Saturday, 2 June 2018

On This Day in Math - June 2


"See if you can use this proof to show the square root of three is irrational. Then try the square root of four. 
If it works, you did something wrong." 
~ Jim Wisemant, *Quotes from Honors Linear Algebra

The 153rd day of the year. 153 is the fixed point attractor of any multiple of three under the process of summing the cubes of the digits. For more detail and explanation see,"The Cubic Attractiveness of 153" ,
 13+53 + 33 = 153. Numbers which are the sum of their own digits raised to the power of the number of digits are called Armstrong numbers. Except for the trivial one digit numbers, it is also the smallest. There are only three other numbers greater than one which are the sum of the cubes of their digits (Go fourth and seek them. hint: this is the only one which is a year date) This makes 153 a narcissistic or Armstrong number. There are 89 narcissistic numbers in base 10, but only 11 in base 4.
And to extend that, the amazing Cliff Pickover shared this:(although the digits are taken in sets)

ALSO, 153 = 1! + 2! + 3! +4! +5!, *Jim Wilder@wilderlab

I had never observed that 153 = 3 x 51, a product that uses all the digits of the number.  HT to INDER J. TANEJA @IJTANEJA There are no numbers below 1000 that have the same digits as their prime factorization in a simple product (no powers) but there is one lingering just above that number, can you find it?


1661 An eager Isaac Newton departs his farm home at Woolsthorpe for Trinity College, Cambridge, although the term would not begin until September. He would remain at Trinity for thirty-five years. He took almost nothing with him. *Thomas Levenson, Newton and The Counterfeiter

1666 John Wallis writes to Oldenburg at the Royal Society on the topic of tides.  "Wallis adopts Galileo’s technique of explaining the tides through the motions of the earth, focusing on a third tidal cycle that Galileo’s theory did not adequately explain: the “menstrual” (i.e., monthly) cycle in which the tides change in accordance with the position of the moon. Wallis argues that the earth and moon revolve once a month around a common centre of gravity, and it is this point that revolves around the sun. The earth is therefore on a small epicycle with a period of one month, and this additional motion affects the timing and level of the tides. " (From PhD thesis of Adam D Richter, with my thanks). This was well before the universal reach of gravity was understood or accepted.  Wallis gives a very mathematical response to inquiries about how he explains this "action at a distance." Wallis maintain that "his goal as a natural philosopher is to recognize phenomena and describe them mathematically, rather than to explain their underlying physical causes. " (A. Richter). 
In addition, he points out that his approach is widely supported by Natural Philosophers acceptance of action at a distance in magnets.

In 1686, the publication of Newton's Principia was arranged in London at the Royal Society. The minutes of the meeting record that the astronomer Edmund Halley would "undertake the business of looking after it and printing it at his own charge."

1692 – Bridget Bishop is the first person to go to trial in the Salem witch trials in Salem, Massachusetts. Found guilty, she is hanged on June 10.

In 1858, the Donati Comet was first seen and named after its discoverer, Giovanni Battista Donati, at Florence. It was the second-brightest comet of the nineteenth century It reached perihelion on 30 Sep 1858. When nearest the earth on 9 Oct 1858, it was about 0.5 AU away, and had developed a scimitar-shaped triple tail. At that time, its very prominent dust tail had with an apparent length of 50°, more than half the distance from the horizon to the zenith, a linear distance of over 72 million km (about 45 million mi). It was the first comet to be photographed. With an orbital period estimated at more than 2000 years, it will not return until about the year 4000. An astronomical unit, AU, equals 93 million miles, the Sun-Earth distance.

1913 Millikan announced the results of his experiment to measure the electron charge. *VFR

1924 – U.S. President Calvin Coolidge signs the Indian Citizenship Act into law, granting citizenship to all Native Americans born within the territorial limits of the United States.

