Thursday 15 June 2023

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 (60601).  *Prime Curios  90901, 9091, and 9901 are all prime, 

166, like 164, uses all the Roman digits from 100 down, once each. A difference is that 166 uses them in order of their size, CLXVI

166!-1 is a factorial minus one prime. It has 298 digits.  (For which n is N! -1 or n! + 1 a prime?  hint: there are thirteen year days  (\ n<366 \) for which  n! +1  is prime  

166 is the sum of three consecutive triangular numbers, 166 = T9 + T10 + T11

166 in binary has the same number of 1's and 0's.  There are 35  8-digit numbers with this property

166  is a Smith number, since the sum of its digits (13) coincides with the sum of the digits of its prime factors. 

166 is the 11-th centered triangular number.1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, ...

More extended number facts for every math day of the year. 


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 Bernard Frenicle de Bessy, 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 attached. 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  (See Deaths below)
A 1786 illustration of the Montgolfier brothers’ hot air balloon, flown by de Rozier and M. le Marquis d’Arlandes, 21 November 1783.

1857 The Great Comet that didn't come, but still created panic. Astronomers became convinced of the periodic nature of many comets, 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

1949  Jay Forrester recorded a proposal for core memory in his notebook. A professor at MIT at the time, Forrester eventually installed magnetic core memory on the Whirlwind computer. Core memory made computers more reliable, faster, and easier to make. Such a system of storage remained popular until the development of semiconductors in the 1970s. *CHM

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 DE, and F that lie on lines BCCA, and AB respectively, the theorem states that lines ADBE 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

1922 Frederick William Sanderson (13 May 1857 – 15 June 1922) was headmaster of Oundle School from 1892 until his death. He was an education reformer, and both at Oundle, and previously at Dulwich College where he had started as assistant master, he introduced innovative programs of education in engineering. Under his headmastership, Oundle saw a reversal of a decline from which it had been suffering in the middle of the 19th century, with school enrollment rising from 92 at the time of his appointment to 500 when he died.
Sanderson was the inspiration for the progressive headmaster character in H. G. Wells' novel Joan and Peter. Wells had sent his own sons to Oundle, and was friendly with Sanderson. After Sanderson's death, which occurred shortly after delivering an address to Wells and others, Wells initially worked on his official biography, entitled Sanderson of Oundle, but later abandoned it in favor of an unofficial biography, The Story of a Great Schoolmaster. *Wik

1971 Wendell Meredith Stanley (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate. Stanley was born in Ridgeville, Indiana, and earned a BS in Chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a Ph.D. in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and achieving his high stature as a Pulitzer Prize nominee.
Stanley was awarded the Nobel Prize in Chemistry for 1946. His other notable awards included the Rosenburger Medal, Alder Prize, Scott Award, and the AMA Scientific Achievement Award. He was also awarded honorary degrees by many universities both American and foreign, including Harvard, Yale, Princeton and the University of Paris. Most of the conclusions Stanley had presented in his Nobel-winning research were soon shown to be incorrect (in particular, that the crystals of mosaic virus he had isolated were pure protein, and assembled by autocatalysis)
Stanley married Marian Staples (1905-1984) in 1929 and had three daughters (Marjorie, Dorothy and Janet), and a son, (Wendell M. Junior). Stanley Hall at UC Berkeley (now Stanley Biosciences and Bioengineering Facility) and Stanley Hall at Earlham College are named in his honor. *Win

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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