## Friday 3 October 2014

### On This Day in Math - October 3

Nature to him (Newton) was an open book, whose letters he could read without effort.
~Albert Einstein

The 276th day of the year; 276 is the sum of twelve consecutive prime numbers (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43). And from the trivia file, 276 is the number of rounds of the longest boxing match in history. Jack Jones beat Pat Tunney in a bare-knuckle fight in 1825 after 4 1/2 hours.
If we let S(n) = the sum of the proper divisors of n (so S(8) = 1 + 2 + 4 = 7)  and make a chain S(n1)  n2 and s(n2) = n3... eventually you get back to a number you already had.  Some numbers  (called perfect numbers) do so immediately. Others form chains of 2 (sociable numbers) or 4 (the most common) or more, but every number will loop back........ almost.  It seems 276 is a maverick and just keeps getting bigger all the time.... No other number is known that does not form a chain.

EVENTS

1533 The mathematical mystic Michael Stifel predicted that on this date a chariot would touch down on a nearby hilltop and conduct him and his followers to heaven. His followers quit their jobs, but as the day approached they became sceptical. Stifel convinced the local constabulary to lock him in jail on the appointed date where he would be safe from his ruined, irate parishioners. *Journal of Recreational Mathematics 6 (1973), pp. 221–223,
A comment by Hans Havermann has pointed out that the Oct 3 date is still subject to debate. The (online) Complete Dictionary of Scientific Biography suggests Oct 18, but also suggest the correct date might be Oct 16 or Oct 19. Der Biograph, p. 473, mentions the 282nd day and the 42nd week of the year."﻿ which would be yet another date. (so maybe at least the month is right)

1842 Arthur Cayley admitted to fellowship at Trinity College Cambridge, at age 21—younger than any other fellow at the College.*VFR

1846 Sir John Herschel published John Couch Adams’s prediction that a new planet (now called Neptune) existed and where to look for it. This provoked a priority controversy as the planet had already been found 23 September 1846 based on Leverrier’s calculations. *VFR

1896 Einstein graduates from high school in Switzerland at the age of 17. In contrast to the commonly held belief that he was a poor student, his marks are very good, with top scores (6) in all the math and physics courses and fives in most of the others. His lowest mark was in French, but he also took German and Italian; and years later on a visit to Jeruselum he gave a lecture in fluent French. *Einstein Gallery
Einstein said "I never failed in mathematics... Before I was fifteen I had mastered differential and integral calculus.

1950 Transistor Inventors Receive Patent. The U.S. Patent Office issued a patent to John Bardeen, Walter Brattain, and William Shockley for the transistor. The three AT&T Bell Laboratories researchers had successfully tested the first of their devices two years earlier. The transistor started a revolution in computer engineering that led to the development of the semiconductors, microprocessors, and integrated circuits common in modern computers. *CHM

In 1967, the X-15 rocket plane achieved a world record speed of Mach 6.7, which is 4,520 mph or over a mile per second, with U.S. Air Force pilot Pete Knight. It reached an altitude of 192,100 feet (58,552 m). Its internal structure of titanium was covered with a skin of Inconel X, a chrome-nickel alloy. To save fuel, the X-15 was air launched from a B-52 aircraft at about 45,000 ft. Test flights between 8 Jun 1959 and 24 Oct 1968 provided data on hypersonic air flow, aerodynamic heating, control and stability at hypersonic speeds and piloting techniques for reentry used in the development of the Mercury, Gemini, and Apollo spaceflight programs. The X-15 reached 354,200 feet (67 miles) on 22 Aug 1963. *TIS

2011 Scientists from Nottingham, England, officially broke the Guinness World Record for writing the world’s smallest periodic table — engraving it on a single strand of hair.
The scientists from the University of Nottingham’s Nanotechnology and Nanoscience Center placed the table of elements on the hair of Martyn Poliakoff, a chemistry professor, using a beam of accelerated gallium ions. It’s so small that a million tables of the same size could fit on a typical Post-it note.
The hair was presented to the Professor as a birthday gift.
Guinness confirmed that it was the smallest periodic table in existence. *ABC