1925 – Because of a lineup revision by Miller Huggins, Wally Pipp is replaced by Lou Gehrig at first base for the New York Yankees, beginning a streak of 2,130 consecutive games played, topped only by Cal Ripken, Jr. in 1995. Exactly 16 years later to the day, in 1941, Gehrig dies from Amyotropic lateral sclerosis (ALS).

1963 Between May 11 and June 2, Donald B. Gillies found three new primes. When the primes were confirmed the UIUC Math dept (which has a postal branch) used this cancellation stamp on all mail from roughly 1964 - 1976, when Appel and Haken proved the four color theorem ("Four Colors Suffice") and a new stamp was created. Trivia question : how far away from Gillies did Appel live in Urbana Illinois ??
Answer : He lived 3 houses away. *Wik
*Wik courtesy of Chris Caldwell

1966 Surveyor 1 Makes soft-landing on the moon. It was the first lunar soft-lander in the unmanned Surveyor program of the National Aeronautics and Space Administration (NASA, United States). It gathered data about the lunar surface that would be needed for the manned Apollo Moon landings that began in 1969. The successful soft landing of Surveyor 1 on the Ocean of Storms was the first by an American space probe onto any extraterrestrial body, and it occurred just four months after the first Moon landing by the Soviet Union's Luna 9 probe.

Surveyor 1 was launched May 30, 1966 and landed on the Moon on June 2, 1966. It transmitted 11,237 still photos of the lunar surface to the Earth by using a television camera and a sophisticated radio-telemetry system. *Wik


1884  Henry Thomas Herbert Piaggio(2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.

1895 Tibor Radó (June 2, 1895 – December 29, 1965) was a Hungarian mathematician who moved to the USA after World War I. He was born in Budapest and between 1913 and 1915 attended the Polytechnic Institute. In World War I, he became a First Lieutenant in the Hungarian Army and was captured on the Russian Front. He escaped from a Siberian prisoner camp and, traveling thousands of miles across Arctic wasteland, managed to return to Hungary.
He received a doctorate from the University of Szeged in 1923. He taught briefly at the university and then became a research fellow in Germany for the Rockefeller Foundation. In 1929, he moved to the United States and lectured at Harvard University and the Rice Institute before obtaining a faculty position in the Department of Mathematics at Ohio State University in 1930. In 1935 he was granted American citizenship.
In the 1920s, he proved that surfaces have an essentially unique triangulation.
In 1933, Radó published "On the Problem of Plateau" in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions".
In World War II he was science consultant to the United States government, interrupting his academic career.
He became Chairman of the Department of Mathematics at Ohio State University in 1948.
His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the Busy Beaver function and its non-computability ("On Non-Computable Functions").
In computability theory, a busy beaver (from the colloquial expression for an "industrious person") is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape. *Wik

1916 Abraham Seidenbergwas  (June 2, 1916 – May 3, 1988)  known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik


1785 Jean Paul de Gua de Malves, (1713, Carcassonne – June 2, 1785, Paris) In 1740 he published a work on analytic geometry which, without the differential calculus, he found tangents, asymptotes, and various singular points of an algebraic function. He gave the proof of Descartes rule of signs which is found in modern texts. It is not known if Descartes ever proved it, and Newton seemed to think it was "obvious". (A short account of the history of mathematics By Walter William Rouse Ball)

