## Saturday, 17 February 2018

### On This Day in Math - February 17

 Statue of Quetelet in Brussels

Inductive inference is the only process known to us by which essentially new knowledge comes into the world.
~Sir Ronald Aylmer Fisher

The 48th day of the year; 48 is the smallest number with exactly ten divisors. (This is an interesting sequence, and students might search for others. Finding the smallest number with twelve divisors will be easier than finding the one with eleven.)

48 is also the smallest even number that can be expressed as a sum of two primes in 5 different ways:

If n is greater than or equal to 48, then there exists a prime between n and 9n/8 This is an improvement on a conjecture known as Bertrand's Postulate. In spite of the name, many students remember it by the little rhyme, "Chebyshev said it, but I'll say it again; There's always a prime between n and 2n ." Mathematicians have lowered the 2n down to something like n+n.6 for sufficiently large numbers.

48 is the smallest betrothed (quasi-amicable) number. 48 and 75 are a betrothed pair since the sum of the proper divisors of 48 is 75+1 = 76 and the sum of the proper divisors of 75 is 48+1=49. (There is only a single other pair of betrothed numbers that can be a year day)

And 48 x 48 = 2304 but 48 x 84 = 4032.

EVENTS
1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (Aczel gives this date as the 19th but this date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

In 1857, the City of New York passed a charter to enable Peter Cooper to found a scientific institution in the city. He established the Cooper Union for the Advancement of Science and Art for the express purpose of improving the working classes by providing free education. Courses included algebra, geometry, calculus, chemistry, physics, mechanics, architectural and mechanical drawing. It also provided a School of Design for Women, a Musical Department, and a Free Library and Reading Room with all the periodicals of the day. By 1868, an article in the New York Times stated there were nearly 1500 students attached to the instiution, and the classes, which included night classes, were universally full. *TIS

In 1869, Dmitri Mendeleev cancelled a planned visit to a factory and stayed at home working on the problem of how to arrange the chemical elements in a systematic way. To begin, he wrote each element and its chief properties on a separate card and arranged these in various patterns. Eventually he achieved a layout that suited him and copied it down on paper. Later that same day he decided a better arrangement by properties was possible and made a copy of that, which had similar elements grouped in vertical columns, unlike his first table, which grouped them horizontally. These historic documents still exist, and mark the beginning of the form of the Periodic Table as commonly used today. (The date is given by the Julian calendar in use in Russia at the time.) *TIS

1994 A small satellite named Dactyl was found which orbits the asteroid Ida. This was the first discovery of a satellite orbiting and asteroid. Dactyl was discovered in images taken by the Galileo spacecraft during its flyby in 1993. Dactyl was found on 17 February 1994 by Galileo mission member Ann Harch, while examining delayed image downloads from the spacecraft.
It was named by the International Astronomical Union in 1994, for the mythological dactyls who inhabited Mount Ida on the island of Crete. It is only 1.4 kilometres (4,600 ft) in diameter. *Wik

In 1996, world chess champion Gary Kasparov defeated Deep Blue, IBM's chess-playing computer, by winning a six-game match 4-2, in a regulation-style match held in Philadelphia, as part of the ACM Computer Science Conference. Deep Blue is an improved version of the older Deep Thought, augmented by parallel special-purpose hardware. Deep Blue uses a selectively deepening search strategy, using improvements of the alpha-beta search strategy, with powerful evaluation functions. Transposition tables help avoid unnecessarily calculating the same position more than once. Two powerful databases further augment Deep Blue's play. *TIS On May 11, 1997, the machine won a six-game match by two wins to one with three draws against world champion Garry Kasparov, the first time the grandmaster ever lost a six-game match in championship play. *Wik

2015 After a weekend of celebrating, the 65th annual International Pancake race will take place in Liberal, Kansas, USA and Olney, England. The celebration is associated with Pancake day, which is often used as a name for Shrove Tuesday in many Western countries. History of the event, and a schedule of the (now) week-long activities is here. The race in 2016 was won by a woman from Olney,  The score now stands with Liberal winning 37 times, Olney 29.although according to legend, Olney Pancake Race began in 144, so Lliberal has to win a bunch of races to catch up.

BIRTHS
 *Wik
1201 Khawaja Muhammad ibn Muhammad ibn Hasan Tūsī (17 February 1201; Ṭūs, Khorasan – 25 June 1274; Baghdad), better known as Nasīr al-Dīn Tūsī was a Persian polymath and prolific writer: An architect, astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, and theologian
Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatory was constructed in Azarbaijan, west of Maragheh, the capital of the Ilkhanate Empire.
Based on the observations in this for the time being most advanced observatory, Tusi made very accurate tables of planetary movements as depicted in his book Zij-i ilkhani (Ilkhanic Tables). This book contains astronomical tables for calculating the positions
of the planets and the names of the stars. His model for the planetary system is believed to be the most advanced of his time, and was used extensively until the development of the heliocentric model in the time of Nicolaus Copernicus.
For his planetary models, he invented a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy's problematic equant for many planets, but was unable to find a solution to Mercury. The Tusi couple was later employed in Ibn al-Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model.
Al-Tusi was the first to write a work on trigonometry independently of astronomy. In his Treatise on the Quadrilateral he gave an extensive exposition of spherical trigonometry, distinct from astronomy. It was in the works of Al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long. He was also the first to list the six distinct cases of a right triangle in spherical trigonometry.
In his On the Sector Figure, appears the famous law of sines for plane triangles.

