Saturday, 15 July 2017

On This Day in Math - July 15

Mathematics is as much an aspect of culture as it is a collection of algorithms.

-Carl Boyer

The 197th day of this year; 197 is the sum of all digits of all two-digit prime numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.  It is simple to show that the sum of one-digit primes is 17. Do the sum of the digits of n-digit primes always end in seven? ( Or perhaps we ask, are there any others that do?

The 196th day of the year, A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its base 10 digits and adding the resulting numbers. 196 is the lowest number conjectured to be a Lychrel number; the process has been carried out for one billion iterations without finding a palindrome, but no one has ever proven that it will never produce one. The number produced on the one billionth iteration had 413,930,770 digits. The name "Lychrel" was coined by Wade VanLandingham—a rough anagram of his girlfriend's name Cheryl. No Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. (Students might try finding the number of iterations of the process to find a palindrome for various n. 195, for example, takes four iterations :
195 + 591 = 786
786 + 687 = 1473
1473 + 3741 = 5214
5214 + 4125 = 9339)
DO not try the numbers 89 or 98. Harry J Saal used a computer to repeatedly iterate this process and finally did come up with a palindrome, the number 8,813,200,023,188 on the 24th iteration.

Jim Wilder noticed that 142 =196 and 132=169... are there other squares of consecutive numbers that share the same digits?

A number is said to be square-full if for every prime, p, that divides it, p2 also divides it. 196 is such a number. Are there cube-full numbers?


622 Mohammed’s flight, the Hegira, from Mecca to Medina began. Traditionally, the Islamic calendar began at sunset on this day.*VFR

1662 The Royal Society of London received its charter. *VFR Its official foundation date is 28 November 1660, when a group of 12 met at Gresham College after a lecture by Christopher Wren, then the Gresham Professor of Astronomy, and decided to found 'a Colledge for the Promoting of Physico-Mathematicall Experimentall Learning'. This group included Wren himself, Robert Boyle, John Wilkins, Sir Robert Moray, and William, Viscount Brouncker.  n 1662 the Society was permitted by Royal Charter to publish and the first two books it produced were John Evelyn's Sylva and Micrographia by Robert Hooke. *Royal Society Web page

1808 Thomas Jefferson writes to Augustin-François Silvestre French inventor and popularizer of science to thank him for sharing copies of " volumes of the Memoirs of the Agricultural Society of the Seine" and shares his ideas about the importance of the plough, including details of a mould board of his own design. "I shall with great pleasure attend to the construction and transmission to the Society of a plough with my mould board. This is the only part of that useful instrument to which I have paid any particular attention. But knowing how much the perfection of the plough must depend, 1st, on the line of traction; 2d, on the direction of the share; 3d, on the angle of the wing; 4th, on the form of the mould-board; " *Letters of Thomas Jefferson,

1828 The Board of Longitude is dissolved by act of Parliament. In the Parliamentary discussions prior to the act, John Crocker, First Secretary of the Admiralty,  argued that the Board was :
"wholly occupied in reading the wild ravings of mad men, who fancied they had discovered perpetual motion and such like chimeras.

1913 A window at Westminster Abbey, in memory of Lord Kelvin, was unveiled.*VFR (If someone has a better image of this window to offer, please send me a copy and I will replace this very small image.)

1928 The first message for transmission by the Enigma was encoded.*VFR The first Enigma was invented by German engineer Arthur Scherbius at the end of World War I. This model and its variants were used commercially from the early 1920s, and adopted by military and government services of several countries — most notably by Nazi Germany before and during World War II. Several different Enigma models were produced, but the German military models are the ones most commonly discussed. *Wik


1808 Sir Henry Cole (15 July 1808 – 18 April 1882) British industrial designer, museum director and writer who produced the first commercial Christmas card.* Cole played a pivotal role in the introduction of the Penny Post, the English postal system (assistant to Rowland Hill, 1837-40), influenced the expansion of railways, helped establish the Victoria and Albert Museum, contributed greatly to the success of London’s Great Exhibition of 1851, and promoted art and science education. In 1843, wishing to save much handwriting of seasonal correspondance, Cole introduced the world's first commercial Christmas card. He commissioned artist John Callcott Horsley to make the artwork for 1000 hand-coloured lithographs. (Individuals' homemade Christmas cards had existed earlier.)

