Friday, 12 February 2016

On This Day in Math - February 12

Nature, when left to universal laws, tends to produce regularity out of chaos.
~Immanuel Kant

The 43rd day of the year; 43 is the number of seven-ominoids. (shapes made with seven equilateral triangles sharing a common edge.)

In March of 1950, Claude Shannon calculated that there are appx $\frac{64!}{32!} (8!)2(2!)6}$, or roughly 1043 possible positions in a chess match.

Planck time (~ 10-43 seconds) is the smallest measurement of time within the framework of classical mechanics. That means that if you could make one unique chess position in each Planck time, you could run through them all in one second.

What is the minimum number of guests that must be invited to a party so that there are either five mutual acquaintances, or five that are mutual strangers? (Sorry we still don't know :-{ But the smallest number must be 43 or larger). I think that means that for any number of points on a circle less than 43, if you colored every segment connecting two of them either red or black, there would be no complete graph of five vertices (K(5)) with all edges of the same color. [And there are 43 choose 5 or 962,598 possible choices of complete graphs to choose from.]

According to Benford's Law, the odds that a random prime begins with a prime digit is more than 43%

And if 42 was the meaning of life, the universe, and everything, just imagine that 43 is MORE than that!

EVENTS
1535 During the night of February 12–13 Tartaglia discovered a method of solving cubic equations that enables him to beat Fiore in a contest. [B. L. van der Waerden in the ﬁlm, “The Great Art: Solving Equations”] *VFR

1824 Goethe praises Lagrange in a conversation with Eckermann: “He was a good man and great for just that reason. For when a good man is gifted with talent, he will always exert a morally positive inﬂuence as an artist, a scientist, a poet, or whatever else it may be.” [J. P. Eckermann, Conversations with Goethe] *VFR

1826 Lobachevsky delivered a paper before the mathematics and physics departments of Kazan University on his “imaginary geometry.” He died on this same date in Kazan in 1856. *H. E. Wolfe. Introduction to Non-Euclidean Geometry, p. 53–56;

1831  A solar eclipse was visible across much of the United States.  For the event, the earliest known map of a solar eclipse printed in the US appeared in The American Almanac of Useful Information for the year 1831. *eclipsemaps.com

1858 George G Stokes writes to Faraday to request a "Laide's ticket" for Faraday's lecture that evening as his wife wishes to accompany him. *Correspondence of Michael Faraday.

In 1878, Frederick W. Thayer, former captain (76 and 77),of the Harvard University Baseball Club, patented the now familiar, baseball catcher's mask. *TIS "In the winter of '76 and '77 the candidates for the Harvard nine were practicing as usual in the old round gymnasium, and Captain Fred Thayer was training them. Harold Ernst, the greatest pitcher the Harvard nine ever had until Nichols made his debut, was to do the pitching, and Jim Tyng was expected to catch him. Although straight arm pitching was still in vogue (I assume this means similar to cricket, but without bouncing the ball), Ernst had a remarkable swift delivery, and after awhile Tyng informed Captain Thayer that he would not catch such pitching unless he could have some contrivance to protect his face. . . . Various experiments were tried, and finally he [Thayer] completed a rude but satisfactory protection for Tyng's phvsiognomy." Thayer received a patent for his invention early in 1878. Later in the year, A. G. Spalding and Brothers Company, the leading American sporting goods dealer, began selling the Thayer Catcher's Mask for \$3. In 1883 Thayer sued Spalding for patent infringement, and Spalding was ultimately forced to pay royalties. *Nebraska State Historical Society.

In 1898 the first car crash resulting in a fatality happened to Henry Lindfield whose electric car's steering gear failed, and he crashed at the bottom of a hill at Purley Corner, Surrey. He was a Brighton business agent for International Cars, on his way to London. The car eventually turned completely round, ran through a wire fence and hit an iron post. The main artery in his leg was cut. Surgeons at Croydon hospital amputated the limb, but he died of shock from the operation the following day. A verdict of accidental death was returned. His passenger, 18 or 19 year-old son Bernard, was thrown clear of the vehicle and escaped almost unhurt. The first pedestrian fatally struck by a car died on 17 Aug 1896. The first petrol-fuelled fatal car crash happened on 25 Feb1899.*TIS I was informed by a comment from Luke Drury that, "Mary Ward (27 April 1827 – 31 August 1869) was an Anglo Irish amateur scientist who was killed when she fell under the wheels of an experimental steam car built by her cousins. As the event occurred in 1869, she is the world's first known fatal motor vehicle accident victim." *Wik