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

He also stated the law of sines for spherical triangles,discovered the law of tangents for spherical triangles, and provided proofs for these laws. *Wik

1723 Tobias Meyer (17 Feb 1723; 20 Feb 1762 at age 38) German astronomer who developed lunar tables that greatly assisted navigators in determining longitude at sea. Mayer also discovered the libration (or apparent wobbling) of the Moon. Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government.
These tables were good enough to determine longitude at sea with an accuracy of half a degree. Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death. The Board of Longitude sent Mayer's widow a payment of 3000 pounds as an award for the tables. *TIS Leonhard Euler described him as 'undoubtedly the greatest astronomer in Europe'. More notes on Meyer can be found on this blog at the Board of Longitude Project from the Royal Museums at Greenwich.
In 1758, Mayer attempted to define the number of colors that the eye can distinguish with accuracy. His color triangle was first published in 1775 by the Göttinger physicist Georg Christoph Lichtenberg — more than 12 years after Mayer’s death.

1765 Sir James Ivory (17 February 1765 – 21 September 1842) was a Scottish mathematician born in Dundee. He was essentially a self-trained mathematician, and was not only deeply versed in ancient and modern geometry, but also had a full knowledge of the analytical methods and discoveries of the continental mathematicians.
His earliest memoir, dealing with an analytical expression for the rectification of the ellipse, is published in the Transactions of the Royal Society of Edinburgh (1796); and this and his later papers on Cubic Equations (1799) and Kepler's Problem (1802) evince great facility in the handling of algebraic formulas. In 1804 after the dissolution of the flax-spinning company of which he was manager, he obtained one of the mathematical chairs in the Royal Military College at Marlow (afterwards removed to Sandhurst); and until the year 1816, when failing health obliged him to resign, he discharged his professional duties with remarkable success.*Wik It has been suggested that Ivory may have suffered from schizophrenia (*ALEX D. D. CRAIK) of some type throughout his life.

Ivory, because of his mental problems, tended to quarrel with his fellow mathematicians. His relations with Wallace deteriorated with arguments over Ivory's Attraction article to Encyclopaedia Britannica. Ivory's article on Capillary action for the same publication led to an argument with Thomas Young. Many other cases were simply caused by Ivory suffering from a quite incorrect belief that he was being persecuted by others. In fact he never joined the Royal Astronomical Society, despite his interests in astronomy, since he believed that members of that Society were systematically working against him. As De Morgan wrote that Ivory was of
... thoroughly sound judgement in every other respect seemed to be under a complete chain of delusions about the conduct of others to himself. But the paradox is this: - I never could learn that Ivory, passing his life under the impression that secret and unprovoked enemies were at work upon his character, ever originated a charge, imputed a bad motive, or allowed himself an uncourteous expression.
*SAU

1874 Thomas J. Watson Sr. is born. A shrewd businessman, Watson started his career as a cash register salesman, eventually taking the helm of IBM and directing it to world leadership in punch card equipment sales. Watson died in 1956 and control of IBM passed on to his son, Thomas Watson, Jr. who brought IBM into the electronic age and, after several bold financial risks, to dominance in the computer industry.*CHM

1888 Otto Stern (17 Feb 1888; 17 Aug 1969 at age 81) German-American scientist and winner of the Nobel Prize for Physics in 1943 for his development of the molecular beam as a tool for studying the characteristics of molecules and for his measurement of the magnetic moment of the proton. *TIS

1890 Ronald Aylmer Fisher FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation. Anders Hald called him "a genius who almost single-handedly created the foundations for modern statistical science" while Richard Dawkins called him "the greatest of Darwin's successors". In 2010 Dawkins named him "the greatest biologist since Darwin". Fisher was opposed to the conclusions of Richard Doll and A.B. Hill that smoking caused lung cancer. He compared the correlations in their papers to a correlation between the import of apples and the rise of divorce in order to show that correlation does not imply causation.
To quote Yates and Mather, "It has been suggested that the fact that Fisher was employed as consultant by the tobacco firms in this controversy casts doubt on the value of his arguments. This is to misjudge the man. He was not above
accepting financial reward for his labours, but the reason for his interest was undoubtedly his dislike and mistrust of puritanical tendencies of all kinds; and perhaps also the personal solace he had always found in tobacco."
After retiring from Cambridge University in 1957 he spent some time as a senior research fellow at the CSIRO in Adelaide, Australia. He died of colon cancer there in 1962.
He was awarded the Linnean Society of London's prestigious Darwin–Wallace Medal in 1958.
Fisher's important contributions to both genetics and statistics are emphasized by the remark of L.J. Savage, "I occasionally meet geneticists who ask me whether it is true that the great geneticist R.A. Fisher was also an important statistician"*Wik The stained glass window is from the Greatroom at Caius College.

