Saturday 16 August 2014

On This Day in Math - August 16

Projective geometry is all geometry.
~Arthur Cayley

The 228th day of the year; 228 is the number of ways, up to rotation and reflection, of dissecting a regular 11-gon into 9 triangles.
bonus, 228 + 1,  822 + 1, and (228 + 822) + 1 are all primes.


1878 Hermite writes to Sylvester at Johns Hopkins concerned about his accepting a Math Chair in America to questioned the ability of the American people to contribute to research-level mathematics. Only three years later he would be reading the paper of Fabian Franklin, a young assistant mathematics instructor at Johns Hopkins, before the French Academy. The paper was on a short, purely graphic, proof of Euler's theorem on pentagonal numbers. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

In 1898, the loop-de-loop Roller Coaster was patented by Edwin Prescott.*TIS The vertical loop is not a recent roller coaster innovation. Its origins can be traced back to the 1850s when centrifugal railways were built in France and Great Britain. In 1901 Prescott built the Loop-the-Loop at Coney Island. This ride used the modern teardrop-shaped loop and a steel structure, however more people wanted to watch the attraction, rather than ride. No more looping roller coasters were built until 1976 when Revolution opened at Six Flags Magic Mountain.*Wik

1966 Stephen Smale, University of California, Berkeley, received the Fields Medal at the International Congress of Mathematicians in Moscow for his work on dynamical systems. Ten days later on the steps of Moscow University he will make a speech condemning American
military activity in Vietnam and Soviet military involvement in Hungary. *VFR

1983 Poland issued a stamp celebrating the 50th anniversary of the Enigma Decoding Machine. VFR


1744 Pierre (-François-André) Méchain (16 Aug 1744; 20 Sep 1804). a French astronomer and hydrographer at the naval map archives in Paris recruited by Jean Delambre. He was a mathematical progidy. In 1790, they were chosen by the National Assembly to establish a decimal system of measurement based on the meter. Since this was defined to be one ten-millionth of the distance between the Earth's pole and the equator, Mechain led a survey of the meridian arc from Dunkirk, France, to Barcelona, Spain. Through his astronomical observations, Mechain discovered 11 comets and provided 26 additions to Messier's catalog. He calculated the orbits of the two comets he found in 1781. Mechain died of yellow fever while making further surveys for the meridian measurement. *TIS

1821 Arthur Cayley, (16 August 1821 – 26 January 1895) English mathematician who played a leading role in founding the modern British school of pure mathematics. He trained first as a lawyer, and from 1849, spent 14 years at the bar, during which time he maintained an interest in mathematics and published about 250 mathematical papers. In 1863, Cayley followed his passion and commenced a new career as professor of Pure Mathematics at Cambridge and during his tenure published 900 papers and notes covering nearly every aspect of modern mathematics. The legacy of his work in n-dimensional geometry was later applied in physics to the study of the space-time continuum. His work on matrices served as a foundation for quantum mechanics developed by Werner Heisenberg in 1925. *TIS

1836 Marc-Antoine Parseval des Chênes (April 27, 1755 – August 16, 1836) was a French mathematician, most famous for what is now known as Parseval's theorem, which presaged the unitarity of the Fourier transform.
He was nominated to the French Academy of Sciences five times, from 1796 to 1828, but was never elected. His only mathematical publications were, apparently, five papers, published in 1806 as Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.) This combined the following earlier monographs:
  1. "Mémoire sur la résolution des équations aux différences partielles linéaires du second ordre," (May 5, 1798).
  2. "Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficients constants," (April 5, 1799).
  3. "Intégration générale et complète des équations de la propagation du son, l'air étant considéré avec ses trois dimensions," (July 5, 1801).
  4. "Intégration générale et complète de deux équations importantes dans la mécanique des fluides," (August 16, 1803).
  5. "Méthode générale pour sommer, par le moyen des intégrales définies, la suite donnée par le théorème de M. Lagrange, au moyen de laquelle il trouve une valeur qui satisfait à une équation algébrique ou transcendante," (May 7, 1804).
It was in the second, 1799, memoir in which he stated, but did not prove (claiming it to be self-evident), the theorem that now bears his name. He further expanded upon it in his 1801 memoir, and used it to solve various differential equations. The theorem was first printed in 1800 as a part (p. 377) of Traité des différences et des séries by Lacroix.

