## Tuesday, 17 October 2017

### On This Day in Math - October 17

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.

The 290th day of the year, 290 is a sphenic (wedge) number, the product of three distinct primes (290 = 2*5*29).

It is also the sum of four consecutive primes (67 + 71 + 73 + 79) [Students might try to construct and examine a list of numbers that can be written as the sum of two or more consecutive primes]

290 is conjectured to be the smallest number such that the Reverse and Add! algorithm in base 4 does not lead to a palindrome.

290 is the tenth prime(29) times ten

EVENTS

1604 In Prague, Kepler first observes the supernova now known as supernova 1604 and Kepler's Star. The first recorded observation of this supernova was in northern Italy on October 9, 1604. It was named after Kepler because his observations tracked the object for an entire year and because of his book on the subject, entitled De Stella nova in pede Serpentarii ("On the new star in Ophiuchus's foot", Prague 1606). Here is an image of Kepler's De Stella Nova, open to the foldout star map placing the supernova of 1604, from the twitter feed of @Libroantiguo . It was the second supernova to be observed in a generation (after SN 1572 seen by Tycho Brahe in Cassiopeia). No further supernovae have since been observed with certainty in the Milky Way, though many others outside our galaxy have been seen since S Andromedae. *Wik

1776 Euler read a paper to the St. Petersburg Academy of Science entitled “De quadratis magicis,” in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. *Peter Ullrich, “An Eulerian square before Euler and an experimental design before R. A. Fisher: On the early history of Latin squares,” Chance, vol. 12, no. 1, Winter 1999, pp. 22–26.

1831 After discovering induced current on October 1st using two electrified coils,  on the 17th of October Michael Faraday  observers the same effect on the galvanometer when he inserts a permanent steel magnet into the electrified coil. *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton Writes to his friend, John Graves, with a description of Quaternions. By December, Graves will have extended the idea to an eight dimensional algebra which will become "octonians".

Observatory, October 17, 1843
My dear Graves,|A very curious train of mathematical speculation occurred to me
yesterday, which I cannot but hope will prove of interest to you. You know that I have long
wished, and I believe that you have felt the same desire, to possess a Theory of Triplets,
analogous to my published Theory of Couplets, and also to Mr. Warren's geometrical representation
of imaginary quantities. Now I think that I discovered1 yesterday a theory of
quaternions which includes such a theory of triplets.

The complete letter is available at this site. *David R. Wilkins, *John Derbyshire, Unkown Quantity
In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. *Wik

1858 DeMorgan writes a letter about Euler’s  prodigious output. *W W Rouse Ball, from The genius of Euler: reflections on his life and work, By William Dunham, pg 89

1933 Albert Einstein seeks asylum in the US, one of many Jewish/left-wing intellectuals fleeing the Nazi govt in Germany and Europe. The Nazi government put a bounty now worth £50,000 on his head while a German magazine included him in a list of the Nazis’ enemies who were 'not yet hanged'.

1952 D. H. Lehmer, University of California, announced that 2n − 1 for n = 2203 and 2281 are Mersenne primes. He was aided by a SWAC computing machine, the ﬁrst result taking 59 minutes. *VFR This may have been predated by Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) at Berkeley may have beaten him by a week or so on October 7th of the same year.
D. H. Lehmer continued his fathers interest in combinatorial computing and in fact wrote the article "Machine tools of Computation," which is chapter one in the book "Applied Combinatorial Mathematics," by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series. In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. (see below)*Wik

1952 The California Supreme Court declared the state loyalty oath unconstitutional and declared that the eighteen faculty members who had refused to sign the oath be reinstated.*VFR

1978 James Burke's history of science series Connections first airs, on BBC Television in the United Kingdom (with accompanying book). *Wik

1983 Gerard Debreu, who holds a joint appointment in Mathematics and Economics at Berkeley, won a Nobel Prize for his work in mathematical economics. For a non-technical description of his work see The Mathematical Intelligencer, 6(1984), no. 2, pp. 61–62. *VFR

