## Wednesday 13 March 2024

### On This Day in Math - March 13

 Many Paris Street signs are named for Mathematicians *The n-Category Cafe

It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.
~Richard Feynman

The 72nd day of the year; 72 is a pronic, heteromecic, or oblong number (and sometimes pronic is spelled promic). They are numbers that are the product of two consecutive integers
Oblong numbers have the property that if they are used in infinite nested radicals, they produce an integer, $\sqrt(72+\sqrt(72+\sqrt(72+...))) = 9$

Newton categorized  72 cubic curves in 1710.

72 is the smallest number whose fifth power is the sum of five smaller fifth powers: $19^5 + 43^5 + 46^5 + 47^5 + 67^5 = 72^5$.

The rule of 72 was once a commonly used approximation in banking and finance for the time it took an investment to double at r%. For a 5% investment, the approximate period would be 72/5 = 14.4 years. The rule applies to compound interest. The rule is based on an approximation of ln(2) = .693..

In typography, point sizes are measured in 1/72 of an inch, 72-point characters are 1 inch tall.

72 is the smallest number that can be expressed as the difference of the squares of consecutive primes in two distinct ways: {192 - 172} and {112 - 72}

The number of integers less than 72 and relatively prime to it is 24.  The same is true for the numbers 78, 84, and 90.  This is the smallest set of four numbers in arithmetic sequence with the same value of Euler's phi function or totient function.  The next string of four begins at 216.  It also has an arithmetic difference of 6, and the repeated totient is (wait for it....)  72

More math facts for every year date here.

EVENTS

1634 First meeting of what would become the Academie Francaise in Paris at the house of Valentin Conrart.
The Académie had its origins in an informal literary group deriving from the salons held at the Hôtel de Rambouillet during the late 1620s and early 1630s. The group began meeting at Valentin Conrart's house, seeking informality. There were then nine members. Cardinal Richelieu, the chief minister of France, made himself protector of the group, and in anticipation of the formal creation of the academy, new members were appointed in 1634. On 22 February 1635, at Richelieu's urging, King Louis XIII granted letters patent formally establishing the council.
On 22 February 1635, at Richelieu's urging, King Louis XIII granted letters patent formally establishing the council.
Cardinal Richelieu

1639 Harvard University named after its London born clergyman founder John Harvard. Harvard was founded in 1636 by vote of the Great and General Court of the Massachusetts Bay Colony, making it the oldest institution of higher learning in the United States. Initially called "New College" or "the college at New Towne", the institution was renamed Harvard College on March 13, 1639. It was named after John Harvard, a young English clergyman from Southwark, London, an alumnus of the University of Cambridge (after which Cambridge, Massachusetts is named), who bequeathed the College his library of four hundred books and £779 pounds sterling, which was half of his estate. *Wik

1641 Vincenzo Renieri wrote to Galileo describing certain experiments on falling bodies, including dropping weights from the Tower in Pisa. In his trial a lead weight and a wooden one, of equal sizes, were dropped but in his trial they arrived three cubits apart. He asked Galileo if he had an explanation. At this time Galileo was already old and blind, and his assistant was Viviani.   “Thus Vincenzo Viviani’s account of the results of Galileo’s experiments that involved dropping different weights from the top of the bell tower of Pisa seems to be completely unfounded.”

1781 Sir William Herschel discovered Uranus at 10:30 PM.(The first planet discovered by a telescope) During his search for double stars Herschel noticed an object appearing as a nonstellar disk. Herschel originally thought it was a comet or a star. He made many more observations of it, and afterwards Russian Academician Anders Lexell computed the orbit and found it to be probably planetary. Herschel determined in agreement that it must be a planet beyond the orbit of Saturn. He called the new planet the 'Georgian star' (Georgium sidus) after King George III, which also brought him favor; the name didn't stick, however. In France, where reference to the British king was to be avoided if possible, the planet was known as 'Herschel' until the name 'Uranus' was universally adopted.
It is the only one of the eight planets whose English name derives from a figure of Greek mythology.
In 1789, Herschel discovered a new moon of Saturn: Mimas, only 250 miles (400 km) in diameter.
*Wik
William and Caroline Herschel polishing a telescope lens (probably a mirror); 1896 lithograph

During 1839, William Robert Grove developed a novel form of electric cell, the Grove cell, which used zinc and platinum electrodes exposed to two acids and separated by a porous ceramic pot. Grove announced the latter development to the Académie des Sciences in Paris in 1839. In 1840 Grove invented one of the first incandescent electric lights, which was later perfected by Thomas Edison.