In 1935, a patent was issued to Robert Jemison Van de Graaff for his Electrostatic Generator design (U.S. No. 1,991,236), able to generate direct-current voltages much higher than the 700,000-V which was the state of the art at the time using other methods. It consisted of two large, hollow approximately spherical metal domes on insulated columns. A silk belt ran on rollers between the base of the column to the interior of the dome. Charges from a 5000-V source are transferred to the belt near the lower roller, carried upward and are collected by a metal comb connected to the dome interior. By nature, rather than accumulating on the interior, the charges move to the exterior of the dome. Two such domes with opposite charges could generate a potential difference of 1,500,000-V between them. *TIS

1935 Robert Watson-Watt submitted the idea for Radar to the Air Ministry in a secret memo, "Detection and location of aircraft by radio methods" . The method would be tested on Feb 26 in a field just off the present day A5 in Northamptonshire near the village of Upper Stowe. Watson-Watt received a patent on his device on April 2.
In strange turn of technology Karma, Watson-Watt reportedly was pulled over for speeding in Canada many years later  by a radar gun-toting policeman. His remark was, "Had I known what you were going to do with it I would never have invented it!"*Wik

In 1973  four metric distance road signs, the first in the U.S., were erected along Interstate 71 in Ohio. They showed the distance in both miles and kilometers between Columbus and Cincinnati, and Columbus and Cleveland. As early as 1790, Thomas Jefferson proposed a decimal measurement system, similar to the metric system. In 1968 a study was ordered by Congress. By 1971, a report recommended a switch to the metric system and established a 10-year target time to accomplish it. This led to a National Metric Conference in 1973, which prompted Ohio to display metric highway signs. The Metric Conversion Act (1975) planned a voluntary conversion to the metric system, which produced little voluntary action. *TIS Does someone in the Columbus Area (or anywhere else in US) know if there are still metric distances posted in the area? would appreciate current picture.
I found a web site at Colorado State Univ which shows metric signs on I-19 between Tucson and Nogales, AZ(below) and a few more near Louisville, Ky on exit signs in both miles and Km.  And now I hear NY state has a plethora of metric signs.  Ahh, America you are coming of age.

1977 Rotenberg Founds The Boston Computer Society:
Young computing enthusiast Jonathan Rotenberg founds the Boston Computer Society. Four people attended the first meeting of this group, whose membership eventually reached several thousand. Early topics of discussion for the society included Community Use of Personal Computers and The Minicomputer Goes to the Racetrack.*CHM

2009 Royal Mail issues a stamp set and commemorative coin in honor of the 200th anniversary of the birth of Charles Darwin.*VFR

BIRTHS
1637 Jan Swammerdam (February 12, 1637, Amsterdam – February 17, 1680) was a Dutch biologist and microscopist. His work on insects demonstrated that the various phases during the life of an insect—egg, larva, pupa, and adult—are different forms of the same animal. As part of his anatomical research, he carried out experiments on muscle contraction. In 1658, he was the first to observe and describe red blood cells. He was one of the first people to use the microscope in dissections, and his techniques remained useful for hundreds of years.*Wik

1685 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church.

1791 Peter Cooper (12 Feb 1791; 4 Apr 1883 at age 92) American inventor, manufacturer and philanthropist who established The Cooper Union for the Advancement of Science and Art in New York (cornerstone laid in 1854) to provide free technical education of the working class. He invented the first American-built steam locomotive for a common-carrier railway, the Tom Thumb, which made its first run on 28 Aug 1830. His iron-rolling mill produced iron structural beams, included those used to build the Cooper Union, which he wanted to be fire-proof. After founding a telegraph company (1854), he joined Cyrus Field's effort to lay the first tranatlantic cable (1857). Cooper lived to the age of 92, and for his life of philanthropy in New York, the city mourned his passing as one of its most-loved citizens. *TIS

