Friday 6 June 2014

On This Day in Math - June 6
Map of 2012 Transit of Venus visibility *Eclipse Maps

No mathematician can be
a complete mathematician unless
he is also something of a poet.
~Karl Weierstrass

The 157th day of the year; 2157 is the smallest "apocalyptic number," i.e., a number of the form 2n that contains '666'. *Prime Curios (Can you find an apocalyptic number of the form 3n)
It is also the largest solution I know for a prime, p, such that \( \frac{p^p-p!}{p} \) is prime.
The number 157 in base ten is equal to \(31_{[52]}\), but don't worry if you get that backwards, \(52_{[31]}\) is also equal to 157 in decimal.

In 1799, the first definitive prototype meter bars (mètre des Archives) and kilograms were constructed in platinum. This followed the legal definition of the metric system by the French National Assembly on 7 Apr 1795, that was itself established during the famous measurements of the Earth's meridian between Dunkerque and Barcelona. The use of a metal bar to define the standard meter continued until replaced in 1960 by a definition based upon a number of wavelengths of light from a certain spectroscopic light source.*TIS

1902 Scottish chemist professor James Dewar exhibits air in the solid state and a jet of liquid air rising six feet above it with beautiful effects, before the Prince and Princess of Wales. *Great Geek Manual

1944, Supreme Allied Commander General Dwight D. Eisenhower gives the go-ahead for largest amphibious military operation in history: Operation Overlord, code named D-Day, the Allied invasion of northern France.

1984 Sweden issued a series of stamps celebrating the centenary of their Patent System. One shows a tetrahedral container pented in 1948. [Scott #1501]. *VFR (I have been unable to find an image of this stamp.. if anyone has one, please advise)

1984 Tetris is a Soviet tile-matching puzzle video game originally designed and programmed by Alexey Pajitnov. It was released on June 6, 1984. A nice post with ten things you did't know about about Tetris is at this blog from Wallifaction, a very good history blog by Adam Richter

2012 Last Chance. The most recent transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit, since the previous Venus transit took place on December 6, 1882. The next transit of Venus will occur on June 5–June 6 in 2012. After 2012, the next transits of Venus will be in December 2117 and December 2125.


1436 Johann Mueller (14 July 1801 – 28 April 1858) , AKA Johannes Regiomontanus after the Latinization of his hometown, Konigsburg. He is the founder of trigonometry as an independent science. The spherical law of sines was first presented by Johann Muller, in his De Triangulis Omnimodis in 1464. This was the first book devoted wholly to trigonometry (a word not then invented). David E. Smith suggests that the theorem was Muller's creation.
The ideas behind the law of sines, like those of the law of cosines, predate the word sine by over a thousand years. Theorems in Euclid on lengths of chords are essentially the same ideas we now call the law of sines. What we now call the law of sines for plane triangles was known to Ptolemy. By the tenth century Abu'l Wefa had clearly expounded the spherical law of sines. It seems that the term "law of sines" was applied sometime near 1850, but I am unsure of the origin of the phrase.

"In Jan 1472 he made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years later (being three returns of the 70 year period comet). He also observed several eclipses of the Moon. His interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. However, instruments of the time lacked the necessary accuracy to use the method at sea. " *TIS {There is a nice blog at The Renaissance Mathematicus about the important role Regiomontanus played in scientific publishing.}

1553 Bernardino Baldi (6 June 1553 – 10 October 1617) was an Italian mathematician and writer.
Baldi descended from a noble family from Urbino, Marche, where he was born. He pursued his studies at Padua, and is said to have spoken about sixteen languages during his lifetime, though according to Tiraboschi the inscription on his tomb limits the number to twelve.
The appearance of the plague at Padua forced him to return to his native city. Shortly afterwards he was called to act as tutor to Ferrante Gonzaga, from whom he received the rich abbey of Guastalla. The oldest biography of Nicolaus Copernicus was completed on 7 October 1588 by him. He held office as abbot for 25 years, and then returned once again to Urbino. In 1612 he was employed by the duke as his envoy to Venice. Baldi died at Urbino on 12 October 1617.
He is said to have written upwards of a hundred different works, the chief part of which have remained unpublished. His various works show his abilities as a theologian, mathematician, geographer, antiquary, historian and poet. One of these has been recently found and is now at the Univ. of Oklahoma.
"Baldi is known to have written a treatise on sun dials and timekeeping. However, this treatise was never published and, since 1783, it has been considered lost. Now we are happy to announce that it has been recently acquired by the History of Science Collections, digitized in high resolution, and made available for study in the Collections’ Online Galleries." The Cronica dei Matematici (published at Urbino in 1707) is an abridgment of a larger work on which he had written for twelve years, and was intended to contain the lives of more than two hundred mathematicians. His life has been written of by Affò, Mazzucchelli and others. *Wik