Later that year, he gave another account of his development at the British Association for the Advancement of Science meeting in Birmingham, where it aroused the interest of Michael Faraday. On Faraday's invitation Grove presented his discoveries at the prestigious Royal Institution Friday Discourse on 13 March 1840
 *Wik

1889 New York Tribune carries report of Senate sidelined by new game, Pigs in Clover, invented by Charles Martin Crandall. :
Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen. A few days later a political cartoon in the March 17, 1889 issue of the New York World lampooned President Benjamin Harrison's advisors and cabinet members showing the group sitting around playing the game. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"
*Antique Toy Collectors of America *Wik

1925 The Butler Act, a law in Tennessee prohibiting the teaching of Darwin’s theory of evolution passed the state senate on March 13, and was signed into law by Governor Austin Peay (for whom the university in Clarksville, Tennessee is named) on March 21. The Butler Act was a 1925 Tennessee law:
That it shall be unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the Story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals.
It would remain the law in Tennessee until repealed on September 1, 1967. *Wik
This led to the famous Scope's Monkey Trial.

 John T Scopes

1926 Erwin Schrodinger's "Quantisierung als Eigenwertproblem ," the first of six remarkable papers laying out his wave formulation of quantum mechanics, was published in Annalen der PHysik *Robert McNess@mcnees

In 1930, the discovery of a ninth planet was announced by Clyde W. Tombaugh at Lowell Observatory. It is only one-tenth as large as Earth and four thousand million miles away. The planet was named Pluto on 24 May 1930.*TIS The discovery made headlines across the globe. The Lowell Observatory, which had the right to name the new object, received over 1,000 suggestions from all over the world, ranging from Atlas to Zymal.
The name Pluto was proposed by Venetia Burney (1918–2009), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, a name for the god of the underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian at the University of Oxford's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in the United States.*Wik

1969 Apollo 9 returns to Earth after completing tests on the lunar module to be used in Apollo 11 landing on the moon.  Having completed all their primary objectives successfully, the crew returned to Earth on 13 March, splashing down east of the Bahamas in the Atlantic Ocean. The mission paved the way for Apollo 10 in May 1969, which would send a crew to lunar orbit for a final landing rehearsal ahead of Apollo 11.  The mission had began on March 3.

1970 Digital Equipment Corp introduces PDP-11 minicomputer. The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a set of products in the Programmed Data Processor (PDP) series. In total, around 600,000 PDP-11s of all models were sold, making it one of DEC's most successful product lines. The PDP-11 is considered by some experts to be the most popular minicomputer.
 * PDP-11 Wik

 Halley's Comet, March 8, 1986
1986 Halley’s comet returns, as he predicted in 1682. The comet last reached perihelion on 9 February 1986, and will next reach it again on 28 July 2061 *Wik   Halley's prediction that it would return in 1758 was incorrect, and observations and calculations led to a another prediction and perihelion to occur on April 13, 1759, but appeared a month early on March 13.  It was sighted on the year he predicted 25 December, when it was observed by German farmer, and armature astronomer, Johan Palitsch. *HT to @RMathematicus

1986 Microsoft Goes Public Ten years after the company's founding, Microsoft Corporation stock goes public at $21$ per share. *CHM Allowing for stock splits and reinvestment of dividends, each $21$ share then would be worth $9239$today (price may be somewhat dated). (I know, you thought computers were just a fad, too.)

