days of Christmas song: 1+(2+1) + (3+2+1) ... which is a series of triangular numbers. The sum of the first n triangular numbers can be expressed as (n+2 Choose 3).

If you put a standard 8x8 chessboard on each face of a cube, there would be 364 squares. Futility closet included this note on such a cube: "British puzzle expert Henry Dudeney once set himself the task of devising a complete knight’s tour of a cube each of whose sides is a chessboard. He came up with this:


If you cut out the figure, fold it into a cube and fasten it using the tabs provided, you’ll have a map of the knight’s path. It can start anywhere and make its way around the whole cube, visiting each of the 364 squares once and returning to its starting point.


EVENTS

1610 Galileo in answer to a question from Father Christoph Clavius SJ about why his large aperture was partly covered; answered that he did this for two reasons:
The first is to make it possible to work it more accurately because a large surface is
more easily kept in the proper shape than a smaller one. The other reason is that if
one wants to see a larger space in one glance, the glass can be uncovered, but it is then
necessary to put a less acute glass near the eye and shorten the tube, otherwise the
objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

In 1873, the American Metrological Society was formed in New York City to improve systems of weights, measures and money. Its activities eventually extended with a committee considering units of force and energy, and another concerned with the adoption of Standard Time for the U.S. On 30 Dec 1884, at the meeting of the American Metrological Society at Columbia College in New York City, Charles S. Peirce read a paper on the determination of gravity. He also participated in a discussion of the adequacy of the standards of weight and measure in the United States and pointed out some of the deficiencies in the current system. As a result of his revelations, the Society passed a resolution recommending the appointment of a committee to advise Congress on the need for establishing an efficient bureau of standards. *TIS


1881 The “Four Fours” problem was first published in Knowledge a magazine of popular science edited by the astronomer Richard Proctor. The problem is to express whole numbers using exactly four fours and various arithmetical signs. For example 52 = 44 + 4 + 4. This can be done for the integers from 1 to 112, but 113 is a problem. Variations of the game allow use of factorials, square roots, decimal points (such as .4) etc. A good source for further study is here.


1902 Leornard Eugene Dickson married Susan Davis. Later he often said of his honeymoon: “It was a great success, except that I only got two research papers written.” In all he published 18 books and hundreds of articles.*VFR

1915 A two day meeting in Columbus, Ohio began to found a new mathematical organization. The new organization would be called the Mathematical Organization of America, and took over the publishing of the American Mathematical Monthly which had been in operation for three years. The first president was Professor E. R. Hedrick of the University of Missouri. The Earle Raymond Hedrick lectures were established by the Mathematical Association in America in his honor.

In 1924, Edwin Hubble announced the existence of another galactic system in addition to the Milky Way. He had found at least one "island universe," or galaxy of stars, lies outside our own Milky Way. Until then, scientists were not certain whether certain fuzzy clouds of light called "nebulae" that had been seen with telescopes were small clusters of clouds within the Milky Way or separate galaxies. Hubble measured the distance to the Andromeda nebula and showed it to be a hundred thousand times as far away as the nearest stars. This proved it was a separate galaxy, as large as our own Milky Way, but very far away.  More galaxies have been found, some a spiral form like the Milky Way; others spheroidal, others without the spiral arms, or of irregular shape.
1952 Harvard mathematician Andrew Gleason received the Newcomb Cleveland Prize, a $1000 financial award, for his contributions toward the solution of Hilbert's Fifth Problem about Lie Groups.


In 1982, a second full moon of the month was visible. Known as a "blue moon," the name does not refer to its color, but it is a rare event, giving rise to the expression, "once in a blue moon" came from. This blue blue moon was more special as a total lunar eclipse also occurred (U.S.). Although there were 41 blue moons in the twentieth century, this was one of four during an eclipse of the moon, and the only total eclipse of a blue moon in the twentieth century. A blue moon happens every 2.7 years because of a disparity between our calendar and the lunar cycle. The lunar cycle is the time it takes for the moon to revolve around the earth, is 29 days, 12 hours, and 44 minutes. *TIS The next blue moon will occur on Setember 30 of 2012.


1985 Version 3.2 of the IBM PC​-DOS operating system is announced
PC-DOS, IBM's version of the DOS operating system used on the IBM PC, released Version 3.2 on this date. The system required 128KB RAM and was available on either one 720KB disk or two 51/4” disks. DOS has remained in use since the introduction of the IBM PC in 1981, with PC-DOS 200 being the latest release in 1998. *CHM




BIRTHS

1850 John Milne (30 Dec 1850; 30 Jul 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease.*TIS


1897 Stanisław Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*wIK


1931 Sir John (Theodore) Houghton (30 Dec 1931, ) Welsh metereologist who began in the late 1960's drawing attention to the buildup of carbon dioxide in the earth's atmosphere and its result of global warming, now known as the greenhouse effect. As director-general (1983) of the British Meteorological Office, he began tracking changing climate patterns. In 1990, he co-chaired a team of scientists working for the United Nations that produced the first comprehensive report on the science of climate change. This led to the 1997 U.N. Conference on Climate Change, in Kyoto, Japan. The Kyoto Protocol that resulted there was a treaty among industrialized and developed nations to combat global warming by voluntarily adhering to progressively stiffening emissions-reduction standards.*TIS


1934 John N. Bahcall (30 Dec 1934, ) American astrophysicist who pioneered the development of neutrino astrophysics in the early 1960s. He theorized that neutrinos (subatomic particles that have no charge and exceedingly weak interaction with matter) can be used to understanding how stars shine. They are emitted by the sun and stars during the fusion energy creation process, and most are able to pass through the Earth without being stopped. He calculated the expected output of neutrinos from the sun, which created an experimental challenge to explain the unexpected result. He won the National Medal of Science (1998) for both his contributions to the planning and development of the Hubble Space Telescope and his pioneering research in neutrino astrophysics.*TIS




DEATHS

1691 Robert Boyle (25 Jan 1627, 30 Dec 1691) Anglo-Irish chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law).*TIS





1695 Sir Samuel Morland (born 1625, 30 Dec 1695) English mathematician and inventor of mechanical calculators. His first machine added and subtracted English money using eight dials that were moved by a simple stylus. Another could multiply and divide using 30 discs with numbers marked around the edge - circular versions of Napier's linear bones. Five more discs handled finding square and cube roots. His third machine made trigonometric calculations. Morland built a speaking trumpet (1671) he claimed would allow a conversation to be conducted over a distance of 3/4 mile. By 1675, he had developed various pumps for domestic, marine and industrial applications, such as wells, draining ponds or mines, and fire fighting. He also designed iron stoves for marine use, and improved barometers. *TIS


