Sunday 16 February 2020

On This Day in Math - February 16

The Goose Girl Fountain in Gottingen

Whenever you can, count.
~Sir Francis Galton

The 47th day of the year; 47 is a Thabit number, named after the Iraqi mathematician Thâbit ibn Kurrah number, of the form 3 * 2n -1 (sometimes called 3-2-1 numbers). He studied their relationship to Amicable numbers. All Thabit numbers expressed in binary end in 10 followed by n ones, 47 in binary is 101111.
(The rule is that if p=3*2n-1 -1, q= 3*2n -1, and r = 9*2n-1 -1, are all prime, then 2npq and 2nr are amicable numbers.

3^3^3^3^3^3^3 has 47 distinct values depending on parentheses. *Math Year-Round ‏@MathYearRound

"The 47 Society is an international interest-group that follows the occurrence and recurrence of the quintessential random number: 47. Many suspect that the coincidental nature of 47 carries some mystical, metaphysical and/or scientific significance." *

Mario Livio has pointed out that this date written month day as 216, 216=63 and also 216=33+43+53

The 47th day gives me a reason to include this brief story of Thomas Hobbes from Aubrey's "Brief Lives". The 47th proposition of Libre I of The Elements (The Pythagorean Theorem) seemed so obviously false to him that, in following the reasoning back, his life was changed:
He was (vide his life) 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman’s library in . . . , Euclid’s Elements lay open, and ’twas the 47 El. libri I. He read the proposition. ‘By† G—,’ sayd he, ‘this is impossible!’So he reads the demonstration of it, which referred him back to such a propo- sition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps,(and so back to the beginning) that at last he was demonstratively convinced of that trueth. This made him in love with geometry.


1615 Galileo sends Piero Dini a modified copy of his letter to Castelli which had been the basis of an accusation of heresy by Nicolo Lorini to the Holy office in Rome. He included a cover letter on this date downplaying some of the points in his original and asked Dini to show it to Cardial Bellarmine, the chief theologian of the church. *Brody & Brody, The Science Class You Wish You Had

1745 Euler in a letter to Goldbach, first mentions factorization of a number using the representation of the sum of two squares . *Oystein Orr, Number Theory and Its History
Included in the letter is the proof that all integers that are the sum of two squares in more than one way must be composite; there are no prime numbers that can be expressed as the sum of two squares in more than one way.

In 1880, the American Society of Mechanical Engineers was founded when 40 engineers from eight states met in New York City in the office of American Machinist. In the same year, an organizational meeting was held on Apr 7, and the first annual meeting took place 4-5 Nov. Robert Henry Thurston was its first president. Thurston had established an engineering school at the new Stevens Institute of Technology in New Jersey and would later create an engineering school at Cornell. *TIS

1910 At 6pm Richard Courant was administered his oral exams by Hilbert (who left early), Voight (who did not appear), and Husserl (who arrived late). Afterwards, “the little Courant” as he was known, gave the customary kiss to the little goose girl in the fountain in the square, and then hired a droschke and his two friends drove him around the city announcing to all “Dr. Courant, Summa Cum Laude.” *Reid, Hilbert, pg 124

1912 ‏Thomas Jennings, hanged 16 Feb 1912, was the first US murder case decided with fingerprint evidence. *@executedtoday

In 1948, Miranda, a famous moon of Uranus, was photographed for first time. It was discovered by Gerard Kuiper, the Dutch astronomer, who also found Neptune's moon Nereid (1949). Miranda is the smallest of the five 5 major satellites of Uranus, and has a diameter of 480 km. When Voyager 2 passed closely by Miranda in 1986, it showed it was one of the most interesting satellites in the solar system, with a complex geological history. The numerous pictures it took of the surface showed a vast and diverse array of fractures, faults, grooves and craters unlike anything ever seen before. The large (318 km diam.) circular region is named the Arden Corona. Miranda is named after a character in Shakespeare's "The Tempest." Arden is the name of a forest, in which his play "As You Like It." is set.*TIS