1856 Arnold Droz-Farny (12 Feb 1856 in La Chaux-de-Fonds, Switzerland - 14 Jan 1912 in Porrentruy, Switzerland) Droz-Farny is best known for results published in the publications of 1899 and 1901 mentioned in this quote. The first of these was Question 14111 in The Educational Times 71 (1899), 89-90. In this he stated the following remarkable theorem without giving a proof:
If two perpendicular straight lines are drawn through the orthocentre of a triangle, they intercept a segment on each of the sidelines. The midpoints of these three segments are collinear.
This is known as the Droz-Farny line theorem, but it is not known whether Droz-Farny had a proof of the theorem. Looking at other work by Droz-Farny, one is led to conjecture that indeed he would have constructed a proof of the theorem. The 1901 paper we mentioned above is, for example, one in which he gives a proof of a theorem stated by Steiner without proof. Droz-Farny's proof appears in the paper Notes sur un théorème de Steiner in Mathesis 21 (1901), 268-271. The theorem is as follows:
If equal circles are drawn on the vertices of a triangle they cut the lines joining the midpoints of the triangle in six points. These six points lie on a circle whose centre is the orthocentre of the triangle.
Droz-Farny died "a long and painful disease".

1870 Horatio Carslaw (12 Feb 1870 - 11 Nov 1954)studied at Glasgow and Cambridge. He lectured at the University of Glasgow before moving to a professorship in Sydney, Australia. He worked on a variety of topics in both pure and applied mathematics. *SAU

1874 Harold Stanley Ruse (12 Feb 1905 in Hastings, England - 20 Oct 1974 in Leeds, England) graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces. He became Secretary of the EMS in 1930 and President in 1935. *SAU

1893 Marcel Gilles Jozef Minnaert (12 Feb 1893; 26 Oct 1970 at age 77)
Flemish astronomer and solar physicist who was one of the pioneering solar researchers during the first half of the 20th century. Applying solar spectrophotometry, he was one of the first to make quantitative measurements of the intensity distribution inside Fraunhofer lines, and interpret from them information about the outer solar layers. His range of study also included comets, nebulae and lunar photometry. During the time he was director of the observatory at the University of Utrecht, (1937-1963) he created a modern astronomical institute to study solar and stellar spectra with resources including a solar telescope, spectrograph, photometer, and mechanical workshop. Minnaert also maintained a strong interest in the education of physics teachers, and as a univeristy professor gave clear, enthusiastic and well-prepared lectures. *TIS

1908 Jacques Herbrand (12 Feb 1908 - 27 July 1931) was a French mathematician who died young but made contributions to mathematical logic.*SAU

1914 Hanna Neumann (12 February 1914 – 14 November 1971) born in Berlin. In 1938 she left her graduate studies in G¨ottingen to join her future husband, the mathematician Bernhard Neumann, in England. She completed her
D. Phil. at Oxford, working with Olga Taussky-Todd in combinatorial group theory. In 1955 she received the D.Sc., the higher doctorate, also at Oxford. Later she became a leading ﬁgure working on varieties of groups. *VFR

1918 Julian Seymour Schwinger (12 Feb 1918; 16 Jul 1994 at age 76.) American physicist who shared the 1965 Nobel Prize in Physics for his contributions to quantum electrodynamics (with Richard Feynman and Shin-Itiro Tomonaga). Schwinger worked on reconciling quantum mechanics with Albert Einstein's special theory of relativity. He published his first physics paper at the age of sixteen. During WW II, he developed important methods in electromagnetic field theory, which advanced the theory of wave guides. His variational techniques were applied in several fields of mathematical physics. In the 1940's he was one of the inventors of the "renormalization" technique. In 1957, he proposed that theoretically there were two different neutrinos: one associated with the electron and one with the muon. Later experimental work provided verification. He invented source theory. *TIS Schwinger was Oppenheimer's most brilliant student. Oppenheimer once said of him, "When ordinary people give a talk, they tell you how to do it. When Julian gives a talk, it is to tell you that only he can do it." *Freeman Dyson, Infinities in all Directions.