1580 Govaert Wendelen (6 June 1580 – 24 October 1667) was a Flemish astronomer who was born in Herk-de-Stad. He is also known by the Latin name Vendelinus. His name is sometimes given as Godefroy Wendelin; his first name spelt Godefroid or Gottfried.
Around 1630 he measured the distance between the Earth and the Sun using the method of Aristarchus of Samos. The value he calculated was 60% of the true value (243 times the distance to the Moon; the true value is about 384 times; Aristarchus calculated about 20 times).
In 1643 he recognized that Kepler's third law applied to the satellites of Jupiter.
Wendelin corresponded with Mersenne, Gassendi and Constantijn Huygens.
The crater Vendelinus on the Moon is named after him.
Wendelin died in Ghent on 24 October 1667. *Wik

1842 Henry Martyn Taylor (6 June 1842, Bristol – 16 October 1927, Cambridge) born in Bristol, England. He was a fellow at Trinity College, Cambridge, and is most remembered because he devised a Braille notation when he was overtaken by blindness in 1894, when engaged in the preparation of an edition of Euclid for the Cambridge University Press. By means of his ingenious and well thought out Braille notation he was enabled to transcribe many advanced scientific and mathematical works, and in 1917, with the assistance of Mr. Emblen, a blind member of the staff of the National Institute for the Blind, he perfected it. It was recognised as so comprehensive that it was soon adopted as the standard mathematical and chemical notation. It seems that in the US it is more common to use the Nemeth code for mathematics and science symbols, first developed around 1947. I am not sure about usage at the present time in the rest of the world.

1850 Karl Ferdinand Braun (6 June 1850 – 20 April 1918) was a German inventor, physicist and Nobel laureate in physics. Braun contributed significantly to the development of the radio and television technology: he shared with Guglielmo Marconi the 1909 Nobel Prize in Physics.
Braun was born in Fulda, Germany, and educated at the University of Marburg and received a Ph.D. from the University of Berlin in 1872. In 1874 he discovered that a point-contact semiconductor rectifies alternating current. He became director of the Physical Institute and professor of physics at the University of Strassburg in 1895.
In 1897 he built the first cathode-ray tube (CRT) and cathode ray tube oscilloscope. CRT technology has been replaced by flat screen technologies (such as liquid crystal display (LCD), light emitting diode (LED) and plasma displays) on television sets and computer monitors. The CRT is still called the "Braun tube" in German-speaking countries (Braunsche Röhre) and in Japan (ブラウン管: Buraun-kan). *Wik

1857 Aleksandr Mikhailovich Lyapunov (June 6[O.S. May 25] 1857 – November 3, 1918) born in Yaroslavl, Russia. He was the creator of the modern theory of stability of differential equations especially as applied to mechanical systems. He also proved the Central Limit Theorem under weaker hypotheses than his predecessors. *VFR He was a student of Chebyshev. In 1901, Lyapunov gave the first prominent proof of the Central Limit Theorem, which made the CLT one of the foundations of probability theory today. (Unlike the classical CLT, Lyapunov’s condition only requires the random variables in question to be independent instead of both independent and identically distributed.)

1906 Max Zorn (June 6, 1906 in Krefeld, Germany – March 9, 1993 in Bloomington, Indiana, United States) To his chagrin, he is most famous for discovering something yellow and equiv­alent to the Axiom of Choice. *VFR (with a smile, I'm sure) He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a powerful tool in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, ordered sets, etc. Zorn's lemma was first discovered by K. Kuratowski (see June 18) in 1922, and then independently by Zorn in 1935.*Wik  Interesting that he was born on 6/6/6. 

1898 Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.
In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theorem based on the idea of dissecting two smaller squares into a larger square. The five-piece dissection that he found may be generated by overlaying a regular square tiling whose prototile is the larger square with a Pythagorean tiling generated by the
two smaller squares. Perigal had the same dissection printed on his business cards, and it also appears on his tombstone.

As well as being interested in mathematics, Perigal was an accomplished lathe worker, and made models of mathematical curves for Augustus De Morgan. He believed (falsely) that the moon does not rotate with respect to the fixed stars, and used his knowledge of curvilinear motion in an attempt to demonstrate this belief to others. *Wik

1928 Luigi Bianchi (January 18, 1856 – June 6, 1928) He did fundamental work on Lie groups. *VFR He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century.
In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.
Through the influence of Luther P. Eisenhart and Abraham Haskel Taub, Bianchi's classification later came to play an important role in the development of the theory of general relativity. Bianchi's list of nine isometry classes, which can be regarded as Lie algebras, Lie groups, or as three dimensional homogeneous (possibly nonisotropic) Riemannian manifolds, are now often called collectively the Bianchi groups.
In 1902, Bianchi rediscovered what are now called the Bianchi identities for the Riemann tensor, which play an even more important role in general relativity. (They are essential for understanding the Einstein field equation.) According to Tullio Levi-Civita, these identities had first been discovered by Ricci in about 1880, but Ricci apparently forgot all about the matter, which led to Bianchi's rediscovery! *Wik

1943 Guido Fubini (19 January 1879 – 6 June 1943) He is best known for a theorem on the exchange of order of integration. his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean geometry, and projective geometry, among other topics. With the outbreak of World War I, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics. *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

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