2012 Car size pieces of Halley's Comet lit up the skies over the Bay Area in California. Hundreds of residents from Oakland, San Francisco and Santa Cruz called ABC News station KGO-TV, reporting a loud boom, explosions and streaks of light around 7:45 p.m. local time. The Orionids are one of two annual meteor showers produced by icy pieces of Halley's Comet. The other shower, called the Eta Aquarids, peaks each year in early May, according to NASA. Video *ABC News

BIRTHS

1759 Jakob II Bernoulli (17 October 1759, Basel – 3 July 1789, Saint Petersburg), younger brother of Johann III Bernoulli. Having finished his literary studies, he was, according to custom, sent to Neuchâtel to learn French. On his return he graduated in law. This study, however, did not check his hereditary taste for geometry. The early lessons which he had received from his father were continued by his uncle Daniel, and such was his progress that at the age of twenty-one he was called to undertake the duties of the chair of experimental physics, which his uncle’s advanced years rendered him unable to discharge. He afterwards accepted the situation of secretary to count de Brenner, which afforded him an opportunity of seeing Germany and Italy. In Italy he formed a friendship with Lorgna, professor of mathematics at Verona, and one of the founders of the Società Italiana for the encouragement of the sciences. He was also made corresponding member of the royal society of Turin; and, while residing at Venice, he was, through the friendly representation of Nicolaus von Fuss, admitted into the academy of St Petersburg. In 1788 he was named one of its mathematical professors. *Wik
He drowned while bathing in the Neva in July 1789, a few months after his marriage with a granddaughter of Leonhard Euler.  (Can't tell your Bernoulli's without a scorecard?  Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1788 Paul Isaak Bernays (17 Oct 1888; 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS

1927 Friedrich Ernst Peter Hirzebruch (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in the Germany of the postwar period.
Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*Wik

DEATHS

1817 John West (10 April 1756 in Logie (near St Andrews), Scotland - 17 Oct 1817 in Morant Bay, Jamaica) The achievements of the little-known Scottish mathematician, John West (1756–1817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of “continental” analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.
First an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described. *abstract for Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica, Alex D.D. Craik

1877 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1923 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.
This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1937 Frank Morley (9 Sept 1860 in Woodbridge, Suffolk, England-17 Oct 1937 in Baltimore, Maryland, USA) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational literature.  Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle. In 1899 he observed the relationship described above, but could find  no  proof. It spread from discussions with his friends to become an item  of  mathematical gossip. Finally in 1909 a trigonometric solution was   discovered by M. Satyanarayana. Later an elementary proof was developed.   Today the preferred proof is to begin with the result and work   backward. Start with an equilateral triangle and show that the vertices   are the intersection of the trisectors of a triangle with any given set   of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25. Find more about this unusual man here.  *PB

1941 John Stanley Plaskett (17 Nov 1865, 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years.*TIS

1952 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.  Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Académie des Sciences in 1943. *SAU

1963 Jacques-Salomon Hadamard (8 Dec 1865, 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n/ln(n) is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vallée Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalization of Green's functions (1932). *TIS

1978 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik

2008 Andrew Mattei Gleason (November 4, 1921 – October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. (In graph theory, the Greenwood–Gleason graph (Image at top of page) is also known as the Clebsch graph. It is an undirected graph with 16 vertices and 40 edges. It is named after Alfred Clebsch, a German mathematician who discovered it in 1868. It is also known as the Greenwood–Gleason graph after the work of Robert M. Greenwood and Andrew M. Gleason (1955), who used it to evaluate the Ramsey number R(3,3,3) = 17 *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

## Monday, 16 October 2017

### On This Day in Math - Oct 16

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.
~Harish-Chandra

The 289th day of the year; 289 is a Friedman number since (8 + 9)2 = 289 (A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷) and sometimes exponentiation.)Students might try to find the first few multi-digit Friedman numbers.