1848 Vilfredo Federico Damaso Pareto (15 July 1848 – 19 August 1923) born Wilfried Fritz Pareto, was an Italian engineer, sociologist, economist, and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices. "His legacy as an economist was profound. Partly because of him, the field evolved from a branch of moral philosophy as practiced by Adam Smith into a data intensive field of scientific research and mathematical equations. His books look more like modern economics than most other texts of that day: tables of statistics from across the world and ages, rows of integral signs and equations, intricate charts and graphs."[1] He introduced the concept of Pareto efficiency and helped develop the field of microeconomics. He also was the first to discover that income follows a Pareto distribution, which is a power law probability distribution. The Pareto principle was named after him and built on observations of his such as that 80% of the land in Italy was owned by 20% of the population. He also contributed to the fields of sociology and mathematics.*Wik

1865 Wilhelm Wirtinger (15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.Wirtinger was greatly influenced by Felix Klein with whom he studied at the University of Berlin and the University of Göttingen. In 1907 the Royal Society of London awarded him the Sylvester Medal, for his contributions to the general theory of functions. *Wik

1895 Rudolf Diesel applies for patent for an internal combustion engine in the US (patented Aug 9, 1898.) "My invention has reference to improvements in apparatus for regulating the fuel supply in slow-combustion motors" *

1906 Adolph Andrei Pavlovich Yushkevich (15 July, 1906 – 17 July, 1993) was one of the leading historians of mathematics in the world. His doctorate was on Russian mathematics during the 18th century and he began publishing in 1929 the first of over 300 works on the history of mathematics. He contributed 21 articles to the Dictionary of Scientific Biography which are referenced in this Archive. This Archive also references over 50 articles by Yushkevich about a wide range of mathematicians from the earliest to modern times. Yushkevich was arguably the leading world authority on Euler and he was one of the leading authorities on medieval mathematics. *SAU

1909 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts) Statistician. In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programme in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programme in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1922 Leon Max Lederman (July 15, 1922 - ) American physicist who, along with Melvin Schwartz and Jack Steinberger, received the Nobel Prize for Physics in1988 for their joint research and discovery (1960-62) of a new subatomic particle, the muon neutrino. Neutrinos are subatomic particles having no detectable mass and no electric charge, which travel at nearly the speed of light. The discovery of muon neutrinos, a new type of neutrino, was followed by discoveries by other scientists of a number of different "families" of subatomic particle. Together, they now form a standard model, a scheme that has been used to classify all known elementary particles. He was director of the Fermi National Accelerator Laboratory in Batavia, Ill.*TIS

1930 Steven Smale (July 15, 1930 - ) born in Flint, Michigan. He earned three degrees at the University of Michigan and now teaches at Berkeley. He has made significant contributions to topology (Fields Medal, 1966), dynamical systems, economics, and numerical analysis. This still leaves time for chess, go, sailing, collecting minerals, and lots of political activism. For an interview with this fa­cinating mathematician, see More Mathematical People (1990), edited by Donald J. Albers, G. L. Alexanderson and Constance Reid.*VFR

1943 Jocelyn Bell Burnel(15 July 1943- ) British astronomer who discovered the first four pulsars. She was a Cambridge University graduate student, age 24, searching for quasars in 1967, when she noticed an unusual stellar radio signal - a rapid series of pulses repeating every 1.337 sec. This interstellar beacon was not man-made, so it was nicknamed in fun as LGM, for Little Green Men. In the next few months, Bell (her maiden name) found three more sources of radio pulses by careful scrutiny of hundreds of feet of pen-recorder paper. These represented a new class of celestial objects - pulsars - which astronomers eventually associated with superdense matter in the final stage of the evolution of massive stars. To date, hundreds more pulsars have been identified. *TIS