1883 John Henry Dallmeyer (6 Sep 1830, 30 Dec 1883) German-born British inventor and manufacturer of lenses and telescopes. He introduced improvements in both photographic portrait and landscape lenses, in object glasses for the microscope, and in condensers for the optical lantern. Dallmeyer made photoheliographs (telescopes adapted for photographing the Sun) for Harvard observatory (1864), and the British government (1873). He introduced the "rapid rectilinear" (1866) which is a lens system composed of two matching doublet lenses, symmetrically placed around the focal aperture to remove many of the aberrations present in more simple constructions. He died on board a ship at sea off New Zealand. *TIS


1932 Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school.  When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.
Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.
The American Mathematical Society established a prize in his honor in 2002. *Wik


1947 Alfred North Whitehead (15 Feb 1861, 30 Dec 1947) English mathematician and philosopher, who worked in logic, physics,  philosophy of science and metaphysics. He is best known for his work with Bertrand Russell on one of probably the most famous books of the century, Principia Mathematica (1910-13) to demonstrate that logic is the basis for all mathematics. In physics (1910-24) his best known work was a theory of gravity, that competed with Einstein's general relativity for many decades. In his later life from 1924 onward at Harvard, he worked on more general issues in philosophy rather than mathematics, including the development of a comprehensive metaphysical system which has come to be known as process philosophy. *TIS


1956 Heinrich Scholz (December 17 1884 in Berlin , December 30 1956 in Muenster, Westphalia ) was a German logician, philosopher and theologian. *Wik


1982 Philip Hall (11 April 1904 in Hampstead, London, England - 30 Dec 1982 in Cambridge, Cambridgeshire, England) Hall was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him.*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

Monday, 29 December 2014

On This Day in Math - December 29



Folium of Descartes, *Wiki



Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk.
God made the integers, all else is the work of man.

~Leopold Kronecker

The 363rd day of the year; 363 is the sum of nine consecutive primes and is also the sum of 5 consecutive powers of three.

EVENTS

1566 A part of Tycho Brahe’s nose was cut off in a duel with another Danish nobleman. The dispute was over a point of mathematics. This he replaced with a prosthesis generally stated to be of silver and gold but containing a high copper content. *VFR
On December 10, 1566, Tycho and the Danish blue blood Manderup Parsbjerg were guests at an engagement party at Prof. Bachmeister in Rostock. The party included a ball, but the festive environment did not keep the two men from starting an argument that went on even over the Christmas period. On December 29, they finished the matter with a rapier duel. During the duel, which started at 7 p.m. in total darkness, a large portion of the nose of Brahe was cut off by his Opponent. It was the most famous cut in science, if not the unkindest. *Neatorama

1692 Huygens, in a letter to L’Hospital, gave the first complete sketch of the folium of Descartes. Although the curve was first discussed 23 August 1638 no complete sketch had previously been given due to a reluctance to use negative numbers as coordinates. *VFR

1763 Nevil Maskelyne wrote his brother Edmund, reporting his safe arrival on 7 November after “an agreeable passage of 6 weeks”. He noted that he had been “very sufficiently employed in making the observations recommended to me by the Commissioners of Longitude” and that it was at times “rather too fatiguing”.
The Princess Louise sailed for Barbados on 23 September. During the voyage Maskelyne and Charles Green took many lunar-distance observations (with Maskelyne later claiming that his final observation was within half of degree of the truth) and struggled a couple of times with the marine chair. Maskelyne’s conclusion was that the Jupiter’s satellites method of finding longitude would simply never work at sea because the telescope magnification required was far too high for use in a moving ship.
*Board of Longitude project, Greenwich

1790 Obituary for Thomas “Tom” Fuller in the Columbian Centinial , Boston Massachusetts. His mathematical ability and its origin became a dueling point between abolitionists and those supporting slavery. 

Died- Negro Tom, the famous African Calculator, aged 80 years. He was the property of Mrs. Elizabeth Cox of Alexandria. Tom was a very black man. He was brought to this country at the age of 14, and was sold as a slave.... This man was a prodigy. Though he could never read or write, he had perfectly acquired the art of enumeration.... He could multiply seven into itself, that product by seven, and the products, so produced, by seven, for seven times. He could give the number of months, days, weeks, hours, minutes, and seconds in any period of time that any person chose to mention, allowing in his calculation for all leap years that happened in the time; he would give the number of poles, yards, feet, inches, and barley-corns in any distance, say the diameter of the earth's orbit; and in every calculation he would produce the true answer in less time than ninety-nine men out of a hundred would produce with their pens. And, what was, perhaps, more extraordinary, though interrupted in the progress of his calculation, and engaged in discourse necessary for him to begin again, but he would ... cast up plots of land. He took great notice of the lines of land which he had seen surveyed. He drew just conclusions from facts; surprisingly so, for his opportunities. Had his [Thomas Fuller] opportunity been equal to those of thousands of his fellow-men ... even a NEWTON himself, need have ashamed to acknowledge him a Brother in Science.

*Univ of Buffalo Math Dept


In 1927, Krakatoa began a new volcanic eruption on the seafloor along the same line as the cones of previous activity. By 26 Jan 1928, a growing cone had reached sea level and formed a small island called Anak Krakatoa (Child of Krakatoa). Sporadic activity continued until, by 1973, the island had reached a height of 622 ft above sea level. It was still in eruption in the early 1980s. The volcano Krakatoa is on Pulau (island) Rakata in the Sunda Strait between Java and Sumatra, Indonesia. It had been quiet since its previous catastrophic eruption of 1883. That threw pumice 33 miles high and 36,380 people were killed either by the ash fall or by the resulting tidal wave. The only earlier known eruption was in 1680, and was only moderate.*TIS

1939 Shockley Makes Historic Notebook Entry
William Shockley records in his laboratory notebook that it should be possible to replace vacuum tubes with semiconductors. Eight years later, he, Walter Brattain and John Bardeen at AT&T Bell Laboratories successfully tested the point-contact transistor. Shockley developed much of the theory behind transistor action, and soon postulated the junction transistor, a much more reliable device. It took about ten years after the 1947 discovery before transistors replaced vacuum tubes in computer design as manufacturers learned to make them reliable and a new generation of engineers learned how to use them. *CHM

1947 George Dantzig announced his discovery of the simplex method at the joint annual meeting of the American Statistical Association and the Institute of Mathematical Statistics. The lecture was poorly attended and the result attracted no interest. *Robert Dorfman, “The discovery of linear programming,” Annals of the History of Computing, 6(1984), 283–295, esp. 292.