289 is the square of the sum of the first four primes, 289 = (2 + 3 + 5 + 7)2

289 is the largest 3-digit square with increasing digits.

289 is the hypotenuse of a primitive Pythagorean triple. Find the legs students!

EVENTS

1707 Roger Cotes elected ﬁrst Plumian Professor of Astronomy and Experimental Philosophy at Cambridge at age 26. He is best known for his meticulous and creative editing of the second edition (1713) of Newton’s Principia. He was also an important developer of the integral calculus. *Ronald Gowing, Roger Cotes, Natural Philosopher, p. 14

1797 Gauss records in his diary that he has discovered a new proof of the Pythagorean Theorem. See Gray, Expositiones Mathematicae, 2(1984), 97–130. *VFR

1819  Thomas Young writes to Fresnel to thank him for a copy of his memoirs (sent to Young by Arago). "I return a thousand thanks, Monsieur, for the gift of your admirable memoir, which surely merits a very high rank amongst the papers which have contributed most to the progress of optics." *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton discovered quaternions while walking along the Royal Canal in Dublin and immediately scratches the multiplication formulas on a bridge. Today a plaque on the bridge reads, "Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a ﬂash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = −1 & cut it in a stone on this bridge." Since 1989, the Department of Mathematics of the National University of Ireland, Maynooth has organized a pilgrimage, where scientists (including the physicists Murray Gell-Mann in 2002, Steven Weinberg in 2005, and the mathematician Andrew Wiles in 2003) take a walk from Dunsink Observatory to the Royal Canal bridge where no trace of Hamilton's carving remains, unfortunately.
Here is how Hamilton described his memory of the discovery of the Quaternions to his son, "Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *from Hamilton By Sir Robert Stawell Ball.

The plaque says:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
i2 = j2 = k2 = i j k = −1
& cut it on a stone of this bridge

(Quatenion was a Latin term before Hamilton used it.  Milton uses it in Paradise Lost to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned. *John Cook )

In 1982, Halley's Comet was observed on its 30th recorded visit to Earth, first detected using the 5-m (200-in) Hale Telescope at the Mount Palomar Observatory by a team of astronomers led by David Jewett and G. Edward Danielson. They found the comet, beyond the orbit of Saturn, about 11 AU (1.6 billion km) from the Sun. While 50 million times fainter than the faintest objects our eyes can see, they needed to use not only the largest American telescope but also special electronic equipment developed for the Space Telescope. In 1705, Halley used Newton's theories to compute the orbit and correctly predicted the return of this comet about every 76 years. After his death, for correctly predicting its reappearance, it was named after Halley. *TIS (The next predicted perihelion of Halley's Comet is 28 July 2061)
In 1982 the first image of the returning Halley's Comet was recorded with the 200-inch Hale telescope at Palomar Mountain. Caltech astronomers David Jewitt and G. Edward Danielson found the comet when it was still beyond the orbit of Saturn, more than 1.6 billion kilometers (960 million miles) from the Sun. *National Air and Space Museum

1988 Connect Four Solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

2016 The 27th Hamilton walk takes place on this day. Students, professors, and math lovers in general will gather at the Dunsink Observatory around 3:30 pm and proceed to Broombridge in Cabra where he had his Eureka moment about Quaternions. (see 1843 in Events above) The annual event is part of Irish Math week.

BIRTHS
1689 Robert Smith (16 October,1689 – 2 February, 1768) was an English mathematician and Master of Trinity College.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. He entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739. From 1716 to 1760 he was Plumian Professor of Astronomy,and was chosen Master in 1742, in succession to Richard Bentley.
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, (which was the principal textbook on Optics in the 18th Century) , and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel.
In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor. *Wik

1879 Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British logician and follower of Bertrand Russell. He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox. He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study. He was London editor for The Monist. *Wik

