Wednesday, 9 November 2016

On This Day in Math - November 9

Our passion for learning is our tool for survival.
~Carl Sagan

The 314th day of the year; 314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways. *What's Special about this number
(Students, can you find the smallest number that can be written as the sum of two distinct squares in at least two ways?)

314 is a semi-prime, and 3142 +1 is prime


1572 - In 1572 a stellar nova became visible from the earth. Cornelius Gemma, the son of Gemma Frisius, made the first recorded observation of it on 9 November. Tycho Brahe first saw it on 11 November. Cornelius, Tycho, and others all observed the nova and determined it to be superlunary, thereby signalling a change in the superlunar sphere contradicting Aristotelian cosmology. *RMAT

1752 William Braikenridge, British mathematician and theologian, elected to the Royal Society. He was mainly interested in plane curves. Braikenridge is well known for his geometrical theorems, in particular he discovered the following theorem now called the Braikenridge - Maclaurin theorem:
"If the sides of a polygon are restricted so that they pass through fixed points and all the vertices except one lie on fixed straight lines, the free vertex will describe a conic or a straight line."
A priority dispute between the two over this and several other theorems was probably unnecessary as it appears that both came to the solutions independently. *SAU

1769 Benjamin Franklin observes a transit of Mercury at Norriton, Pennsylvania in the distinguished company of William Smith, D. D. Provost of the College of Philadelphia (later the Univ of Pennsylvania); John Lukens Esq; Surveyor General of Pennsylvania; David Rittenhouse (astronomer, inventor, clockmaker, mathematician, surveyor, scientific instrument craftsman and Friend of Jefferson), M. A. and Mr. Owen Biddle. Franklin, as President of the Philosophical Society at Philadelphia would communicate the results to the Royal Society in London.

1862 ? A clipping in Charles Dodgson's (Lewis Carroll) scrapbook of a letter to the editor of the Star newspaper contains a 'solution' to the problem of squaring the circle which, in the writer's words, " will not admit of the terms ordinarily used, 'approximated,' or 'nearly." The writer has found the square root of pi accurately to 26 decimal places,which is no minor feat. Dodgson seems, unlike many mathematicians then or now, to have spent a great amount of energy trying to explain to circle-squarers where they had erred.

1957 France issued the world’s first postage stamp with a portrait of Newton. [Scott #861]. *VFR By 1977 his picture had appeared on stamps from Poland, Benin, Hungary, Mali and Monaco.

1957 On 9 Nov 1957, during a sleepless Saturday night, Gordon Gould had the inventor's inspiration and began to write down the principles of what he called a laser (from the initial letters of "Light Amplification by Stimulated Emission of Radiation.") in his notebook. Although Charles Townes and Arthur Schawlow, also successfully developed the laser, eventually Gould gained his long-denied patent rights. *TIS

In 1965, the biggest electricity grid failure in U.S. history caused a 13-hour blackout in northeast America and parts of Canada. The power lines from Niagara Falls to New York City were operating near their maximum capacity. At about 5:15 pm, a transmission line relay failed. Now there was insufficient line capacity for New York City. New England and New York are inter-connected on a power grid, and the power that had been flowing toward New York City had to go elsewhere, instantly. Unable to handle this overload, generator operators shut down to protect their equipment. Almost the entire grid failed, affecting 80,000 square miles, and 25 million people. In the subways of New York, 800,000 people were trapped. *TIS

2004 Firefox 1.0 Introduced. Sometimes abbreviated as FF, Firefox was Mozilla's next generation browser and included such features as tabbed browsing and popup blocking. Mozilla Firefox became a popular alternative for Microsoft Internet Explorer (IE) users who sought alternatives that could prevent spyware as well as a host of other Firefox features.*CHM


1806 Benjamin Banneker (9 Nov 1731; 9 Oct 1806) Black-American astronomer, inventor and mathematician, compiler of almanacs and one of the first important black American intellectuals who was the self-educated son of a freed slave. He was the first to record the arrival of the "seventeen-year locusts" or periodical cicadas. In 1753, Banneker built a wooden clock that kept accurate time even though he had only previously seen a sundial and a pocket watch. He calculated the clock's gear ratios and carved them with a pocket knife. In 1789, he successfully predicted an eclipse. He helped survey the site of Washington D.C. (1791-3). Banneker was also an early antislavery publicist who worked to improve the lot of black people in the U.S *TIS