1917 William Henry Besant FRS (1 November 1828, Portsea, Portsmouth – 2 June 1917, Cambridge) was a British mathematician, brother of novelist Walter Besant.
In a competition, William won a scholarship to Corpus Christi College, Cambridge in 1844. He took part in Cambridge Mathematical Tripos in 1850, gaining the title of Senior Wrangler. He was also winner of Smith's Prize.
In 1853 William became a Fellow of Saint John's College, Cambridge where he was a lecturer in mathematics until 1889. His pupils included William Burnside, A. W. Flux and G. B. Mathews. Besant served as an examiner for Tripos in 1856, 1857, and 1885. He was also an examiner for University of London from 1859 to 1864. Besant was also a coach for students taking the Tripos; twenty-one of his students placed in the ranks of top ten wranglers. According to Mathews, "he had the great advantage (for a coach) of being equally good in geometry, analysis, and dynamics."
In 1859 Besant vacated his Fellowship with Saint John's college to marry Margaret Elizabeth Willis, daughter of Rev. Robert Willis, a professor of natural philosophy at Cambridge. They had two sons and a daughter. In 1863 Besant published Elementary Hydrostatics, a textbook on fluid statics containing mathematical exercises such as students might face in examination. The book was reprinted several times, and revised in 1892. He also wrote Treatise on Hydromechanics (1867) covering fluid mechanics. His book Elementary Conics came out in 1901.
Besant was a Fellow of the Royal Astronomical Society from 10 February 1854. He became a Fellow of the Royal Society in 1871. In 1883 Cambridge University bestowed upon him, and Edward Routh, the degree Sc.D.. He died on 2 June 1917 and is buried at the Parish of the Ascension Burial Ground in Cambridge.

He created the term Glissettes for his studies on the objects for Notes on Roulettes and Glissettes(1871). He writes in the preface:

1929 Otto Schreier (3 March 1901 in Vienna, Austria - 2 June 1929 in Hamburg, Germany) He will be best remembered for his work on subgroups of free groups which he studied in his habilitation thesis. He published the results in 1927 in the paper Die Untergruppen der freien Gruppe which is described as "... one of the most important papers ever published on combinatorial group theory. It took a long time for all its aspects to become effective, and it contains much more than the title indicates. "
In January 1926 Schreier attended a lecture given by Reidemeister in Hamburg on finding presentations for normal subgroups of finitely presented groups. Reidemeister published his method later in 1926. Schreier, who took a more algebraic approach compared to Reidemeister's geometrical approach, was able to extend Reidemeister's method to arbitrary subgroups and, by cleverly choosing generators for the subgroup, was able to greatly simplify the presentation obtained. Schreier published his method in his 1927 paper Die Untergruppen der freien Gruppe.
Other work of Schreier is described as follows:
... Schreier made important contributions to other parts of group theory. The classical Lie groups ... can be considered as topological spaces. Schreier (1927) showed that the fundamental group of such a space is always abelian. Schreier (1928) found an important refinement of the fundamental Jordan-Hölder theorem, 39 years after the publication of Hölder's paper. It is rare that such a widely used and basic theorem can be deepened after such a long time. (In this case, something even more unusual happened. Zassenhaus (1934) discovered a second improvement of the theorem.)

1942 Andrew Russell Forsyth (18 June 1858, Glasgow – 2 June 1942, South Kensington)   was a Scottish mathematician. He worked in differential equations, and function theory.
He studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881.[1] He was elected a fellow of Trinity and then appointed to the chair of mathematics at the University of Liverpool at the age of 24. He returned to Cambridge as a lecturer in 1884 and became Sadleirian Professor of Pure Mathematics in 1895. He resigned his chair in 1910 after an affair with Marion Amelia Boys, the wife of C. V. Boys, who divorced her husband to marry him: this was unacceptable in Edwardian Cambridge. He became professor at the Imperial College of Science in 1913 and retired in 1923, remaining mathematically active into his seventies. He was elected a Fellow of the Royal Society in 1886 and won its Royal Medal in 1897.
He is now remembered much more as an author of treatises, than as an original researcher. His books have, however, often been criticized (for example by J. E. Littlewood, in his Mathematician's Miscellany). E. T. Whittaker was his only official student, according to the Mathematical Genealogy site. *Wik

1946 William Peddie (31 May 1861 in Papa Westray, Orkney, Scotland - 2 June 1946 in Ninewells, Dundee, Scotland) graduated from Edinburgh University and then lectured in Physics. He was appointed Professor of Physics at Queen's College Dundee and held this post for 37 years. He was a founder member of the EMS and became President in 1895 and 1932. *SAU

*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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