1882 Ernst Erich Jacobsthal (16 October 1882, Berlin – 6 February 1965, Überlingen) was a German mathematician, and brother to the archaeologist Paul Jacobsthal.
In 1906, he earned his PhD at the University of Berlin, where he was a student of Georg Frobenius, Hermann Schwarz and Issai Schur; his dissertation, Anwendung einer Formel aus der Theorie der quadratischen Reste (Application of a Formula from the Theory of Quadratic Remainders), provided a proof that prime numbers of the form 4n + 1 are the sum of two square numbers. *Wik

1930 John Charlton Polkinghorne KBE FRS (born 16 October 1930) is an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest in 1982. He served as the president of Queens' College, Cambridge from 1988 until 1996.*Wik

DEATHS

1937 William Sealy Gosset (13 June 1876 in Canterbury, England - 16 October 1937 in Beaconsfield, England) Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.

Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.
Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.

McMullen says:-

To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.

From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.
Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU

1983 Harish-Chandra (11 October 1923 – 16 October 1983) was an Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.*Wik

1998 Jonathan Bruce Postel (6 Aug 1943, 16 Oct 1998) American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*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

## Sunday, 15 October 2017

### On This Day in Math - October 15

Many have argued that a vacuum does not exist, others claim it exists only with difficulty in spite of the repugnance of nature; I know of no one who claims it easily exists without any resistance from nature.
— Evangelista Torricelli in a Letter to Michelangelo Ricci

The 288th day of the year; 288 is the super-factorial of four. 1! x 2! x 3! x 4! =288. It is important that math students learn not to say this number in public as it is two gross. (I apologize for the really bad pun)

288 is also the sum of the first four integers raised to their own power $1^1 + 2^2 + 3^3 + 4^4 = 288$

288 is the smallest non-palindrome, non-square, that when multiplied by its reverse is a square: 288 x 882 = 254,016 = 5042.

EVENTS

1582 St Theresa of Avila died overnight on the night between the 4th and the 15th of October. On that day the Gregorian calendar went into effect in Spain and the day after the 4th, was the 15th in order to catch up for the misalignment of the Julian Calendar. *VFR

1698 King William III commissioned Edmund Halley as Royal Naval Captain of the HMS
Paramore and provided him with a complete set of instructions. The Admiralty’s instructions to Halley dated 15 October 1698 were :
Whereas his Maty. has been pleased to lend his Pink the Paramour for your proceeding with her on an Expedition, to improve the knowledge of the Longitude and variations of the Compasse, which Shipp is now compleatly Man’d, Stored and Victualled at his Mats. Charge for the said Expedition ... *Lori L. Murray, The Construction of Edmond Halley’s 1701 Map of Magnetic Declination

1783 The ﬁrst manned ascension in a balloon. After the ﬂight of September 19, 1783, Louis XVI forbade men to go aloft, making the adventurers furious. Later he extended the privilege to convicts, ﬁguring they were expendable. de Rozier’s loud fulmigations against such glory for “vile criminals” soon changed the king’s mind. The hydrogen balloon, Aerostat Reveillon, carrying Pilâtre, first man to leave the earth, rose to the end of its 250- ft tether. It stayed aloft for 15 minutes, then landed safely nearby.
On 21 Nov 1783, untethered, Pilâtre and Marquis d'Arlande made the first manned free flight, across Paris. On 15 Jun 1785, Pilâtre attempt the first east-to-west crossing of the English Channel with a hybrid balloon combining lift from both hydrogen and hot air. Within minutes of launch, the craft exploded, and plunged to the rocks on the coast of Wimereux. Neither Pilâtre nor his co-pilot, Romain, survived the crash. *TIS (American Scientist and U S emissary to the court of Louis XVI, Ben Franklin, was present for some of the Balloon ascensions in 1783. When asked what was the use of Ballooning, he replied, “Of what use is a newborn baby?”)