1891 Abraham Halevi (Adolf) Fraenkel (February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel) known as Abraham Fraenkel, was an Israeli mathematician born in Germany. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo–Fraenkel axioms.*Wik

1905 Rózsa Péter (orig.: Politzer) (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 In 1951 she wrote the ﬁrst monograph on recursive function theory.

1950 Viktor Aleksandrovich Gorbunov (17 Feb 1950 in Russia - 29 Jan 1999 in Novosibirsk, Russia) He published his first paper in 1973 being a joint work with A I Budkin entitled Implicative classes of algebras (Russian). The implicative class of algebras is a generalisation of quasivarieties. The structural characteristics of the implicative class are studied in this paper. A second join paper with Budkin On the theory of quasivarieties of algebraic systems (Russian) appeared in 1975. In the same year he published Filters of lattices of quasivarieties of algebraic systems (Russian), this time written with V P Belkin. In fact he had written six papers before his doctoral thesis On the Theory of Quasivarieties of Algebraic Systems was submitted. He received the degree in 1978. Gorbunov continued working at Novosibirsk State University, being promoted to professor. He also worked as a researcher in the Mathematics Institute of the Siberian Branch of the Russian Academy of Sciences. *SAU

DEATHS
1600 Giordano Bruno (born 1548 - 17 Feb 1600)Italian philosopher, astronomer, mathematician and occultist whose theories anticipated modern science. The most notable of these were his theories of the infinite universe and the multiplicity of worlds, in which he rejected the traditional geocentric (or Earth-centred) astronomy and intuitively went beyond the Copernican heliocentric (sun-centred) theory, which still maintained a finite universe with a sphere of fixed stars. Although one of the most important philosophers of the Italian Renaissance, Bruno's various passionate utterings led to opposition. In 1592, after a trial he was kept imprisoned for eight years and interrogated periodically. When, in the end, he refused to recant, he was burned at the stake in Rome for heresy.*TIS Professor Rickey of USMA disagrees about Bruno's "failure to recant." "It is a nineteenth century myth that he refused to recant his view that the earth moves." *VFR

1680 Jan Swammerdam (February 12, 1637, Amsterdam – February 17, 1680) was a Dutch biologist and microscopist. His work on insects demonstrated that the various phases during the life of an insect—egg, larva, pupa, and adult—are different forms of the same animal. As part of his anatomical research, he carried out experiments on muscle contraction. In 1658, he was the first to observe and describe red blood cells. He was one of the first people to use the microscope in dissections, and his techniques remained useful for hundreds of years.*Wik

1865 George Phillips Bond (20 May 1825, 17 Feb 1865 at age 39) American astronomer who made the first photograph of a double star, discovered a number of comets, and with his father discovered Hyperion, the eighth moon of Saturn. *TIS

1867 Alexander Dallas Bache (19 Jul 1806, 17 Feb 1867 at age 60) was an American physicist who was Ben Franklin's great grandson and trained at West Point. Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth (1856) by studying records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2.2- mile average depth for the Pacific (which is within 15% of the presently accepted value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats. *TIS

1874 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832.  It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.

1875 Friedrich Wilhelm August Argelander (22 Mar 1799, 17 Feb 1875 at age 75)
German astronomer who established the study of variable stars as an independent branch of astronomy and is renowned for his great catalog listing the positions and brightness of 324,188 stars of the northern hemisphere above the ninth magnitude. He studied at the University of Königsberg, Prussia, where he was a pupil and later the successor of Friedrich Wilhelm Bessel. In 1837, Argelander published the first major investigation of the Sun's motion through space. In 1844 he began studies of variable stars.*TIS

1947 Ettore Bortolotti (6 March 1866 in Bologna, Kingdom of Sardinia (now Italy) - 17 Feb 1947 in Bologna, Italy) Italian mathematician who worked in various areas in analysis. He was interested in the history of mathematics. *SAU

1974 Heinrich Franz Friedrich Tietze contributed to the foundations of general topology and developed important work on subdivisions of cell complexes. The bulk of this work was carried out after he took up the chair at Munich in 1925.*SAU

2012 Nicolaas Govert "Dick" de Bruijn (9 July 1918 – 17 February 2012) was a Dutch mathematician, affiliated as professor emeritus with the Eindhoven University of Technology. He received his Ph.D. in 1943 from Vrije Universiteit Amsterdam.
De Bruijn covered many areas of mathematics. He is especially noted for the discovery of the De Bruijn sequence. He is also partly responsible for the De Bruijn–Newman constant, the De Bruijn–Erdős theorem (in both incidence geometry and graph theory) and the BEST theorem. He wrote one of the standard books in advanced asymptotic analysis (De Bruijn, 1958). De Bruijn also worked on the theory of Penrose tilings. In the late sixties, he designed the Automath language for representing mathematical proofs, so that they could be verified automatically (see automated theorem checking). Lately, he has been working on models for the human brain.*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