Wednesday 15 June 2011

On This Day in Math - June 15

 A statistician is someone who is good with numbers
but lacks the personality to be an accountant.
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

1640  Bernard Lamy 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. 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

1894 Algebraist Nikolai Tschebotarjow born.Chebotaryov proved his density theorem generalising Dirichlet's theorem on primes in an arithmetical progression.  *SAU 


1734  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 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

*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

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