1997 Phoenix lights seen at night over Phoenix, Arizona by hundreds of people, and by millions on television. Now a hotly debated controversy.The Phoenix Lights (sometimes called the "Lights Over Phoenix") were a series of widely sighted unidentified flying objects observed in the skies over the southwestern states of Arizona and Nevada on March 13, 1997.
Lights of varying descriptions were seen by thousands of people between 7:30 pm and 10:30 pm MST, in a space of about 300 miles (480 km), from the Nevada line, through Phoenix, to the edge of Tucson. Some witnesses described seeing what appeared to be a huge carpenter's square-shaped UFO containing five spherical lights. There were two distinct events involved in the incident: a triangular formation of lights seen to pass over the state, and a series of stationary lights seen in the Phoenix area. Both sightings were due to aircraft participating in Operation Snowbird, a pilot training program of the Air National Guard based in Davis-Monthan Air Force Base in Tucson, Arizona. *Wik
====================================================================
2003 The journal Nature reports that 350,000-year-old footprints of an upright-walking human have been found in Italy.
"Italian scientists, who identified three separate fossilised trackways, say the people that made them walked on two feet using their hands only to steady themselves on a difficult descent.
"They're the oldest footprints to be found of the genus Homo, the group that we belong to," the researchers told the BBC.
Commentators say the prints were probably made by Homo heidelbergensis, a forerunner of Neanderthals, that dominated Europe at this time." *BBCNews

BIRTHS

1585 Federico Cesi (13 Mar 1585 OR 26 Feb (sources differ, but Thony Christie did some research to suggest the Feb date is the correct one); 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847.

1733 Joseph Priestley (13 Mar 1733, 6 Feb 1804) English chemist, clergyman and political theorist who discovered the element oxygen. His early scientific interest was electricity, but he is remembered for his later work in chemistry, especially gases. He investigated the "fixed air" (carbon dioxide) found in a layer above the liquid in beer brewery fermentation vats. Although known by different names at the time, he also discovered sulphur dioxide, ammonia, nitrogen oxides, carbon monoxide and silicon fluoride. Priestley is remembered for his invention of a way of making soda-water (1772), the pneumatic trough, and recognizing that green plants in light released oxygen. His political opinions and support of the French Revolution, were unpopular. After his home and laboratory were set afire (1791), he sailed for America, arriving at New York on 4 Jun 1794 *TIS
The book below gives a wonderful history of scientific cooperation in this period. "This 18th century group of science fans and practitioners centred around Charles Darwin’s maternal and paternal grandfathers, Josiah Wedgwood and Erasmus Darwin, met monthly at full moon to facilitate the members journey home in the dark. Apart from Priestley, Darwin and Wedgwood notable other members, some corresponding, were Boulton and Watt of steam engine fame, Benjamin Franklin, James Hutton, Joseph Banks, William Herschel and a host of other scientific worthies." *Thony Christie, The lunatic who invented fizzy pop.

1842 Joseph Valentin Boussinesq (13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
In 1897 he published Théorie de l' écoulement tourbillonnant et tumultueux des liquides, a work that greatly contributed to the study of turbulence and hydrodynamics.*Wik

1855 Percival Lowell (13 Mar 1855, 12 Nov 1916) American astronomer who predicted the existence of the planet Pluto and initiated the search that ended in its discovery. Lowell was also passionately committed to finding proof of intelligent life on Mars. In 1894, he founded the Lowell Observatory, atop Mars Hill, at Flagstaff as Arizona's first astronomical observatory. Studying Mars, Lowell drew in intricate detail, the network of several hundred fine, straight lines and their intersection in a number of "oases." Lowell concluded that the bright areas were deserts and the dark ones were patches of vegetation. He believed further, that water from the melting polar cap flowed down the canals toward the equatorial region to revive the vegetation. *TIS
The image of Mars below may seem incredibly clear for a telescope photo.  The oddity is that the images are photographs of a Martian globe, rather than the planet itself, a globe that was evidently made by Lowell or the Observatory staff, depicting a Mars covered with canals.
Percival built an observatory in Flagstaff, Arizona, solely for the purpose of observing Mars. He equipped it with the best of telescopes, began a regular observing program, and was soon convinced that the canals were real, and that Martians had built them long ago to bring water from the polar ice caps to a dying planet. He published three books on Mars between 1895 and 1908. *Linda Hall Org