1921 Kathleen "Kay" McNulty Mauchly Antonelli (February 12, 1921 – April 20, 2006) was one of the six original programmers of the ENIAC, the first general-purpose electronic digital computer. *Wik
 Betty Snyder Holberton, Jean Jennings Bartik, Kathleen McNulty Mauchly Antonelli, Marlyn Wescoff Meltzer,
photo credit  www.chw.net

1936 Fang Lizhi (12 Feb 1936 - ) Chinese astrophysicist and dissident. He graduating from university in 1956, and was soon expelled from Communist Party for expressing his beliefs in intellectual freedom and reforms. In 1972, he published a paper on the big bang theory, previously a forbidden topic in China, which met condemnation from the Communists; the Marxists claimed that the universe was infinite. As human rights activist in China, he is often compared to Soviet dissident Andrei Sakharov. Lizhi was blamed for student unrest and resulting rebellion in Tiananmen Square (1987). Since 1990, Lizhi has lived in exile in England and the U.S. He does theoretical work in cosmology, extracting the history of the universe from the remaining physical evidence, such as the cosmic background radiation, and the existence of antimatter *TIS

DEATHS
1612 Christopher Clavius (March 25, 1538 – February 12, 1612 {many sources give Feb 6 for the date of death}), the Euclid of the sixteenth-century, born in the German town of Bamberg, the see of the prince-bishop of Franconia. He was also the leader of the Gregorian calendar reform. Perhaps his greatest contribution was as an educational reformer. *Renaissance Mathematicus He was a German Jesuit mathematician and astronomer who was a major supporter of the modern Gregorian calendar. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in Europe and even in more remote lands (on account of being used by missionaries). As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the orthodox model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon. Later, a large crater on the Moon was named in his honour. *Wik

1804 Immanuel Kant (22 Apr 1724, 12 Feb 1804 at age 79)German philosopher, trained as a mathematician and physicist, who published his General History of Nature and theory of the Heavens in 1755. This physical view of the universe contained three anticipations of importance to astronomers. 1) He made the nebula hypothesis ahead of Laplace. 2) He described the Milky Way as a lens-shaped collection of stars that represented only one of many "island universes," later shown by Herschel. 3) He suggested that friction from tides slowed the rotation of the earth, which was confirmed a century later. In 1770 he became a professor of mathematics, but turned to metaphysics and logic in 1797, the field in which he is best known.*TIS

1856 Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) Russian mathematician who, with János Bolyai of Hungary, is considered the founder of non-Euclidean geometry. Lobachevsky constructed and studied a type of geometry in which Euclid's parallel postulate is false (the postulate states that through a point not on a certain line only one line can be drawn not meeting the first line). This was not well received at first, but his greatest vindication came with the advent of Einstein's theory of relativity when it was demonstrated experimentally that the geometry of space is not described by Euclid's geometry. Apart from geometry, Lobachevsky also did important work in the theory of infinite series, algebraic equations, integral calculus, and probabilty. *TIS William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Lobachevsky is the subject of songwriter/mathematician Tom Lehrer's humorous song "Lobachevsky" from his Songs by Tom Lehrer album. In the song, Lehrer portrays a Russian mathematician who sings about how Lobachevsky influenced him: "And who made me a big success / and brought me wealth and fame? / Nikolai Ivanovich Lobachevsky is his name." Lobachevsky's secret to mathematical success is given as "Plagiarize!", as long as one is always careful to call it "research". According to Lehrer, the song is "not intended as a slur on [Lobachevsky's] character" and the name was chosen "solely for prosodic reasons".*Wik (The lyrics are here) And you can hear Tom sing his song (1953) with the lyrics on screen, almost like following the bouncing ball in the old cartoons.

1857 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

1916 (Julius Wilhelm) Richard Dedekind (6 Oct 1831, 12 Feb 1916 at age 84) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. *TIS A 1904 academic calendar marked September fourth, 1899 as the day Dedekind died. He wrote the publisher saying that while 4 September might be correct, 1899 certainly was not, for on that day he had enjoyed a stimulating mathematical discussion with his dinner guest and honored friend, Georg Cantor. *VFR

1950 Dirk Coster (5 Oct 1889, 12 Feb 1950 at age 60) Dutch physicist who (working with Georg von Hevesy) discovered the element hafnium by skillfully applying Moseley's method of X-ray analysis to distinguish the spectral lines of hafnium, despite the distraction of some extraneous lines. Niels Bohr had suggested they look closely at an ore of zirconium, a homologue, for the new element. Bohr heard by telephone of their success on the day of his Nobel Prize lecture (11 Dec 1922), in which he then announced their discovery. The element, at. no.72, was named for Hafnia, the old Roman name for Copenhagen. Earlier, working at Bohr's laboratory in Copenhagen, Coster had used X-rays to provide experimental data to support Bohr's theory of atomic structure and the periodic table. He died from a spinal disease which progressively totally paralysed him.*TIS