1979 Edward Lorenz presents a paper at the 139th Annual Meeting of the American Association for the Advancement of Science with the title, "Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" *TIS  According to Lorenz, upon failing to provide a title for a talk he was to present at the meeting Philip Merilees concocted the title. The idea that one butterfly could have a far-reaching ripple effect on subsequent events seems first to have appeared in a 1952 short story by Ray Bradbury about time travel. It seems that Merilees was  was not familiar with Bradbury’s story. *Wik




BIRTHS

1256 Birthdate of Ibn Al-Banna who studied the magic properties of numbers and letters. *VFR He was an Islamic mathematician who wrote a large number of works including an introduction to Euclid's Elements, an algebra text and various works on astronomy.*SAU

1796 Johann Christian Poggendorff (29 December 1796 – 24 January 1877), was a German physicist and science historian born in Hamburg. By far the greater and more important part of his work related to electricity and magnetism. Poggendorff is known for his electrostatic motor which is analogous to Wilhelm Holtz's electrostatic machine. In 1841 he described the use of the potentiometer for measurement of electrical potentials without current draw.
Even at this early period he had conceived the idea of founding a physical and chemical scientific journal, and the realization of this plan was hastened by the sudden death of Ludwig Wilhelm Gilbert, the editor of Gilbert's Annalen der Physik, in 1824 Poggendorff immediately put himself in communication with the publisher, Barth of Leipzig. He became editor of Annalen der Physik und Chemie, which was to be a continuation of Gilbert's Annalen on a somewhat extended plan. Poggendorff was admirably qualified for the post, and edited the journal for 52 years, until 1876. In 1826, Poggendorff developed the mirror galvanometer, a device for detecting electric currents.
He had an extraordinary memory, well stored with scientific knowledge, both modern and historical, a cool and impartial judgment, and a strong preference for facts as against theory of the speculative kind. He was thus able to throw himself into the spirit of modern experimental science. He possessed in abundant measure the German virtue of orderliness in the arrangement of knowledge and in the conduct of business. Further he had an engaging geniality of manner and much tact in dealing with men. These qualities soon made Poggendorff's Annalen (abbreviation: Pogg. Ann.) the foremost scientific journal in Europe.
In the course of his fifty-two years editorship of the Annalen Poggendorff could not fail to acquire an unusual acquaintance with the labors of modern men of science. This knowledge, joined to what he had gathered by historical reading of equally unusual extent, he carefully digested and gave to the world in his Biographisch-literarisches Handworterbuch zur Geschichte der exacten Wissenschaften, containing notices of the lives and labors of mathematicians, astronomers, physicists, and chemists, of all peoples and all ages. This work contains an astounding collection of facts invaluable to the scientific biographer and historian. The first two volumes were published in 1863; after his death a third volume appeared in 1898, covering the period 1858-1883, and a fourth in 1904, coming down to the beginning of the 20th century.
His literary and scientific reputation speedily brought him honorable recognition. In 1830 he was made royal professor, in 1838 Hon. Ph.D. and extraordinary professor in the University of Berlin, and in 1839 member of the Berlin Academy of Sciences. In 1845, he was elected a foreign member of the Royal Swedish Academy of Sciences.
Many offers of ordinary professorships were made to him, but he declined them all, devoting himself to his duties as editor of the Annalen, and to the pursuit of his scientific researches. He died at Berlin on 24 January 1877.
The Poggendorff Illusion is an optical illusion that involves the brain's perception of the interaction between diagonal lines and horizontal and vertical edges. It is named after Poggendorff, who discovered it in the drawing of Johann Karl Friedrich Zöllner, in which he showed the Zöllner illusion in 1860. In the picture to the right, a straight black line is obscured by a dark gray rectangle. The black line appears disjointed, although it is in fact straight; the second picture illustrates this fact.*Wik

1856 Birth of Thomas Jan Stieltjes, who did pioneering work on the integral. *VFR Thomas Stieltjes worked on almost all branches of analysis, continued fractions and number theory. *SAU

1861 Kurt Hensel (29 Dec 1861 in Königsberg, Prussia (now Kaliningrad, Russia) - 1 June 1941 in Marburg, Germany)  invented the p-adic numbers, an algebraic theory which has proved important in later applications. From 1901 Hensel was editor of the prestigious and influential Crelle's Journal.*SAU

1905 Henri-Gaston Busignies (29 Dec 1905; 20 Jun 1981) French-born American electronics engineer whose invention (1936) of high-frequency direction finders (HF/DF, or "Huff Duff") permitted the U.S. Navy during World War II to detect enemy transmissions and quickly pinpoint the direction from which a radio transmission was coming. Busignies invented the radiocompass (1926) while still a student at Jules Ferry College in Versailles, France. In 1934, he started developing the direction finder based on his earlier radiocompass. Busignies developed the moving target indicator for wartime radar. It scrubbed off the radar screen every echo from stationary objects and left only echoes from moving objects, such as aircraft. *TIS

1911 (Emil) Klaus (Julius) Fuchs (29 Dec 1911; 28 Jan 1988) was a German-born physicist who was convicted as a spy on 1 Mar 1950, for passing nuclear research secrets to Russia. He fled from Nazi Germany to Britain. He was interned on the outbreak of WW II, but Prof. Max Born intervened on his behalf. Fuchs was released in 1942, naturalized in 1942 and joined the British atomic bomb research project. From 1943 he worked on the atom bomb with the Manhattan Project at Los Alamos, U.S. By 1945, he was sending secrets to Russia. In 1946, he became head of theoretical physics at Harwell, UK. He was caught, confessed, tried, imprisoned for nine of a 14 year sentence, released on 23 Jun 1959, and moved to East Germany and resumed nuclear research until 1979. *TIS

1944 Joseph W. Dauben (born 29 December 1944, Santa Monica- ) is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York. He obtained his Ph.D. from Harvard University.
His fields of expertise are history of science, history of mathematics, the scientific revolution, sociology of science, intellectual history, 17-18th centuries, history of Chinese science, and the history of botany.
His book Abraham Robinson was reviewed positively by Moshé Machover, but he noted that it avoids discussing any of Robinson's negative aspects, and "in this respect [the book] borders on the hagiographic, painting a portrait without warts."
Dauben in a 1980 Guggenheim Fellow and is a Fellow of the American Association for the Advancement of Science, and a Fellow of the New York Academy of Sciences (since 1982).
Dauben is an elected member (1991) of the International Academy of the History of Science and an elected foreign member (2001) of German Academy of Sciences Leopoldina.
He delivered an invited lecture at the 1998 International Congress of Mathematicians in Berlin on Karl Marx's mathematical work. *Wik



DEATHS

1720 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

1731 Brook Taylor (18 Aug 1685, 29 Dec 1731) British mathematician, best known for the Taylor's series, a method for expanding functions into infinite series. In 1708, Taylor produced a solution to the problem of the centre of oscillation. His Methodus incrementorum directa et inversa (1715; “Direct and Indirect Methods of Incrementation”) introduced what is now called the calculus of finite differences. Using this, he was the first to express mathematically the movement of a vibrating string on the basis of mechanical principles. Methodus also contained Taylor's theorem, later recognized (1772) by Lagrange as the basis of differential calculus. A gifted artist, Taylor also wrote on basic principles of perspective (1715) containing the first general treatment of the principle of vanishing points.*TIS