BIRTHS

1830 George Bailey Brayton (3 Oct 1830; 17 Dec 1892) was an American engineer who invented the first commercial gas internal combustion engine (patented 2 Apr 1872), which he manufactured and sold in the Providence, Rhode Island, area. Its principle of continuous ignition later became the basis for the turbine engine. A pressurized air-fuel mixture from a reservoir was ignited upon entering a water-cooled cylinder. The Brayton engine was given trials powering watercraft, one of John Holland's submarines and one used for a few months installed in a carriage (1872-3). His earlier career included developing steam engines.*TIS

1863 Stanisław Zaremba (October 3, 1863 – November 23, 1942) was a Polish mathematician. His research in differential equations, applied mathematics, classical analysis, particularly on harmonic analysis, was widely recognized. He was a mathematician who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Zaremba wrote a number of university textbooks and monographies.
He was a professor of the Jagiellonian University (since 1900), member of Academy of Learning (since 1903), co-founder and president of the Polish Mathematical Society (1919).*Wik

1944 Pierre René Deligne(3 Oct 1944, ) Belgian mathematician who was awarded the Fields Medal at the International Congress of Mathematicians in Helsinki, Finland, in 1978 for his work in algebraic geometry. His work originated with André Weil's ideas on polynomial equations which led to three questions on what properties of a geometric object can be determined purely algebraically. These three problems quickly became major research challenges to mathematicians. A solution of the three Weil conjectures was given by Deligne. This work brought together algebraic geometry and algebraic number theory. The solution to these problems had required the development of a new kind of algebraic topology. *TIS

DEATHS

1891 François Edouard Anatole Lucas (4 April 1842, 3 Oct 1891)    Lucas is best known (to formal mathematicaticians) for his results in number theory: in particular he studied the Fibonacci sequence and the associated Lucas sequence is named after him. He gave the well-known formula for the Fibonacci numbers
√5 fn = ((1 + √5)/2)n - ((1 - √5)/2)n.
Lucas also devised methods of testing primality, essentially those used today. In 1876 he used his methods to prove that the Mersenne number 2127 - 1 is prime. This remains the largest prime number discovered without the aid of a computer.   (For recreational mathematicians), Lucas is also well known for his invention of the puzzle and other mathematical recreations. The Tower of Hanoi puzzle appeared in 1883 under the name of M. Claus. Notice that Claus is an anagram of Lucas! His four volume work on recreational mathematics Récréations mathématiques (1882-94) has become a classic.*SAU  Lucas is also remembered for his unusual death, caused by a waiter dropping a plate which shattered sending a piece of plate into his neck. Lucas died several days later from a deadly inflamation of the skin and subcutaneous tissue caused by streptococcus. The disease, officially listed as erysipelas (from the Greek for "red skin") was more commonly known as "Saint Anthony's Fire". *Pballew.net

1914 René Eugène Gateaux (5 May 1889 - 3 October 1914), was a French mathematician. He is known for the Gâteaux derivative. Part of his work has been posthumously published by Paul Lévy. Gâteaux was killed during World War I. *Wik

1932 Maximilian Franz Joseph Cornelius Wolf (21 Jun 1863, 3 Oct 1932) was a German astronomer who founded and directed the Königstuhl Observatory. He used wide-field photography to study the Milky Way and used statistical treatment of star counts to prove the existence of clouds of dark matter. He was among the first astronomers to show that the spiral nebulae have absorption spectra typical of stars and thus differ from gaseous nebulae. His most important contribution was the introduction of photography to discover hundreds of asteroids, the first of which he named Brucia in honor of the donor of his 16-inch double telescope, Catherine Wolfe Bruce. *TIS

1951 William Leslie Thomson studied at Edinburgh and Cambridge. He taught at Kirkwall, at Kilmarnock and at George Heriot's School in Edinburgh. He became President of the EMS in 1904. *SAU

2006 John Crank (6 February 1916 – 3 October 2006) was a mathematical physicist, best known for his work on the numerical solution of partial differential equations.
He worked on ballistics during the Second World War, and was then a mathematical physicist at Courtaulds Fundamental Research Laboratory from 1945 to 1957. In 1957, he was appointed as the first Head of Department of Mathematics at Brunel College in Acton. He served two terms of office as Vice-Principal of Brunel before his retirement in 1981, when he was granted the title of Professor Emeritus.
Crank's main work was on the numerical solution of partial differential equations and, in particular, the solution of heat-conduction problems. He is best known for his work with Phyllis Nicolson on the heat equation, which resulted in the Crank–Nicolson method.*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