Monday, 15 June 2015

On This Day in Math - June 15

 A statistician is someone who is good with numbers
but lacks the personality to be an accountant.
(my apologies to all the statisticians out there)
The 166th day of the year; the reverse (661) of 166 is a prime. If you rotate it 180o (991) it is also prime. The same is true if you put zeros between each digit (10606).  *Prime Curios

166!-1 is a factorial minus one prime.  (For which n is N! -1 or n! + 1 a prime?  hint: there are three more year days (\ n<366 \) for which  n! +1 or n! -1 is prime

762 BC An eclipse more than 27 centuries old is regarded as one of the earliest events that can be pinpointed by scholars of the Near East. The June 15, 762 B.C. total solar eclipse is mentioned in Assyrian texts as well as the Book of Amos in the Hebrew Bible. While hotly debated (at least among archeo-astronomical types, who love to debate such things) the mention of this eclipse serves as a valuable reference point between ancient Assyrian and Hebrew chronology.*

1641  In a letter to Frenicle, Fermat called the theorem that every prime of the form 4n+1 is the sum of two squares, the fundamental theorem of right triangles.  He stated that he had a proof that was "irrefutable".  Later he suggested he had a proof by infinite descent.  Euler is credited with the first correct proof of the theorem, still called Fermat's theorem. 

In 1752, Ben Franklin's kite-flying experiment proved lightning and electricity were related while flying a kite with a key attatched. In Sep 1752, he equipped his house with a lightning rod, connecting it to bells that ring when rod is electrified. He explained how to perform a kite experiment in the 19 Oct 1752 issue of the Pennsylvania Gazette. He had earlier proposed use of lightning rods to protect houses in a 2 Mar 1750  letter to Collinson and in the same year, on 29 Jul 1750, he devised an experiment involving a sentry-box with a pointed rod on its roof, to be erected on hilltop or in church steeple, with rod attached to a Leyden jar which would collect the electrical charge, and thus prove lightning to be a form of electricity. *TIS

1785 Pilâtre de Rozier became aviation’s first casualty when he died attempting the second aerial crossing of the
English Channel. Rozier had piloted the first manned flight in a balloon from Paris in 1783. He and other supporters of Hydrogen balloons had competed with the Montgolfier brothers and supporters of the hot air ballons. Pilatre had reasoned that since both hydrogen and hot-air balloons had their separate advantages a combination of the two would be even better. Rozier was accustomed to living dangerously—one of his favorite chemical lecture-demonstrations consisted of flushing his lungs with hydrogen and then speaking in the resulting high-pitched
voice (today we tend to use helium). The final flourish (today we would tend to omit this!) was to light the hydrogen as it issued from his mouth. Such a man was obviously the “Right Stuff” to fly a hybrid hot-air-
hydrogen balloon. Alas, his luck ran out, and he and a companion crashed shortly after takeoff from Boulogne. *Derek A. Davenport, How the Right Professor Charles Went Up in the Wrong Kind of Balloon; ChemMatters
December 1983 Page 14, American Chemical Society

1857 The Great Comet that didn't come, but still created panic. Astronomers became convinced of the periodic nature of many comments, and loose speculation began about their possible times of return.
an obscure prediction, apparently originally made by the German (or Belgian) Laensberg in his Liege Almanac, In his entry for the week commencing 15 Jun 1857, Laensberg had warned, “about this time, expect a comet”. Through the vagaries of reporting, this eventually came to be understood to be a specific prediction that not only would the comet appear on that date, but that it would also collide with the Earth, and that this would result in the end of the World.
While this prediction was treated with scorn by many, it was also taken very seriously by large parts of the population. All this was a fertile field for satirists such as the French caricaturist Honoré Daumier. He gently mocked the Parisians’ comet obsession in a series of cartoons published in Le Charivari, and represented the offending German prognosticator as a magician playing a magic trick by releasing a comet-like duck. The joke, of course, was that the French for duck, “canard”, also means “hoax”
More about this and related comet tails here.

1915 The U.S. minted the only octagon-shaped coin in U.S. history. The coin was one of two $50 coins (the other one was round) issued as part of a set of five commemorative gold coins designed for the Panama-Pacific International Exposition held in San Francisco between February and December 1915. One hundred years later the coins trade for over a quarter-million dollars each. *Felicity Nie, Ready for Zero Blog

2015 Astronomers discovered the most powerful supernova ever seen, a star in a galaxy billions of light-years away that exploded with such force it briefly shone nearly 600 billion times brighter than our Sun and 20 times brighter than all the stars in the Milky Way combined. The explosion released 10 times more energy than the Sun will radiate in 10 billion years.
Discovered by ASAS-SN’s twin 14-centimeter telescopes operating in Cerro Tololo, Chile, the supernova just appeared as a transient dot of light in an image, and wasn’t immediately recognized as particularly special. *scientificamerican
Beijing Planetarium / Jin Ma / Wayne Rosing (artist rendering)

1640  Bernard Lamy (15 June 1640, in Le Mans, France – 29 January 1715, in Rouen) was a French mathematician who wrote on geometry and mechanics. He developed the idea of a parallelogram of forces at about the same time as Newton and Verignon.  The Law of Sines as applied to three static forces in mechanics is sometimes called Lamy's Rule. 