1737 Joseph Saurin (1659 at Courtaison – December 29, 1737 at Paris) was a French mathematician and a converted Protestant minister. He was the first to show how the tangents at the multiple points of curves could be determined by mathematical analysis. He was accused in 1712 by Jean-Baptiste Rousseau of being the actual author of defamatory verses that gossip had attributed to Rousseau.*Wik

1891 Leopold Kronecker (7 Dec 1823, 29 Dec 1891) died of a bronchial illness in Berlin, in his 69th year. Kronecker's primary contributions were in the theory of equations. *VFR   
A German mathematician who worked to unify arithmetic, algebra and analysis, with a particular interest in elliptic functions, algebraic equations, theory of numbers, theory of determinants and theory of simple and multiple integrals. However the topics he studied were restricted by the fact that he believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps. He believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs, and believed that transcendental numbers did not exist. The Kronecker delta function is named in his honour. *TIS

1941 William James Macdonald (1851 in Huntly, Aberdeenshire, Scotland
Died: 29 Dec 1941 in Edinburgh, Scotland) graduated from the University of St Andrews. He taught at Madras College St Andrews, at Merchiston Castle School and at Donald Stewart's College in Edinburgh. He was a pioneer of the introduction of modern geometry to the mathematical curriculum. He was a founder member of the EMS and became the sixth President in 1887. *SAU

1941 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors Méthodes de calcul differential absolu et leures applications in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1989 Adrien Albert (19 November 1907, Sydney - 29 December 1989, Canberra) was a leading authority in the development of medicinal chemistry in Australia. Albert also authored many important books on chemistry, including one on selective toxicity.
He was awarded BSc with first class honours and the University Medal in 1932 at the University of Sydney. He gained a PhD in 1937 and a DSc in 1947 from the University of London. His appointments included Lecturer at the University of Sydney (1938-1947), advisor to the Medical Directorate of the Australian Army (1942-1947), research at the Wellcome Research Institute in London (1947-1948) and in 1948 the Foundation Chair of Medical Chemistry in the John Curtin School of Medical Research at the Australian National University in Canberra where he established the Department of Medical Chemistry. He was a Fellow of the Australian Academy of Science.
He was the author of Selective Toxicity: The Physico-Chemical Basis of Therapy, first published by Chapman and Hall in 1951.
The Adrien Albert Laboratory of Medicinal Chemistry at the University of Sydney was established in his honour in 1989.[1] His bequest funds the Adrien Albert Lectureship, awarded every two years by the Royal Society of Chemistry *Wik

1989 Hermann (Julius) Oberth (25 Jun 1894, 29 Dec 1989)  was a German scientist who was one of three founders of space flight (with Tsiolkovsky and Goddard). After injury in WWI, he drafted a proposal for a long-range, liquid-propellant rocket, which the War Ministry dismissed as fanciful. Even his Ph.D. dissertation on his rocket design was rejected by the University of Heidelberg. When he published it as Die Rakete zu den Planetenräumen (1923; “The Rocket into Interplanetary Space”) he gained recognition for its mathematical analysis of the rocket speed that would allow it to escape Earth's gravitational pull. He received a Romanian patent in 1931 for a liquid-propellant rocket design. His first such rocket was launched 7 May 1931, near Berlin. *TIS


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

Sunday, 28 December 2014

How the term Scientist came to be-


Reposted from a 2/18, 2011 Post:

John Cook, at the Endeavour just wrote a nice tid-bit about science/language regarding the creation of the word scientist. I knew the story, but apparently from a flawed source as I had credited the wrong poet (I had Wordsworth... not a bad poet, but not correct) .. so I will correct my notes, and along the way, supplement John's blog with a little more interesting detail from my notes about the topic.. (I think most of this is right).
John Wrote:
For most of history, scientists have been called natural philosophers. You might expect that scientist gradually and imperceptibly replaced natural philosopher over time. Surprisingly, it’s possible pinpoint exactly when and where the term scientist was born.

It was June 24, 1833 at a meeting of the British Association for the Advancement of Science. Romantic poet Samuel Taylor Coleridge was in attendance. (He had previously written about the scientific method.) Coleridge declared that although he was a true philosopher, the term philosopher should not be applied to the association’s members. William Whewell responded by coining the word scientist on the spot. He suggested

by analogy with artist, we may form scientist.

Since those who practice art are called artists, those who practice science should be called scientists.

This story comes from the prologue of Laura Snyder’s new book The Philosophical Breakfast Club. The subtitle is “Four Remarkable Friends Who Transformed Science and Changed the World.” William Whewell was one of these four friends. The others were John Herschel, Richard Jones, and Charles Babbage.




John Cook was good enough to share some material from the book and I would strongly recommend it to anyone who enjoys the history of science, or just a good story. This is my first read of anything by Laura Snyder, but I hope it will not be the last.

And now, here is the part from my notes which I hope adds to the story:
Whewell was also frequently in correspondence with Michael Faraday, and created the scientific terms anode, cathode, and ion. A letter between the two discussing these three terms is in the Wren Library at Trinity College in Cambridge. I have tried to capture an image below, but the library does not allow flash and the image is taken through the glass case... my apologies that it is not clearer.

In spite of its creation at such a high academic level, the word scientist was not well accepted for a long time. Its eventual acceptance came first in America, but it seems even there it encountered fierce opposition to its formal use well into the Twentieth Century. In The American Language in 1921, H. L. Mencken wrote
The last-named scientist was coined by William Whewell, an Englishman, in 1840, but was first adopted in America. Despite the fact that Fitzedward Hall and other eminent philologists used it. Despite this fact an academic and ineffective opposition to it still goes on. On the Style Sheet of the Century Magazine it is listed among the "words and phrases to be avoided." It was prohibited by the famous Index Expurgatorius prepared by William Cullen Bryant for the New York Evening Post, and his prohibition is still theoretically in force, but the word is now actually permitted by the Post. The Chicago Daily News Style Book, dated July 1, 1908, also bans it. The use of the word aroused almost incredible opposition in England. So recently as 1890 it was denounced by the London Daily News as "an ignoble Americanism," and according to William Archer it was finally accepted by the English only "at the point of the bayonet."

The term Natural Philosopher which scientist replaced had not been around long itself. Prior to the time of Galileo a Philosopher was indifferent to the observed facts, and dealt only with moral and logical theory. Galileo thought that,"The proper object of Philosophy is the great book of nature..." and not the words of other men. Eventually these new students of the "book of nature" became the "Natural Philosophers".

Despite several common assertions to the fact that Whewell coined the term in 1840,[Did they get the wrong date?... see date above in John Cook's story] the OED lists an earlier use in print, "1834 Q. Rev. LI. 59 Science..loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings..in the last three summers... Philosophers was felt to be too wide and too lofty a term,..; savans was rather assuming,..; some ingenious gentleman proposed that, by analogy with artist, they might form scientist, and added that there could be no scruple in making free with this termination when we have such words as sciolist(see below), economist, and atheist but this was not generally palatable."