1837 Joseph-Marie de Tilly,(16 Aug 1837 in Ypres, Belgium - 4 Aug 1906 in Munich, Germany) Belgian mathematician, born. In 1899 he was dismissed from his teaching post at the Ecole Militaire for unduly emphasizing the scientific education of future officers and using the notions of the infinitely small and the differential. *VFR

1845 Gabriel Lippman (16 Aug 1845; 13 Jul 1921).French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS

1905 Marian Adam Rejewski (16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in 1932 solved the plugboard-equipped Enigma machine, the main cipher device used by Germany. The success of Rejewski and his colleagues Jerzy Różycki and Henryk Zygalski jump-started British reading of Enigma in World War II; the intelligence so gained, code-named "Ultra", contributed, perhaps decisively, to the defeat of Nazi Germany.
While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff's Biuro Szyfrów (Cipher Bureau), which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using his "cyclometer," and the "cryptologic bomb."
Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the fall of France in June 1940, but within months returned to work undercover in Vichy France. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician Henryk Zygalski fled, via Spain, Portugal and Gibraltar, to Britain. There they worked at a Polish Army unit, solving low-level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967. *Wik

1907 Dura Kurep (16 Aug 1907, 2 Nov 1993)The topics which Kurepa investigated are very varied but lie mostly within topology, set theory and number theory. He published over 200 papers but this number rises to over 700 items if we include books, articles and reviews. He was fascinated by the continuum hypothesis and the axiom of choice. Perhaps best known is his work on trees and partitions, especially Aronszajn and Suslin trees. His book The Theory of Sets written in Serbo-Croatian and published in 1951 illustrates his interests in that particular area. After introducing the fundamental concepts and elementary operations in Chapter 1, he looks at cardinal numbers in the second chapter, then partially ordered sets and ordinal numbers in the third. Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.
In number theory he made many contributions, but perhaps his most famous is his open problem on the left factorial function. In 1971 he published his definition of !n, the left factorial function, defined by
!n = 0! + 1! + 2! + 3! + ... + (n-1)!.
Kurepa conjectured that the greatest common divisor of !n and n! was 2 for all n > 1. There are many equivalent forms of the conjecture, but one of the most natural was given by Kurepa in the same 1971 paper, namely that !n is not divisible by n for any n > 2. If the left factorial conjecture is false we certainly know that it will fail for n > 1000000.*SAU
The same left factorial notation is more commonly used for the subfactorial used in derangements. Many mathematicians simply use "factorial sum" for Kurepa's !n. It is interesting that no one seems to have picked up on the use of an inverted exclamation point as suggested by G. Chrystal in his "Algebra, an Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges", (1889 (pg 25))

1920 Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik


1705 Jakob Bernoulli . (27 December 1654 – 16 August 1705) He was so fascinated with the way the logarithmic spiral reproduces itself in its involute, its evolute, and its caustics of reflection and refraction, that he requested it be engraved on his tombstone, together with the inscription Eadem mutata resurgo (Though changed, I will arise the same). *VFR (the spiral on his tombstone is not logarithmic, but Archimedian... perhaps he is spinning in his grave even yet.)
 He 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.(a nice exercise to try) 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). He was the first of the Bernoulli family of mathematicians. *TIS
Jacob Bernoulli’s Ars Conjectandi from 1713 is the first major book on the theory of probability and statistics. It is because of its 300 years anniversary that 2013 was named the international year of Statistics. The exhibited copy is in fact a first edition! It is showing the proof of the law of large numbers, one of the results for which it is famous. * University of Copenhagen Dept of Math Sciences

1920 Sir Joseph Norman Lockyer (17 May 1836, 16 Aug 1920) British astronomer who in 1868 discovered and named the element helium that he found in the Sun's atmosphere before it had been detected on Earth. He also applied the name chromosphere for the sun's outer layer. Lockyer discovered, together with Pierre J. Janssen, the prominences (red flames) that surround the solar disk. He was also interested in the classification of stellar spectra and developed the meteoric hypothesis of stellar evolution. His works include the books Contributions to Solar Physics (1873), The Sun's Place in Nature (1897) and Inorganic Evolution (1900). *TIS

1995 Thomas Brooke Benjamin​, FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations. *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

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