1982 Sweden issued three stamps picturing impossible figures. Does this twisted triangle have a name? [Scott #1396–8] *VFR  Yes, The figure is called a Tribar, and sometimes a Penrose Triangle.  It was firstly painted in 1934 by swedish painter Oscar Reutersvärd. He drew his version of triangle as a set of cubes in parallel projection.  Roger Penrose, and his father, Lionel also independently discovered the triangle in the 1950's.  Maurice Escher used and popularized the idea even more in his drawings. 
There are at least two sculptures depicting the tribar when viewed from the right perspective.  One is in Perth Australia (shown below), and another in  Gotschuchen, Austria.

1984 In a Dungeons of Doom computer adventure game at the University of Texas at Austin, the Rogue, manipulated by an expert system, descended through the 26 levels of the dungeons, fought off all monsters, seized the Amulet of Yendor, amassed a considerable pile of gold and returned safely to the surface, being the first ever to do so. See Scientific American, February 1985, esp. p. 19. *VFR

1993 Great Britain issues a set of stamps with four views (dial and hands; train remontoire; temperature compensation-curb; top plate and balance-brake) of Harrison’s Marine Timekeeper number four to commemorate the 300th anniversary of Harrison’s birth year (his birthdate and date of death were both March 24). Harrison was a self-educated English clockmaker. He invented the marine chronometer, a long-sought device in solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionizing and extending the possibility of safe long distance sea travel in the Age of Sail. The problem was considered so intractable that the British Parliament offered a prize of £20,000 (comparable to £2.87 million in modern currency) for the solution.*Wik

1514 Georg Joachim Rheticus (16 Feb 1514; 4 Dec 1576 at age 62) German astronomer and mathematician who was among the first to adopt and spread the heliocentric theory of Nicolaus Copernicus. He was first taught by his father, a physician, who was beheaded for sorcery (1528) while Rheticus was still a teenager. He is best known as the first disciple of Copernicus. In 1540, Rheticus published the first account of the heliocentric hypothesis which had been elaborated by Copernicus, entitled Narratio prima, which was explicitly authorised by Copernicus, who also asked for his friend's aid in editing the edition of his De revolutionibus orbium coelestium ("On the revolutions of the heavenly spheres"). Rheticus was the first mathematician to regard the trigonometric functions in terms of angles rather than arcs of a circle.*TIS

For much of his life, Rheticus displayed a passion for the study of triangles, the branch of mathematics now called trigonometry. In 1542 he had the trigonometric sections of Copernicus' De revolutiobis published separately under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles). In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). Neither did he use the current names for any of them. Prior to Rheticus, European mathematicians used only the sine, and the versed sine (although Johannes Regiomontanus, Tabulae directionum et profectionum, Augsburgii 1490 had calculated what is essentially the tangent.) Rheticus seems to have had an aversion to the term sine. He called his principal units the perpendicular of the first species (sine), the base of the first species (cosine) with the hypotenuse being the hypotenuse was the radius for the first species triangle. Then, he decided to construct a triangle of the second species with the base as a radius. Then the perpendicular of the second species (tangent) and the hypotenuse of the second species(secant). For the third species he chooses the perpendicular of the triangle as the radius, and so the base of the third species (cotangent) and hypotenuse of the thrid species (cosecant) are found.
This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements.
At his death, the Science of Triangles was still unfinished. However, paralleling his own relationship with Copernicus, Rheticus had acquired a student who devoted himself to completing his teacher's work. Valentin Otto oversaw the hand computation of approximately 100,000 ratios to at least ten decimal places. When completed in 1596, the volume, Opus palatinum de triangulis, filled nearly 1,500 pages. Its tables were accurate enough to be used in astronomical computation into the early twentieth century. *Wik