1847 Carlo Alberto Castigliano (9 November 1847, Asti – 25 October 1884, Milan) was an Italian mathematician and physicist known for Castigliano's method for determining displacements in a linear-elastic system based on the partial derivatives of strain energy. *Wik

1869 Virgil Snyder (9 Nov 1869 in Dixon, Iowa, USA 4 Jan 1950 in Ithaca, New York, USA ) Up until the 1920s, Snyder's prolific output and his talents as a teacher made him, together with Frank Morley of Johns Hopkins, one of the most influential algebraic geometers in the nation. Together with Henry White, in fact, Snyder emerged as a principal heir to Klein's geometric legacy. *SAU

1885 Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory. *Wik

1885 Hermann Weyl (9 Nov 1885; 8 Dec 1955) German-American mathematician whose widely varied contributions in mathematics linked pure mathematics and theoretical physics. He made significant contributions to quantum mechanics and the theory of relativity. He attempted to incorporate electromagnetism into the geometric formalism of general relativity. Weyl published Die Idee der Riemannschen Fläche (1913) which united analysis, geometry and topology. He produced the first gauge theory in which the Maxwell electromagnetic field and the gravitational field appear as geometrical properties of space-time. He evolved (1923-38) the concept of continuous groups using matrix representations. Applying group theory to quantum mechanics he set up the modern subject. *TIS

1905 Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was an American mathematician. In 1939, he received the first American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices. He is best known for his work on the Albert–Brauer–Hasse–Noether theorem on finite-dimensional division algebras over number fields and as the developer of Albert algebras, which are also known as exceptional Jordan algebras. *Wik

1906 Yaroslav Borisovich Lopatynsky (9 Nov 1906 in Tbilisi, Georgia, Russia - 10 March 1981 in Donetsk, USSR) Lopatynsky's contributions to the theory of differential equations are particularly important, with important contributions to the theory of linear and nonlinear partial differential equations. He worked on the general theory of boundary value problems for linear systems of partial differential equations of elliptic type, finding general methods of solving boundary value problems. *SAU

1934 Carl Sagan (9 Nov 1934; 20 Dec 1996) U.S. astronomer and exobiologist and writer of popular science books. His studies were far-ranging. He coauthored a scientific paper about the dangers of nuclear winter. He researched the atmosphere of Venus, seasonal changes on Mars, surface conditions on planets, and created popular interest in the universe with his television series Cosmos. Sagan was a leading figure in the search for extraterrestrial intelligence. He urged the scientific community to listen with large radio telescopes for signals from intelligent extraterrestrial lifeforms. Sagan also played a prominent role in the U.S. space program, with his involvement in the Mariner, Viking, and Voyager spacecraft expeditions. *TIS (and now he is truly "star stuff")

1922 Imre Lakatos (November 9, 1922 – February 2, 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes. Lakatos' philosophy of mathematics was inspired by both Hegel's and Marx' dialectic, by Karl Popper's theory of knowledge, and by the work of mathematician George Polya.
The 1976 book Proofs and Refutations is based on the first three chapters of his four chapter 1961 doctoral thesis Essays in the logic of mathematical discovery. But its first chapter is Lakatos’s own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963-4 in The British Journal for the Philosophy of Science. It is largely taken up by a fictional dialogue set in a mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties of polyhedra, namely that for all polyhedra the number of their (V)ertices minus the number of their (E)dges plus the number of their (F)aces is 2: (V – E + F = 2). The dialogue is meant to represent the actual series of attempted proofs which mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Often the students 'quote' famous mathematicians such as Cauchy.
What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. *Wik


1830 Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer at the turn of the 18th and 19th centuries.
Born in Żnin, Śniadecki studied at Kraków University and in Paris. He was rector of the Imperial University of Vilnius, a member of the Commission of National Education, and director of astronomical observatories at Kraków and Vilnius. He died at Jašiūnai Manor near Vilnius.
Śniadecki published many works, including his observations on recently discovered planetoids. His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability. *Wik He is considered as the best Polish mathematician born in the 18th century.

1954 Frederick Francis Percival Bisacre (20 June 1885 in Tonbridge, Kent, England
- 9 Nov 1954 in Helensburgh, Scotland) was an engineer who was educated at Cambridge and worked for the Edinburgh publishers Blackie with whom he published a Calculus textbook. He wrote some research papers on X-ray diffraction. *SAU

1966 Daniel Edwin Rutherford (4 July 1906 in Stirling, Scotland - 9 Nov 1966 in St Andrews, Fife, Scotland) studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *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

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