1866 Dayton Clarence Miller (13 Mar 1866, 22 Feb 1941 at age 74)American physicist. Author of The Science of Musical Sounds (1916). Miller's collection of nearly 1,650 flutes and other instruments, and other materials mostly related to the flute, is now at the Library of Congress. To provide a mechanical means of recording sound waves photographically, he invented the phonodeik (1908).( The Phonodeik converts sound waves into visual images. The name, from "to show sound" was suggested by Edward W. Morley. Before electronic oscilloscopes, this device was used for analyzing sounds waves. The Phonodeik can be modified to project sound waves on a screen for public demonstration.*Wik) He became expert in architectural acoustics. During WW I, he was consulted concerning using his photodeik to help locate enemy guns. Miller spent considerable research effort on repeating the Michelson and Morley experiment, proposed by Maxwell, to detect a stationary aether. He spent some time working with Morley (1902-4), then more time at Mt. Wilson, recording results favoring the presence of the aether.*TIS
Based on an error analysis, Miller's critics argued that he overestimated the precision of his results, and that his measurements were actually perfectly consistent with a fringe difference of zero—the null result that every other experiment was recording. However, Miller continued to defend his results, claiming that the probable reason for the so-called null results were that they were not being done at high locations (such as mountain tops), where the ether wind (drift) was supposedly much higher due to less ether drag.  During his trials, however, Miller developed the most sensitive interferometer in the world at that time.

1899 John Hasbrouck Van Vleck (13 Mar 1899, 27 Oct 1980) was an American physicist and mathematician who shared the Nobel Prize for Physics in 1977 with Philip W. Anderson and Sir Nevill F. Mott. The prize honoured Van Vleck's contributions to the understanding of the behaviour of electrons in magnetic, noncrystalline solid materials. In about 1930, he introduced the contribution of the second-order Zeeman effect into the theory of the paramagnetic susceptibility for the ions of the elements samarium and europium, thus bringing calculations into agreement with experimental results. Hans Bethe's theoretical work (c.1929), was extended by Van Vleck to develop the ligand, or crystal, field theory of molecular bonding. He also studied the theory for the nature of the chemical bond, especially as related to its magnetic properties, and contributed to theory of the spectra of free molecules.*TIS
Van Vleck (left) receives the Lorentz Medal from Hendrik Brugt Gerhard Casimir at the Royal Netherlands Academy of Arts and Sciences, Amsterdam.

1925 John Torrence Tate Jr. (March 13, 1925, ) is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. Tate has been described as "one of the seminal mathematicians for the past half-century" by William Beckner, Chairman of the Department of Mathematics at the University of Texas.*Wik
In 2010 the Norwegian Academy of Science and Letters, of which he was a member,[14] awarded him the Abel Prize, citing "his vast and lasting impact on the theory of numbers". According to a release by the Abel Prize committee, "Many of the major lines of research in algebraic number theory and arithmetic geometry are only possible because of the incisive contributions and illuminating insights of John Tate. He has truly left a conspicuous imprint on modern mathematics."

1928 Paulo Ribenboim (March 13, 1928, )is a mathematician who specializes in number theory. Ribenboim was born in Recife, Brazil, and has lived in Canada since 1962.He has authored 13 books and 120 articles. Ribenboim has been a professor of mathematics at Queen's University in Kingston, Ontario, and is now a professor emeritus.*Wik

DEATHS
1833 Daniel Friedrich Hecht (8 July 1777 in Sosa – 13 March 1833 in Saxony) was a German mathematician. He was a mine manager, then a teacher and finally a professor of mathematics. He is most notable for writing high school textbooks on maths and geometry. *Wik

1884 Siegfried Heinrich Aronhold (16 July 1819 Angerburg, East Prussia – 13 March 1884, Berlin, Germany) was a German mathematician who worked on invariant theory and introduced the symbolic method.*Wik

1933 Robert Thorburn Ayton Innes (10 Nov 1861; 13 Mar 1933) was a Scottish astronomer who discovered Proxima Centauri (1915), the closest star to earth after the Sun. Invited by David Gill to the Cape Observatory, South Africa (1894), he became a successful binary star observer with the 7-inch refractor (1628 discoveries). His most famous discovery, Proxima Centauri is a faint star near the binary star Alpha Centauri, which is so far south it is
 photo by Lowell Observatory
not visible from most of the northern hemisphere. He was also one of the first to see the Daylight Comet of 1910, though this comet was found independently by so many people in the Southern Hemisphere that no single "original" discoverer could be named. Innes recorded it on 17 Jan 1910. *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