998 Abu'l-Wafa (10 June 940 – 15 July 998) was an Islamic astronomer and mathematician who wrote commentaries on the works of earlier mathematicians. He made astronomical observations and constructed accurate trigonometric tables.*SAU
He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text.
He is also credited of compiling tables of sines and tangents at 15' intervals. He also introduced the sec and cosec and studied the interrelations between the six trigonometric lines associated with an arc. His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived. *Wik

1841 Félix Savary (October 4, 1797, Paris - July 15, 1841 in Estagel) was a student at the École Polytechnique completing his studies in 1815. He then taught at the École, becoming a professor of astronomy and geodesy there in 1831. There he became a founder of studies into surveying and machines.
Savary also served as librarian at the Bureau des Longitudes from 1823 to 1829. Then on 24 December 1832, in recognition of his achievements, he was elected to the Académie des Sciences.
He worked on electromagnetism and electrodynamics, some work being done jointly with Ampère. In particular, on this topic, he wrote Mémoire sur l'application du calcul aux phenomènes élecro-dynamique (1823).
Savary also developed a theorem (named after him) on the curvature of a roulette, the curve traced out by a point on a fixed curve which rolls on a second curve.
He wrote on the rotation of magnets, studied the intensity of magnetism through an electrical discharge (1827), and applied the laws of gravity to determine the orbits of double stars in close orbit round each other (1827). In fact, on the topic of double stars, he published Mémoire sur les orbites des étoiles doubles (1827), and Sur la détermination des orbites que décrivent autour de leur centre de gravité deux étoiles très rapprochées l'une de l'autre (1827) in Connaissance des Temps. The star x Ursae Majoris is a double star and Savary demonstrated that the two stars move in elliptical orbits with the centre of gravity at the focus of the ellipses. Although this might appear to be a fairly simple consequence of Newton's law of gravitation, nevertheless it was important for it was the first verification of the laws for objects outside the solar system. This was the first verification of the universal nature of Newton's laws.*SAU

1931 Ladislaus Josephowitsch Bortkiewic studied law at St Petersburg, graduating in 1890 and then went on to study political economy and statistics for a year of postgraduate work. He studied at Strasbourg from 1891 to 1892, then at Göttingen under Lexis in 1892, going on to also study at Vienna and Leipzig. After submitting a dissertation, he was awarded a doctorate in 1893 from Göttingen.
After lecturing in statistics and actuarial science from 1895 to 1897 as a privatdozent in Strasbourg he went to St Petersburg where he was a clerk in the Railway Office from 1897 until 1901. However, during this time he returned to academic life, teaching statistics from 1899 until December 1900 at the Alexandrowskii Lyceum. Then in 1901 he was appointed as an extraordinary professor of statistics at the University of Berlin. Bortkiewicz became an ordinary professor of statistics and political economy at the University of Berlin in 1920 and he spent the rest of his life there. An unfortunate argument with an Italian statistician Gini, who accused Bortkiewicz of plagiarism, led to an unhappy episode near the end of Bortkiewicz's life.
Bortkiewicz worked on mathematical statistics and applications to actuarial science and political economy. His work on actuarial science was largely concerned with mortality tables. He examined life expectancy in an increasing population and showed in 1893, contrary to what had previously been believed, that life expectancy in such a population could only be computed from mortality tables and was not a function of the observed birth rate and death rate. He published on mortality rates again in publication of 1904 and 1911 where he examined methods to compare mortality rates.
Good argues that the Poisson distribution should have been named the von Bortkiewicz distribution. Bortkiewicz was interested in the law of small numbers and he used the divergence coefficient Q, deducing its expectation and standard deviation. He published a work The Law of Small Numbers in 1898. In this he was the first to note that events with low frequency in a large population followed a Poisson distribution even when the probabilities of the events varied.Other areas to which Bortkiewicz applied his statistical methods include radioactivity (1913), order statistics, and applications to legal studies. *SAU

1961 Nina Karlova Bari (November 19, 1901, Moscow – July 15, 1961, Moscow) was hit by a train in Moscow Metro. It is unclear whether it was an accident or a suicide brought on by despondency over the death of Nikolai Nikolaevich Luzin (1883–1950), her teacher and reported lover.*VFR

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
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