It seems like they are talking about the same event with a different date on this article.

William Whewell is buried in Trinity College Chapel in Cambridge, UK. A memorial marker in the chapel is shown here and there is a statue in the ante-chapel

Addendum:  I recently came across notes that suggest that Faraday didn't really accept the term dispite his close relation with Whewell and his public endorsement of it; "As for hailing [the new term] scientist as 'good', that was mere politeness: Faraday never used the word, describing himself as a natural philosopher to the end of his career."     It also appears he didn't like physisist, "[The new term] Physicist is both to my mouth and ears so awkward that I think I shall never use it. The equivalent of three separate sounds of i in one word is too much."  *Sydney Ross Nineteenth-Century Attitudes: Men of Science (1991), 10. 




*** Sciolist..... If you recognized this term you are ahead of me...I looked it up and found:

Noun1.sciolist - an amateur who engages in an activity without serious intentions and who pretends to have knowledge
a dabbler,  a dilettant  (thank goodness they didn't use my name or picture)

[From Late Latin sciolus, smatterer, diminutive of Latin scius, knowing, from scre, to know; (This is the same root that gives us science.)

Geometric Vanishes, A Little HIstory



The image above represents one of the most famous "vanish" puzzles of all time. It was created in 1898 by Sam Loyd, America's greatest puzzlist at the end of the 19th century. It is said that during his life time over ten million copies of this puzzle were published around the world. Since then there have been almost that many variations created, including several variations by Sam Loyd himself. Several of these can be seen on Robs Puzzle Page involving cards, eggs, cowboys and more.

The original puzzle had Chinese warriors around the rim of a circular piece of cardboard fastened at the center to a larger piece of cardboard so it can be turned. Part of each warrior is inside the circle and part is outside.
Count carefully, when rotated from its initial position to its second position, one warrior disappears! The challenge is to explain how this "disappearing act" works.

The animation above comes from a web site which also includes a copy you can print and make your own version.

For students, these may be less instructive than the more obviously geometric vanishes. One of the most popular in classrooms is the Curry Triangle Paradox shown below (Not to be confused with Curry's Paradox in Logic).



The Wikipedia Article includes, "According to Martin Gardner, this particular puzzle was invented by a New York City amateur magician, Paul Curry, in 1953. The principle of a dissection paradox has however been known since the start of the 16th century."

A nice video by James Tanton gives an explanation of the paradox if the reader can't explain it.

I found information about the earliest "vanish" puzzle at a puzzle blog by Marianno Tomatis .
The first example of vanishing area puzzles was reported in the 1566 book Libro d'Architettura Primo by Sebastiano Serlio (1475-1554), an Italian architect of the Renaissance. He cites the case of a 3×10 rectangle which can be converted into a rectangle 4×7 and two triangles 1×3. Curiously, Serlio didn't seem to noticed that the sum of the three resulting areas (31 square feet) was greater than the original one (30 square feet):


In 1769 Edmé Gilles Guyot (1706-1786) described the vanish area paradox in the second volume of his Nouvelles récréations physiques et mathématiques (read it here): a 10 × 3 square can be divided in four pieces which, rearranged, define a 5 × 4 and a 6 × 2 rectangle. 

This puzzle is often quoted as the first vanish puzzle but attributed to William Hooper in his 1774 Rational Recreations.  The fact that Hooper took the puzzle directly from Guyot is made clear when it is pointed out that the original edition of Guyot had the puzzle mis-drawn.  The same mis-drawn image appeared in Hooper's first edition.  Both second editions had the error corrected. 

Hooper's book is a collection of many scientific experiments and amusements, and includes "an Appendix of Miscellaneous Recreations".

Probably the biggest boost to a rebirth of interest in these puzzles came from an article by the great Martin Gardner when he wrote about such geometric vanishes in his Mathematics, Magic and Mystery in 1956. If you are interested in this type of puzzle, this book is still a great resource.


Before I leave this topic, I should point out the first version I ever encountered which I found a nice illustration of at a puzzle page by Dr. Ron Knott from the UK.



This is the one I most think can be used effectively in the classroom.

Enjoy

On This Day in Math - December 28





Shadow Family in Cowtown


Anyone who considers arithmetical methods of producing random digits is,
of course,
in the state of sin.
~John Von Neumann


The 362nd day of the year; 362 and its double and triple all use the same number of digits in Roman numerals.*What's Special About This Number.


EVENTS

1612 Galileo observed Neptune, but did not recognize it as a planet. Galileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. (The official discovery is usually cited as September 23, 1846, Neptune was discovered within 1° of where Le Verrier had predicted it to be.) During the period of his first observation in December 1612, Neptune was stationary in the sky because it had just turned retrograde that very day. This apparent backward motion is created when the orbit of the Earth takes it past an outer planet. Since Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope.*Wik

1893 Simon Newcomb gives a speech to the New York Mathematical Society with comments on the fourth dimension; "It is a perfectly legitimate exercise .... if we should not stop at three dimensions in geometry, but construct one for space having four... and there is room for an indefinite number of universes". He also called his speculations on the fourth dimension, "the fairlyland of geometry."
The speech appears a short time later on February 1, 1894 in Nature. His comments would also be commented on in H. G. Wells, Time Machine. "But some philosophical people have been asking ... - Why not another direction at right angles to the other three? ... Professor Simon Newcomb was expanding on this only a month or so ago." *Alfred M. Bork, The Fourth Dimenson in Nineteenth-Century Physics, Isis, Sept 1964 pg 326-338

In 1893, Professor James Dewar gave six well-illustrated lectures on "Air gaseous and liquid," at the Royal Institution, London, 28 Dec 1893 - 9 Jan 1894. Some of the air in the room was liquified in the presence of the audience and it remained so for some time, when enclosed in a vacuum jacket. Again, 1 Apr 1898.
My favorite stupid joke about Thermos Bottles: "You put hot stuff in a thermos, it stays hot. You put cold stuff in a thermos, it stays cold. BUT How does the Thermos know which is which?"

1895 Wilhelm Conrad RÖNTGEN announces that he has taken an x-ray of his wife’s hand in a paper, "Ein neue Art von Strahlen", to the Würzburg Physical-Medical-Society on 28 Dec and it appeared in their 1895 proceedings. By January he was famous. In the next year some 50 books and 1000 papers appeared on the subject! A journal devoted to the subject was founded in May 1896.