In 1827, Charles Darwin was accepted into Christ's College at Cambridge, but did not start until winter term because he needed to catch up on some of his studies. A grandson of Erasmus Darwin of Lichfield, and of Josiah Wedgwood, he had entered the University of Edinburgh in 1825 to study medicine, intending to follow his father Robert's career as a doctor. However, Darwin found himself unenthusiastic about his studies, including that of geology. Disappointing his family that he gave up on a medical career, he left Edinburgh without graduating in April 1827. His scholastic achievements at Cambridge were unremarkable, but after graduation, Darwin was recommended by his botany professor to be a naturalist to sail on HM Sloop Beagle. *TIS

1956 The first FORTRAN reference manual is released on October 15, 1956, six months before the first compiler's release. Only 60 pages long, with large print and wide margins, that first programming language was miniscule by today's standard. The original FORTRAN development team comprised John Backus, Sheldon Best, Richard Goldberg, Lois Mitchell Haibt, Harlan Herrick, Grace Mitchell, Robert Nelson, Roy Nutt, David Sayre, Peter Sheridan, and Irving Ziller.*CHM

In 2003, China became the third nation to send a man into space. Lieutenant Colonel Yang Liwei, 38, was launched on a Long March CZ-2F rocket in the Shenzhou-5 spacecraft at 9 am local time (1 am GMT). He completed 14 Earth orbits during a 21-hour flight which ended with a parachute-assisted landing in the on the grasslands of Inner Mongolia in northern China. The Shenzhou spacecraft was based on the three-seat Russian Soyuz capsule, but with extensive modifications. The country began planning manned spaceflight in 1992. Russia began providing advice on technology and astronaut training in 1995. The first of four unmanned test flights of a Shenzhou craft (took place in Nov 1999. The name Shenzhou translates as "divine vessel." *TIS

BIRTHS

1608 Evangelista Torricelli (15 Oct 1608; 25 Oct 1647) Born in Faenza, Italy, Torricelli was an Italian physicist and mathematician who invented the barometer and whose work in geometry aided in the eventual development of integral calculus. Inspired by Galileo's writings, he wrote a treatise on mechanics, De Motu ("Concerning Movement"), which impressed Galileo. He also developed techniques for producing telescope lenses. The barometer experiment using "quicksilver" filling a tube then inverted into a dish of mercury, carried out in Spring 1644, made Torricelli's name famous. The Italian scientists merit was, above all, to admit that the effective cause of the resistance presented by nature to the creation of a vacuum (in the inverted tube above the mercury) was probably due to the weight of air. *TIS He succeeded his teacher, Galileo as professor of mathematics at Florence. One of his most amazing discoveries was a solid which had inﬁnite length but ﬁnite volume. He also invented the mercury barometer.*VFR

1735 Jesse Ramsden FRSE (15 October 1735 – 5 November 1800) was an English astronomical and scientific instrument maker.
Ramsden created one of the first high-quality dividing engines. This machine permitted the automatic and highly accurate division of a circle into degrees and fractions of degrees of arc.The machine  led to mass production of precision octants and sextants and gave British manufacturers dominance in the field of marine instruments for decades.  His invention was so valuable to the nation’s maritime interests that he received a share of the Longitude Prize.
His most celebrated work was a 5-feet vertical circle, which was finished in 1789 and was used by Giuseppe Piazzi at Palermo in constructing his catalog of stars. He was the first to carry out in practice a method of reading off angles (first suggested in 1768 by the Duke of Chaulnes) by measuring the distance of the index from the nearest division line by means of a micrometer screw which moves one or two fine threads placed in the focus of a microscope.
Ramsden's transit instruments were the first which were illuminated through the hollow axis; the idea was suggested to him by Prof. Henry Ussher in Dublin. He published a Description of an Engine for dividing Mathematical Instruments in 1777.
Ramsden is also responsible for the achromatic eyepiece named after him, and also worked on new designs of electrostatic generators. He was elected to the Royal Society in 1786. The exit pupil of an eyepiece was once called the Ramsden disc in his honour. In 1791 he completed the Shuckburgh telescope, an equatorial mounted refractor telescope.
In about 1785, Ramsden provided a new large theodolite for General William Roy of the Royal Engineers, which was used for a new survey of the distance between Greenwich, London and Paris. This work provided the basis for the subsequent Ordnance Survey of the counties of Britain. For his part with Roy in this work he received the Copley Medal in 1795. He died five years later at Brighton, England.*Wik