1698 Pierre Bouguer (16 Feb 1698; 15 Aug 1758 at age 60) In 1727 he won the prize competition of the Acad´emie Royal des Sciences on the masting of ships. In this competition Euler only received the “accessit.” *VFR
Two days before (Aug 13)Charles-Etienne-Louis Camas was elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. (did Bouguer get the other half? Did Euler get any? is one, or more of these three pieces of information incorrect?)*PB
French physicist whose work founded photometry, the measurement of light intensity. He was a child prodigy, a professor at age 15, following his father, Jean Bouguer, in hydrography - the study of bodies of water, both salt and fresh. He participated on the expedition to Peru (1735-44) to measure an arc of the meridian near the equator. In 1729, he invented a photometer to compare the intensity of two light sources illuminating separate halves of translucent paper. The eye itself, he determined, could not be used as a meter, but could establish the equality of brightness of adjacent surfaces. He determined the sun was 300 times brighter the moon. Bouguer's law gives the attenuation of a beam of light by an optically homogeneous (transparent) medium.*TIS

1822 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map in The Times *TIS

1838 Henry Adams born. In his autobiography, The Education of Henry Adams, he wrote in the third person: “At best he would never have been a mathematician; at worst he would never have cared to be one; But he needed to read mathematics, like any other universal language, and he never reached the alphabet.” *VFR

1903 Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigour of modern algebraic geometry. Another contribution of his was the introduction of finite and non-continuous structures into geometry. In his best known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: combinatorial geometry.
In 1938 he lost his professorship as a result of the anti-Jewish laws enacted under Benito Mussolini's government; he spent the next 8 years in Great Britain (mostly at the University of Manchester), then returned to Italy to resume his academic career *Wik

1937 Yuri Ivanovitch Manin (1937, Simferopol - ) is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations. The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties. He wrote an influential book on cubic surfaces and cubic forms, showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra. He also indicated the role of the Brauer group, via Grothendieck's theory of global Azumaya algebras, in accounting for obstructions to the Hasse principle, setting off a generation of further work. He has also written on Yang-Mills theory, quantum information, and mirror symmetry.*Wik

1636 Henry Gellibrand (17 Nov 1597, 16 Feb 1636 at age 38) English astronomer and mathematician who co-discovered (with John Marr) the geomagnetic secular variation. This refers to the magnetic declination of the earth's magnetic field, the angle between magnetic north and true north, changing on a long-term time scale over years. He detected the direction of a compass needle in London had changed by seven degrees over a period of a half-century. He became professor of astronomy at Gresham College, London on 2 Jan 1627. His navigation textbooks helped improve English navigation at the time.Using manuscripts left unfinished when his friend Henry Briggs died (1630), he completed volume two of Briggs's Trigonometrica Britannica, in 1633. Gellibrand published A Discourse Mathematicall on the Variation of the Magneticall Needle, in 1635. He died the following year, at age 39.*TIS He was Professor at Gresham College, succeeding Edward Gunter in 1626. He was buried in St Peter Le Poer. (London, demolished in 1907) *Wik

1892 Thomas Archer Hirst FRS (22 April 1830 – 16 February 1892) was a 19th century mathematician, specializing in geometry. He was awarded the Royal Society's Royal Medal in 1883.Hirst was a projective geometer in the style of Poncelet and Steiner. He was not an adherent of the algebraic geometry approach of Cayley and Sylvester, despite being a personal friend of theirs. His specialty was Cremona transformations.*Wik

1956 Meghnad Saha FRS (6 October 1893 – 16 February 1956) was an Indian astrophysicist best known for his development of the Saha ionization equation, used to describe chemical and physical conditions in stars. Saha was the first scientist to relate a star's spectrum to its temperature, developing thermal ionization equations that have been foundational in the fields of astrophysics and astrochemistry. He was repeatedly and unsuccessfully nominated for the Nobel Prize in Physics. Saha was also politically active and was elected in 1952 to India's parliament. *Wik