1895 The Lumières held their first public screening of projected motion pictures in 1895. The Lumière brothers, Auguste Marie Louis Nicolas [oɡyst maʁi lwi nikɔla] (19 October 1862, Besançon, France – 10 April 1954, Lyon) and Louis Jean (5 October 1864, Besançon, France – 6 June 1948, Bandol) were the earliest filmmakers in history. (Appropriately, "lumière" translates as "light" in English.)
Their first public screening of films at which admission was charged was held on December 28, 1895, at Salon Indien du Grand Café in Paris. This history-making presentation featured ten short films, including their first film, Sortie des Usines Lumière à Lyon (Workers Leaving the Lumière Factory). Each film is 17 meters long, which, when hand cranked through a projector, runs approximately 50 seconds. *Wik


1923 George David Birkhoff of Harvard received the first Bocher Memorial Prize for his paper “Dynamical systems with two degrees of freedom.” *VFR

1938 Kurt G¨odel lectures to the annual AMS meeting, Williamsburg, on the consistency of the axiom of choice and the generalized continuum hypothesis. Independence was proved in 1963 by Paul Cohen. *VFR

In 1931, Irene Joliot-Curie reported her study of the unusually penetrating radiation released when beryllium was bombarded by alpha particles seen by the German physicists, Walter Bothe and H. Becker in 1930. Joliot-Curie (daughter of Marie and Pierre Curie) agreed with them that the radiation was energetic gamma rays. She further discovered that if the emitted radiation passed through paraffin (or other hydrogen containing materials), large numbers of protons were released. Since this was, in fact, a previously unknown result for gamma rays, she lacked an explanation. It was to be the experiments of James Chadwick performed during 7-17 Feb that would discover the radiation was in fact new particles - neutrons.*TIS

1973 For a really big ellipse, consider the orbit of the comet Kahoutek, which reached perihelion on this date. The length of the major and minor axes are 3,600 and 44 Astronomical Units. The comet’s eccentricity is approximately 0.99993. *UMAP Journal, 4(1983), p. 164
Comet Kohoutek is a long-period comet; its previous apparition was about 150,000 years ago, and its next apparition will be in about 75,000 years. The comet was discovered on March 18th on photographic plates taken on March 7th and 9th by Czech astronomer Luboš Kohoutek, for whom the comet is named. *Wik

In 2005, the first in a network of satellites, named Galileo, was launched by a consortium of European goverments and companies. By 2011, Galileo will consist of 30 satellites providing worldwide coverage as an alternative to the U.S. monopoly with its Global Positioning System (GPS). At a cost of $4 billion, it's Europe's biggest-ever space project, with one-third contributed by governments and the balance from eight companies. Since the American GPS is controlled by the military, the European satellite network is designed to ensure independance for civilian use, but also offer more precision for a paid service. Customers are expected to include service for small airports, transportation, and mobile phone manufacturers to build in navigation capabilities.*TIS

2009 Longest flight by a paper-only plane-Takuo Toda sets world record
TOKYO, Japan--Using a specially designed 10cm long paper plane, Japanese origami plane virtuoso Takuo Toda's origami flight in a Japan Airlines hangar near Tokyo's Haneda Airport lasted 26.1s - setting the world record for the Longest flight by a paper-only plane.
This one was made strictly in keeping with traditional rules of the ancient Japanese art; only one sheet of paper was folded by hand, with no scissors or glue. He had previously set a record for time aloft with a plane that included tape. *worldrecordsacademy.org
There is a video here.

2013 Voyager 1 is a 722-kilogram (1,590 lb) space probe launched by NASA on September 5, 1977 to study the outer Solar System. Operating for 36 years, 3 months, and 23 days as of 28 December 2013, the spacecraft communicates with the Deep Space Network to receive routine commands and return data. At a distance of about 127.21 AU (1.903×1010 km) from the Earth as of 28 December 2013, it is the farthest humanmade object from Earth. *Wik


BIRTHS

1798 Thomas Henderson (28 Dec 1798; 23 Nov 1844) Scottish astronomer, the first Scottish Astronomer Royal (1834), who was first to measure the parallax of a star (Alpha Centauri, observed at the Cape of Good Hope) in 1831-33, but delayed publication of his results until Jan 1839. By then, a few months earlier, both Friedrich Bessel and Friedrich Struve had been recognized as first for their measurements of stellar parallaxes. Alpha Centauri can be observed from the Cape, though not from Britain. It is now known to be the nearest star to the Sun, but is still so distant that its light takes 4.5 years to reach us. As Scottish Astronomer Royal in 1834, he worked diligently at the Edinburgh observatory for ten years, making over 60,000 observations of star positions before his death in 1844. *TIS

1808 Victoire Louis Athanase Dupré (December 28 1808 ; August 10 1869 ) was a French mathematician and physicist.
He worked on number theory and in the 1860s with thermodynamics and from him comes the textbook mécanique Théorie de la Chaleur (1869), which is essentially the distribution of this then-new field of knowledge in France contributed. Together with his son Paul Dupré experimental research, he examined the capillary and the surface tension of liquids. This work also led to a formulation of Young's equation which is known today as the Young-Dupré equation. *Wik

1873 William Draper Harkins (28 Dec 1873; 7 Mar 1951) American nuclear chemist who was one of the first to investigate the structure and fusion reactions of the nucleus. In 1920, Harkins predicted the existence of the neutron, subsequently discovered by Chadwick's experiment. He made pioneering studies of nuclear reactions with Wilson cloud chambers. In the early 1930's, (with M.D. Kamen) he built a cyclotron. Harkins demonstrated that in neutron bombardment reactions the first step in neutron capture is the formation of an "excited nucleus" of measurable lifetime, which subsequently splits into fragments. He also suggested that subatomic energy might provide enough energy to power the Sun over its lifetime.*TIS

1882 Sir Arthur Stanley Eddington (28 Dec 1882; 22 Nov 1944) English astrophysicist, and mathematician known for his work on the motion, distribution, evolution and structure of stars. He also interpreted Einstein's general theory of relativity. He was one of the first to suggest (1917) conversion of matter into radiation powered the stars. In 1919, he led a solar eclipse expedition which confirmed the predicted bending of starlight by gravity. He developed an equation for radiation pressure. In 1924, he derived an important mass-luminosity relation. He also studied pulsations in Cepheid variables, and the very high densities of white dwarfs. He sought fundamental relationships between the prinicipal physical constants. Eddington wrote many books for the general reader, including Stars and Atoms. *TIS  One of my favorite stories about Eddington is this one: Ludwick Silberstein approached Eddington and told him that people believed he was one of only three people in the world who understood general relativity, and that included Einstein. When Eddington didn't respond for a moment he prodded, come on, don't be modest, and Eddington replied, "Oh, no.  It's not that.  I was just trying to figure out who the third was?"  *Mario Livio, Brilliant Blunders

1898 Carl-Gustaf Arvid Rossby (28 Dec 1898; 19 Aug 1957) Swedish-U.S. meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. His work contributed to developing meteorology as a science. Rossby first theorized about the existence of the jet stream in 1939, and that it governs the easterly movement of most weather. U.S. Army Air Corps pilots flying B-29 bombing missions across the Pacific Ocean during World War II proved the jet stream's existence. The pilots found that when they flew from east to west, they experienced slower arrival times and fuel shortage problems. When flying from west to east, however, they found the opposite to be true. Rossby created mathematical models (Rossby equations) for computerized weather prediction (1950). *TIS