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.
He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.
In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.
He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1776 Peter Barlow (15 Oct 1776, 1 March 1862) Peter Barlow was self-educated but this education was sufficiently good that he was able to compete successfully to became an assistant mathematics master at the Royal Military Academy at Woolwich. He was appointed to the post in 1801 and he began publishing mathematical articles in the Ladies Diary and he became sufficiently well established as a leading authority on mathematics that after a while he was asked to contribute various articles on mathematics for encyclopedias.
In addition to these articles, Barlow also published several important books, for example in 1811 he published An elementary investigation of the theory of numbers and three years later he published A new mathematical and philosophical dictionary.
He is remembered most for two important contributions. In 1814 he produced a second book, in addition to the one described above, entitled New mathematical tables. These soon became known as Barlow's Tables and this work gives factors, squares, cubes, square roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10 000. The book "...was considered so accurate and so useful that it has been regularly reprinted ever since. "
In the mathematical library at the University of St Andrews we have several well worn copies of these tables which must have been used intensely for many years. Today, however, they are only of historical interest since they were made completely obsolete by calculators and computers.
Barlow's second major contribution makes his name still well known by amateur astronomers today. He invented the Barlow lens, a telescope lens consisting of a colorless liquid between two pieces of glass, the "Barlow lens", a modification of this telescope lens, is a negative achromatic combination of flint glass and crown glass.
In 1819 Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal ... *SAU
Barlow is quoted on SAU as saying, "230(231-1) is the greatest perfect number that will ever be discovered, for, as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it."

1829 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1837 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend.*Wik

1867 Jacques Inaudi (October 15, 1867 – November 10, 1950) Born to a poor family in the Italian Piedmont, Jacques Inaudi began life as a shepherd but soon discovered a prodigious talent for calculation, and soon he was giving exhibitions in large cities.
Camille Flammarion wrote, “He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes — while amusing himself with another activity.”
“The subtraction of numbers consisting of twenty-four figures is an easy matter for him,” reported Scientific American. “Problems for which logarithm tables are generally used he solves mentally with wonderful precision.”
Unlike other prodigies, Inaudi did not visualize his work. “I hear the figures,” he told Alfred Binet, “and it is my ear which retains them; I hear them resounding after I have repeated them, and this interior sensation remains for a long time.”
Inaudi’s father had approached Flammarion hoping that his son could be educated toward a career in astronomy. “It had been an error, whichever way one looked at it,” Flammarion wrote 10 years later. “In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation.” It was just as well: “Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory.” *Greg Ross, Futility Closet

1905 Baron C(harles) P(ercy) Snow (15 Oct 1905; 1 Jul 1980) British former physicist, turned novelist and government administrator. In 1959, C.P. Snow gave a controversial lecture called The Two Cultures and the Scientific Revolution claiming there were two cultures - the literary intellectuals and the scientists, who didn't understand each other and didn't trust each other. The split was not new; Snow noted that in the 1930s, literary theorists had begun to use the word "intellectual" to refer only to themselves. He illustrated this gap by asking a group of literary intellectuals to tell him about the Second Law of Thermodynamics, which he called the scientific equivalent of Have you read a work of Shakespeare?'" Since then, debate about this polarization has continued.*TIS

1875 André-Louis Cholesky (October 15, 1875 – August 31, 1918,) a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique".*Wik

Bernhard Hermann Neumann (15 Oct 1909, 21 Oct 2002) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *SAU
(check the dates of birth and death between this entry and the next... I checked, it seems to be correct, PB)