1957 Sir John Sealy Edward Townsend (7 Jun 1868, 16 Feb 1957 at age 88) British physicist who pioneered in the study of electrical conduction in gases. In 1898 he made the first direct measurement of the unit electrical charge (e). As a postgraduate, he was a research student of J. J. Thomson. In 1897, Townsend developed the falling-drop method for measuring e, using saturated clouds of charged water droplets (extended by Robert Millikan's highly accurate oil-drop method). He was first to explain how electric discharges pass through gases (Electricity in Gases, 1915) whereby motion of electrons in an electric field releases more electrons by collision. These in turn collide releasing even more electrons in a multiplication of charges known as an avalanche. *TIS

1977 Rózsa Péter (orig.: Politzer), Hungarian name Péter Rózsa, (17 February 1905–16 February 1977) was a Hungarian mathematician. She is best known for her work with recursion theory.
Péter was born in Budapest, Hungary, as Rózsa Politzer (Hungarian: Politzer Rózsa). She attended Eötvös Loránd University, where she received her PhD in 1935. After the passage of the Jewish Laws of 1939 in Hungary, she was forbidden to teach because of her Jewish origin. After the war she published her key work, Recursive Functions.
She taught at Eötvös Loránd University from 1955 until her retirement in 1975. She was a corresponding member of the Hungarian Academy of Sciences (1973).*Wik

1980 Edward Copson (21 Aug 1901; 16 Feb 1980) English mathematician known for his studies in classical analysis, differential and integral equations, and their use in mathematical physics. After graduating from Oxford University with a B.A. degree in 1922, he moved to Scotland where he spent the nearly all of his career. His first book, The Theory of Functions of a Complex Variable (1935) was immediately successful. He was a co-author for his next book, The Mathematical Theory of Huygens' Principle (1939). By 1975, he had published four more books, on asymptotic expansions, metric spaces and partial differential equations. Many of the papers he wrote bridged mathematics and physics, of which his last showed his interest in astrophysics, Electrostatics in a Gravitational Field (1978) which was relevant to Black Holes.*TIS

1997 Chien-Shiung Wu (simplified Chinese: 吴健雄; traditional Chinese: 吳健雄; pinyin: Wú Jiànxióng, May 31, 1912 – February 16, 1997) was a Chinese American experimental physicist who made significant contributions in the field of nuclear physics. Wu worked on the Manhattan Project, where she helped develop the process for separating uranium metal into uranium-235 and uranium-238 isotopes by gaseous diffusion. She is best known for conducting the Wu experiment, which contradicted the hypothetical law of conservation of parity. This discovery resulted in her colleagues Tsung-Dao Lee and Chen-Ning Yang winning the 1957 Nobel Prize in physics, and also earned Wu the inaugural Wolf Prize in Physics in 1978. Her expertise in experimental physics evoked comparisons to Marie Curie. Her nicknames include "the First Lady of Physics", "the Chinese Madame Curie", and the "Queen of Nuclear Research".*Wik

1997 Leon Bankoff (December 13, 1908, New York City, NY -February 16, 1997, Los Angeles, CA), was an American dentist and mathematician.
After a visit to the City College of New York, Bankoff studied dentistry at New York University. Later, he moved to Los Angeles, California, where he taught at the University of Southern California; while there, he completed his studies. He practiced over 60 years as a dentist in Beverly Hills. Many of his patients were celebrities.
Along with Bankoff's interest in dentistry were the piano and the guitar. He was fluent in Esperanto, created artistic sculptures, and was interested in the progressive development of computer technology. Above all, he was a specialist in the mathematical world and highly respected as an expert in the field of flat geometry. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with Paul Erdős in a mathematics paper and therefore has an Erdős number 1.
From 1968 to 1981, Bankoff was the editor of the Problem Department of Pi Mu Epsilon Journals, where he was responsible for the publication of some 300 top problems in the area of plane geometry, particularly Morley's trisector theorem, and the arbelos of Archimedes. Among his discoveries with the arbelos was the Bankoff circle, which is equal in area to Archimedes' twin circles. Martin Gardner called Bankoff, “one of the most remarkable mathematicians I have been privileged to know.” *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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