1903 John von Neumann is born in Budapest, Hungary.(28 Dec 1903, 8 Feb 1957) His prodigious abilities were recognized in the early childhood. He obtained a degree in chemical engineering attending the University of Berlin (1921-1923) and the Technische Hochschule in Zurich (1923-1926). *CHM
He made important contributions in quantum physics, logic, meteorology, and computer science. He invented game theory, the branch of mathematics that analyses strategy and is now widely employed for military and economic purposes. During WW II, he studied the implosion method for bringing nuclear fuel to explosion and he participated in the development of the hydrogen bomb. He also set quantum theory upon a rigorous mathematical basis. In computer theory, von Neumann did much of the pioneering work in logical design, in the problem of obtaining reliable answers from a machine with unreliable components, the function of "memory," and machine imitation of "randomness." *TIS

1929 Maarten Schmidt (28 Dec 1929, ) Dutch-born American astronomer who in 1963 discovered quasars (quasi-stellar objects). The hydrogen spectrum of these starlike objects shows a huge redshift, which indicates they are more distant than normal stars, travelling away at greater speed, and are among the oldest objects observed. In turn, this indicates they existed only when the universe was very young, and provides evidence against the steady state theory of Fred Hoyle. Schmidt is currently seeking to find the redshift above which there are no quasars, and he also studies x-ray and gamma ray sources.*TIS



DEATHS

1663 Francesco Maria Grimaldi (2 Apr 1618, 28 Dec 1663) Italian mathematician and physicist who studied the diffraction of light. He observed the image on a screen in a darkened room of a tiny beam of sunlight after it passed pass through a fine screen (or a slit, edge of a screen, wire, hair, fabric or bird feather). The image had iridescent fringes, and deviated from a normal geometrical shadow. He coined the name diffraction for this change of trajectory of the light passing near opaque objects (though, more specifically, it may have been interferences with two close sources that he observed). This provided evidence for later physicists to support the wave theory of light. With Riccioli, he investigated the object in free fall (1640-50), and found that distance of fall was proportional to the square of the time taken.*TIS

1827 Robert Woodhouse (28 April 1773 – 23 December 1827) was an English mathematician. His earliest work, entitled the Principles of Analytical Calculation, was published at Cambridge in 1803. In this he explained the differential notation and strongly pressed the employment of it; but he severely criticized the methods used by continental writers, and their constant assumption of non-evident principles. This was followed in 1809 by a trigonometry (plane and spherical), and in 1810 by a historical treatise on the calculus of variations and isoperimetrical problems. He next produced an astronomy; of which the first book (usually bound in two volumes), on practical and descriptive astronomy, was issued in 1812, and the second book, containing an account of the treatment of physical astronomy by Pierre-Simon Laplace and other continental writers, was issued in 1818.
He became the Lucasian Professor of Mathematics in 1820, and subsequently the Plumian professor in the university. As Plumian Professor he was responsible for installing and adjusting the transit instruments and clocks at the Cambridge Observatory.[3] He held that position until his death in 1827. *Wik

1871 John Henry Pratt (4 June 1809 - 28 December 1871) was a British clergyman and mathematician who devised a theory of crustal balance which would become the basis for the isostasy principle. *Wik

1896 Horatio (Emmons) Hale (3 May 1817, 28 Dec 1896) was an American anthropologistwhose contributions to the science of ethnology, included his theory of the origin of the diversities of human languages and dialectsa theory suggested by his study of child languages (the languages invented by little children). He emphasized the importance of languages as tests of mental capacity and as criteria for the classification of human groups. Hale was the first to discover that the Tutelos of Virginia belonged to the Siouan family, and to identify the Cherokee as a member of the Iroquoian family of speech. He sailed with the scientific corps of the Wilkes Exploring Expedition (1838-42) collecting linguistic materials. He used the drift of the Polynesian tongue as a clue to the migration of this race. *TIS

1919 Johannes Robert Rydberg​, (‘Janne’ to his friends), (November 8, 1854 – December 28, 1919), was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to predict the wavelengths of photons (of light and other electromagnetic radiation) emitted by changes in the energy level of an electron in a hydrogen atom.
The physical constant known as the Rydberg constant is named after him, as is the Rydberg unit. Excited atoms with very high values of the principal quantum number, represented by n in the Rydberg formula, are called Rydberg atoms. Rydberg's anticipation that spectral studies could assist in a theoretical understanding of the atom and its chemical properties was justified in 1913 by the work of Niels Bohr (see hydrogen spectrum). An important spectroscopic constant based on a hypothetical atom of infinite mass is called the Rydberg (R) in his honour. *Wik

1923 Gustave Eiffel (15 Dec 1832, 28 Dec 1923) French civil engineer who specialized in metal structures, known especially for the Eiffel Tower in Paris. He built his first of his iron bridges at Bordeaux (1858) and was among the first engineers to build bridge foundations using compressed-air caissons. His work includes designing the rotatable dome for Nice Observatory on the summit of Mont Gros (1886), and the framework for the Statue of Liberty now in New York Harbor. After building the Eiffel Tower (1887-9), which he used for scientific research on meteorology, aerodynamics and radio telegraphy, he also built the first aerodynamic laboratory at Auteuil, outside Paris, where he pursued his research work without interruption during WW I. *TIS

1964 Edwin Bidwell Wilson (25 April 1879 in Hartford, Connecticut, USA - 28 Dec 1964 in Brookline, Massachusetts, USA) Wilson graduated from Yale with a Ph.D. in 1901 and, in the same year, a textbook which he had written on vector analysis was published. Vector analysis (1901) was based on Gibbs' lectures and , "This beautiful work, published when Wilson was only twenty-two years old, had a profound and lasting influence on the notation for and the use of vector analysis." Wilson had been inspired by Gibbs to work on mathematical physics and he began to write papers on mechanics and the theory of relativity. In 1912 Wilson published the first American advanced calculus text. World War I had seen another move in Wilson's research interests for he had undertaken war work which involved aerodynamics and this led him to study the effects of gusts of wind on a plane. In 1920 he published his third major text Aeronautics and gathered round him a group of students working on this topic.
Wilson had already worked in a number of quite distinct areas and his work on aeronautics did not become the major topic for the rest of his career. Not long after the publication of his important text on Aeronautics his interests moved again, this time towards probability and statistics. He did not study statistics for its own, however, but he was interested in applying statistics both to astronomy and to biology. He was the first to study confidence intervals, later rediscovered by Neyman. In 1922 Wilson left the Massachusetts Institute of Technology to become Professor of Vital Statistics at the Harvard School of Public Health. He continued to hold this post until he retired in 1945, when he became professor emeritus. After he retired, Wilson spent a year in Glasgow, Scotland when he was Stevenson lecture on Citizenship. From 1948 he was a consultant to the Office of Naval Research in Boston. *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, 27 December 2014