1765 Henry T. Colebrook (June 15, 1765 – March 10, 1837) Sanscrit Scholar and British civil servant in India who translated "algebra with arithmetic and mensuration, from the sanscrit of Brahmagupta and Bhascara."  *Wik

1765 Johann Gottlieb Friedrich von Bohnenberger (15 June 1765 – 19 April 1831) was born at Simmozheim, Württemberg. He studied at the University of Tübingen. In 1798, he was appointed professor of mathematics and astronomy at the University.
He published: Anleitung zur geographischen Ortsbestimmung, (1795); Astronomie, (1811); and Anfangsgründe der höhern Analysis, (1812).  In 1817, he discovered the gyroscope effect. *Wik

1884 William Watson (15 June 1884 in Musselburgh, East Lothian, Scotland -28 June 1952 in Edinburgh, Scotland) William Watson graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh. *SAU

1894 Nikolai Tschebotarjow (15 June[O.S. 3 June]1894 – 2 July 1947) or Chebotaryov proved his density theorem generalizing Dirichlet's theorem on primes in an arithmetical progression. *SAU (both spellings are used)

1906 (William) Gordon Welchman (June 15, 1906, Bristol, England – October 8, 1985, Newburyport, Massachusetts, USA) was a British mathematician, university professor, World War II codebreaker at Bletchley Park, and author.
Just before World War II, Welchman was invited by Commander Alastair Denniston to join the Government Code & Cypher School at Bletchley Park, in case war broke out. He was one of four early recruits to Bletchley (the others being Alan Turing, Hugh Alexander, and Stuart Milner-Barry), who all made significant contributions at Bletchley, and who became known as 'The Wicked Uncles'. They were also the four signatories to an influential letter, delivered personally to Winston Churchill in October 1941, asking for more resources for the code-breaking work at Bletchley Park. Churchill responded with one of his 'Action This Day' written comments.
Welchman moved to the United States in 1948, and taught the first computer course at MIT in the United States. He followed this by employment with Remington Rand and Ferranti. He became a naturalised American citizen in 1962. In that year, he joined the MITRE Corporation, working on secure communications systems for the US military. He retired in 1971, but was still retained as a consultant. In 1982 his book The Hut Six Story was published by McGraw-Hill in the USA, and by Allen Lane in Britain. The National Security Agency disapproved. The book was not banned, but Welchman lost his security clearance (and therefore his consultancy with MITRE), and was forbidden to discuss with the media either the book or his wartime work. Welchman died in 1985. His final conclusions and corrections to the story of wartime codebreaking were published posthumously in 1986 in the paper 'From Polish Bomba to British Bombe: the birth of Ultra' in Intelligence & National Security, Vol 1, No l. The entire paper was included in the revised edition of The Hut Six Story published in 1997 by M & M Baldwin. *Wik

Giovanni Ceva (December 7, 1647 – June 15, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry. His brother, Tommaso Ceva was also a well known poet and mathematician. *Wik
Ceva's theorem is a theorem in elementary geometry. Given a triangle ABC, and points D, E, and F that lie on lines BC, CA, and AB respectively, the theorem states that lines AD, BE and CF are concurrent, if and only if,
\frac{AF}{FB}  \cdot \frac{BD}{DC} \cdot \frac{CE}{EA} = 1,
where AF indicates the directed distance between A and F (i.e. distance in one direction along a line is counted as positive, and in the other direction is counted as negative).
There is also an equivalent trigonometric form of Ceva's Theorem, that is, AD,BE,CF concur if and only if
\frac{\sin\angle BAD}{\sin\angle CAD}\times\frac{\sin\angle ACF}{\sin\angle BCF}\times\frac{\sin\angle CBE}{\sin\angle ABE}=1.
The theorem was proved by Giovanni Ceva in his 1678 work De lineis rectis, but it was also proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza.
Associated with the figures are several terms derived from Ceva's name: cevian (the lines AD, BE, CF are the cevians of O), cevian triangle (the triangle DEF is the cevian triangle of O); cevian nest, anticevian triangle, Ceva conjugate. (Ceva is pronounced Chay'va; cevian is pronounced chev'ian.)*Wik

1785 Jean-François Pilatre de Rozier (30 March 1754 – 15 June 1785)French physicist and aeronaut who, with Marquis Francois Laurant d'Arlandes, became the first men to fly. Their hot-air balloon, built by the Montgolfier brothers, lifted off from La Muettte, a royal palace in the Bois de Boulogne, Paris. They flew nearly 6 miles in 25 mins, reaching an altitude of around 300-ft. King Louis XVI, who offered to send two prisoners for the test flight, but Rozier wanted to deny criminals the glory of being the first men to go into the atmosphere. Rozier died in attempt to cross English Channel in an apparatus composed of two balloons, one filled with hydrogen and the other with warm air. Thus, he was also the first man to die in an air crash. *TIS

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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