1958 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser. *Wik

1960 Oskar Johann Viktor Anderson (2 August 1887, Minsk, Belarus – 12 February 1960, Munich, Germany) was a German-Russian mathematician. He was most famously known for his work on mathematical statistics.Anderson was born from a German family in Minsk (now in Belarus), but soon moved to Kazan (Russia), on the edge of Siberia. His father, Nikolai Anderson, was professor in Finno-Ugric languages at the University of Kazan. His older brothers were the folklorist Walter Anderson and the astrophysicist Wilhelm Anderson. Oskar Anderson graduated from Kazan Gymnasium with a gold medal in 1906. After studying mathematics for one year at University of Kazan, he moved to St. Petersburg to study economics at the Polytechnic Institute. From 1907 to 1915, he was Aleksandr Chuprov's assistant. In 1912 he started lecturing at a commercial school in St. Petersburg. In 1918 he took on a professorship in Kiev but he was forced to flee Russia in 1920 due to the Russian Revolution, first taking a post in Budapest (Hungary) before becoming a professor at the University of Economics at Varna (Bulgaria) in 1924. In 1935 he was appointed director of the Statistical Institute for Economic Research at the University of Sofia and in 1942 he took up a full professorship of statistics at the University of Kiel, where he was joined by his brother Walter Anderson after the end of the second world war. In 1947 he took a position at the University of Munich, teaching there until 1956, when he retired.*Wik

1962 Joseph Jean Camille Pérès (31 Oct 1890 in Clermont-Ferrand, France, 12 Feb 1962 in Paris, France) Pérès' work on analysis and mechanics was always influenced by Volterra, extending results of Volterra's on integral equations. His work in this area is now of relatively little importance since perhaps even for its day it was somewhat old fashioned.
A joint collaboration between Pérès and Volterra led to the first volume of Theorie generale des fonctionnelles published in 1936. Although the project was intended to lead to further volumes only this one was ever published. This work is discussed in where the author points out that the book belongs to an older tradition, being based on ideas introduced by Volterra himself from 1887 onwards. By the time the work was published the ideas it contained were no longer in the mainstream of development of functional analysis since topological and algebraic concepts introduced by Banach, von Neumann, Stone and others were determining the direction of the subject. However, the analysis which Pérès and Volterra studied proved important in developing ideas of mathematical physics rather than analysis and Pérès made good use of them in his applications. *SAU

1977 Ebenezer Cunningham (7 May 1881, Hackney, London – 12 February 1977) was a British mathematician who is remembered for his research and exposition at the dawn of special relativity.
He went up to St John's College, Cambridge in 1899 and graduated Senior Wrangler in 1902, winning the Smith's Prize in 1904.
In 1904, as lecturer at University of Liverpool, he began work on a new theorem in relativity with fellow lecturer Harry Bateman. They brought the methods of inversive geometry into electromagnetic theory with their transformations:
Each four-dimensional solution [to Maxwell's equations] could then be inverted in a four-dimensional hypersphere of pseudo-radius K in order to produce a new solution. Central to Cunningham's paper was the demonstration that Maxwell's equations retained their form under these transformations.
He worked with Karl Pearson in 1907 at University College London. Cunningham married Ada Collins in 1908.
His book The Principle of Relativity (1914) was one of the first treatises in English about special relativity, along with those by Alfred Robb and Ludwik Silberstein. He followed with Relativity and the Electron Theory (1915) and Relativity, Electron Theory and Gravitation (1921). McCrea writes that Cunningham had doubts whether general relativity produced "physical results adequate return for mathematical elaboration."
He was an ardent pacifist, strongly religious, a member of Emmanuel United Reformed Church, Cambridge and chairman of the Congregational Union of England and Wales for 1953-54.*Wik

1980 Carl Einar Hille (born Carl Einar Heuman; 28 June 1894 – 12 February 1980) was a Swedish American mathematician. Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem.*Wik In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR

2001 Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still (as of 2007) in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).*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