On This Day in Math - December 27


At ubi materia, ibi Geometria.
Where there is matter, there is geometry.
~Johannes Kepler


The 361st day of the year, 2361 is an apocalyptic number, it contains 666. 2361=4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952 That's 109 digits.
361 = 192 *Lord Karl Voldevive ‏@Karl4MarioMugan

EVENTS

1612 Galileo observed Neptune, but did not recognize it as a planet. Galileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. (The official discovery is usually cited as September 23, 1846, Neptune was discovered within 1° of where Le Verrier had predicted it to be.) During the period of his first observation in December 1612, Neptune was stationary in the sky because it had just turned retrograde that very day. This apparent backward motion is created when the orbit of the Earth takes it past an outer planet. Since Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope.*Wik

In 1831, Charles Darwin set sail from Plymouth harbour on his voyage of scientific discovery aboard the HMS Beagle, a British Navy ship. The Captain Robert FitzRoy was sailing to the southern coast of South America in order to complete a government survey. Darwin had an unpaid position as the ship's naturalist, at age 22, just out of university. Originally planned to be at sea for two years, the voyage lasted five years, making stops in Brazil, the Galapogos Islands, and New Zealand. From the observations he made and the specimens he collected on that voyage, Darwin developed his theory of biological evolution through natural selection, which he published 28 years after the Beagle left Plymouth. Darwin laid the foundation of modern evolutionary theory. *TIS

In 1956, the formerly believed "law" of conservation of parity was disproved in the first successful results from an experiment conducted by Madame Chien-Shiung Wu at Columbia University on the beta-decay of cobalt-60. It had been suggested in a paper published by Lee and Yang on 1 Oct 1956. There had been problems to overcome working with the cobalt sample and detectors in a vacuum at a working temperature of one-hundredth of a kelvin. Wu's team repeated the experiment, doing maintenance on the apparatus as necessary, until on 9 Jan 1957 further measurements confirmed the initial results. Leon Lederman performed an independent test of parity with Columbia's cyclotron. They held a press conference on 15 Jan 1957.*TIS



BIRTHS

1571 Johannes Kepler (27 Dec 1571; 15 Nov 1630) German astronomer who formulated three major laws of planetary motion which enabled Isaac Newton to devise the law of gravitation. Working from the carefully measured positions of the planets recorded by Tycho Brahe, Kepler mathematically deduced three relationships from the data: (1) the planets move in elliptical orbits with the Sun at one focus; (2) the radius vector sweeps out equal areas in equal times; and (3) for two planets the squares of their periods are proportional to the cubes of their mean distances from the sun. Kepler suggested that the tides were caused by the attraction of the moon. He believed that the universe was governed by mathematical rules, but recognized the importance of experimental verification.*TIS

1654 Jacob Jacques Bernoulli (27 Dec 1654; 16 Aug 1705) was a Swiss mathematician and astronomer who was one of the first to fully utilize differential calculus and introduced the term integral in integral calculus. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra (1685), work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines. By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. He published five treatises on infinite series (1682 - 1704). Jacob was intrigued by the logarithmic spiral and requested it be carved on his tombstone. He was the first of the Bernoulli family of mathematicians. *TIS (see more about the family of Bernoulli's at the Renaissance Mathematicus )

Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in the narrowest limits no limit in here.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!

Ars Conjectandi

1773 Sir George Cayley (27 Dec 1773; 15 Dec 1857)(6th Baronet ) English aeronautical pioneer who built the first successful man-carrying glider (1853). He made extensive anatomical and functional studies of bird flight. By measuring bird and human muscle masses, he realized it would be impossible for humans to strap on a pair of wings and take to the air. His further studies in the principles of lift, drag and thrust founded the science of aerodynamics from which he discovered stabilizing flying craft required both vertical and horizontal tail rudders, that concave wings produced more lift than flat surfaces and that swept-back wings provided greater stability. Cayley also invented the caterpillar tractor (1825), automatic railroad crossing signals, self-righting lifeboats, and an expansion-air (hot-air) engine.
*TIS (He was a distant cousin of the father of mathematician Arthur Cayley)

1915 Jacob Lionel Bakst Cooper (27 December 1915, Beaufort West, Cape Province, South Africa, 8 August 1979, London, England) was a South African mathematician who worked in operator theory, transform theory, thermodynamics, functional analysis and differential equations.*Wik



DEATHS

1771 Henri Pitot (3 May 1695, 27 Dec 1771) French hydraulic engineer who invented the Pitot tube (1732), an instrument to measure flow velocity either in liquids or gases. With subsequent improvements by Henri Darcy, its modern form is used to determine the airspeed of aircraft. Although originally a trained mathematician and astronomer, he became involved with an investigation of the velocity of flowing water at different depths, for which purpose he first created the Pitot tube. He disproved the prevailing belief that the velocity of flowing water increased with depth. Pitot became an engineer in charge of maintenance and construction of canals, bridges, drainage projects, and is particularly remembered for his kilometer-long Roman-arched Saint-Clément Aqueduct (1772) at Montpellier, France. *TIS

1930 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU

1973 Raymond Woodard Brink (4 Jan 1890 in Newark, New Jersey, USA - 27 Dec 1973 in La Jolla, California, USA) was an American mathematician who studied at Kansas State University, Harvard and Paris. He taught at the University of Minnesota though he spent a year in Edinburgh in 1919. He worked on the convergence of series. *SAU

1992 Alfred Hoblitzelle Clifford (July 11, 1908 – December 27, 1992) was an American mathematician who is known for Clifford theory and for his work on semigroups. The Alfred H. Clifford Mathematics Research Library at Tulane University is named after him.*Wik

1995 Boris Vladimirovich Gnedenko (January 1, 1912 - December 27, 1995) was a Soviet mathematician and a student of Andrey Nikolaevich Kolmogorov. He was born in Simbirsk (now Ulyanovsk), Russia, and died in Moscow. He is perhaps best known for his work with Kolmogorov, and his contributions to the study of probability theory. Gnedenko was appointed as Head of the Physics, Mathematics and Chemistry Section of the Ukrainian Academy of Sciences in 1949, and also became Director of the Kiev Institute of Mathematics in the same year.*Wik

1996 Sister Mary Celine Fasenmyer, R.S.M., (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was a mathematician. She is most noted for her work on hypergeometric functions and linear algebra.*Wik

2006 Peter L. Hammer (December 23, 1936 - December 27, 2006) was an American mathematician native to Romania. He contributed to the fields of operations research and applied discrete mathematics through the study of pseudo-Boolean functions and their connections to graph theory and data mining.*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