1909 Jesse L. Greenstein (15 Oct 1909; 21 Oct 2002) American astronomer who was a co-discoverer of quasars. His interest in astronomy began at age 8 when his grandfather gave him a brass telescope. By age 16, he was a student at Harvard University, and later earned his Ph.D.(1937), then joined the Yerkes Observatory under Otto Struve. Thereafter, he spent most of his career at the California Institute of Technology.. He measured the composition of stars, through which he found less heavy elements in the stars of globular clusters, thus proving they are younger than our Sun. In 1963, he and Maarten Schmidt were the first to correctly describe the nature of quasars, by interpreting their red shift as compact, very distant and thus very old objects. With Louis Henyey he designed and constructed a new spectrograph and wide-view camera to improve astronomical observations. *TIS

DEATHS

1959 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU

1965 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

1980 Mikhail Alekseevich Lavrentev(19 Nov 1900 in Kazan, Russia, 15 Oct 1980 in Moscow) is remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1990 Wilhelm Magnus (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*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

## Saturday, 14 October 2017

### On This Day in Math - October 14

An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity.

Howard W. Eves, Mathematical Circles, Boston

The 287th day of the year; 287 is not prime, but it is the sum of three consecutive primes (89 + 97 + 101), and also the sum of five consecutive primes (47 + 53 + 59 + 61 + 67), and wait, it is also the sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

287 is the smallest non-prime Kynea number, an integer of the form 4n + 2n − 1, studied by Cletus Emmanuel who named them after a baby girl. The binary expression of these numbers is interesting, 287[2] is 100011111. Each Kynea number has a one, followed by n-1 zeros, followed by n+1 ones. The Keyna primes are all two less than a square number. There are four year days that are Kynea numbers, but 287 is the only one that is composite.

EVENTS
1608 Two weeks after Hans Lippershey applied for a patent for his "distance seeing instrument" a was note made in the meeting of the board of the province of Zeeland, on stating that an unnamed person [the clerck has not filled in his name] also claimed to have ‘the art of making an instrument to see far away objects near by’. Within days a third person,Jacob Adriaensz [Metius] of Alkmaar, the son of one of the most prominent engineers of the Dutch Republic, would claim to posses the knowledge.
Lippershey, on request of the council to develop his instrument to be used with both eyes, delivered the first binocular instrument in mid-December1608, and the other two in February
1609. All three instruments were considered to be working satisfactorily by the deputies
of the States General who had tested the instruments. The amount of 900 guilders Lippershey
received for his three instruments was large enough for him to buy his neighbor’s house in Middelburg, which he appropriately named ‘The Three Telescopes’ (the ‘Dry Vare Gesichten’). *Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of 400 years of debate, Royal Netherlands Academy of Arts and Sciences, Amsterdam 2010

1806 The French, under Napoleon, defeated the Prussians in the Battle of Jena. Killed was the Duke of Brunswick, patron of Gauss. *VFR

1863 Alfred Nobel was granted his first patent, a Swedish patent for the preparation of nitroglycerin. The end of the Crimean War (1856) brought bankruptcy for his father, Immanuel Nobel, whose factory manufactured war materiel. Studying chemistry, Alfred learned of the powerful new explosive, nitroglycerine. Around 1860, Alfred conducted repeated experiments involving great risks. He succeeded in manufacturing sufficient quantities of nitroglycerine without any mishaps. His father had been making similar experiments, but with less success. When his father realized his son's greater discoveries, he assisted Alfred patent the explosive that he aptly called "blasting oil." Later, in 1868, Nobel patented dynamite as a form for safer handling.*TIS

In 1885, after 15-year-old Jean Baptiste Jupille was severely bitten while with his bare hands he killed an attacking rabid dog to protect five other young shepherds in Villers-Farley, France. He shortly became the second person treated by Louis Pasteur's experimental vaccine for rabies. He was fortunate to be taken to Pasteur's laboratory. Pasteur's collaborator Emile Roux had thought of attenuating the power of the infection by exposing strips of fresh spinal marrow taken from a rabbit that had died of rabies to dry, sterile air for various lengths of time. The vaccine was a small piece of marrow ground up and suspended in sterilized broth. It had first been used on Joseph Meister on 6 Jul 1885. By 12 Apr 1886, 726 people had been treated.*TIS

1913 In letter to George Hale, Einstein sketched Sun's deflection of starlight (to be tested in eclipse) but got angle wrong (later revised)
*Paul Halpern‏ @phalpern

1947 Captain Charles E. Yeager was the ﬁrst pilot to exceed the speed of sound, ﬂying the exper-imental Bell XS-1 rocket-propelled research plane at Mach 1.06 (700 mph or 1,127 kph) at 43,000 feet. Previously, many felt that turbulence would prevent planes from breaking the sound barrier. *VFR

In 1960, the 4th legal definition of the meter was made to be 1,650,763.73 wavelengths in vacuum of the orange-red light radiation of the krypton-86 atom (transition between levels 2p10 and 5d5). This was now 100 times more accurate than the previous 3rd legal definition adopted in 1889. *TIS

BIRTHS
1687 Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow. The pedal line of a triangle is sometimes called the "Simson line" after him. Edmond Halley suggested to him that he might devote his considerable talents to the restoration of the work of the early Greek geometers, such as Euclid and Apollonius of Perga These are works that only survive in abbreviated accounts given by later mathematicians such as Pappus of Alexandria. He first studied Euclid's so-called porisms. Playfair's 1792 definition of porism is "a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions."
Simson's work on Euclid's porisms was published in 1723 in the Philosophical Transactions of the Royal Society, and his restoration of the Loci Plani of Apollonius appeared in 1749. Further work of his on porisms and other subjects including logarithms was published posthumously in 1776 by Lord Stanhope at his own expense. Simson also set himself the task of preparing an edition of Euclid's Elements in as perfect a form as possible, and his edition of Euclid's books 1-6, 11 and 12 was for many years the standard text and formed the basis of textbooks on geometry written by other authors. The work ran through more than 70 different editions, revisions or translations published first in Glasgow in 1756, with others appearing in Glasgow, Edinburgh, Dublin, London, Cambridge, Paris and a number of other European and American cities. Recent editions appeared in London and Toronto in 1933 under the editorship of Isaac Todhunter and in São Paolo in 1944. Simson's lectures were delivered in Latin, at any rate at the beginning of his career. His most important writings were written in that language, however, his edition of Euclid, after its first publication in Latin, appeared in English, as did a treatise on conic sections that he wrote for the benefit of his students.
the Simson line does not appear in his work but Poncelet in Propriétés Projectives says that the theorem was attributed to Simson by Servois in the Gergonne's Journal. It appears that the theorem is due to William Wallace.
The University of St Andrews awarded Simson an honorary Doctorate of Medicine in 1746.
In 1753 Simson noted that, as the Fibonacci numbers increased in magnitude, the ratio between adjacent numbers approached the golden ratio, whose value is
(1 + √5)/2 = 1.6180 . . . . *SAU

1801 physicist J. Plateau (14 October 1801 – 15 September 1883)  Plateau’s problem asks for the minimal surface through a given curve in three dimensions. A minimal surface is the surface through the curve with the least area. Mathematically the problem is still unsolved, but physical solutions are easy: dip a curved wire in a soap solution. The “soap bubble” that results is the minimal surface for that curve. *VFR Jesse Douglas found a solution holding for an arbitrary simple closed curve. He was awarded the (one of the first two) Fields Medal in 1936 for his efforts.

In 1829 Joseph Plateau submitted his doctoral thesis to his mentor Adolphe Quetelet for advice. It contained only 27 pages, but formulated a great number of fundamental conclusions. It contained the first results of his research into the effect of colors on the retina (duration, intensity and color), his mathematical research into the intersections of revolving curves (locus), the observation of the distortion of moving images, and the reconstruction of distorted images through counter revolving
discs Prior to going blind was the first person to demonstrate the illusion of a moving image. To do this he used counter rotating disks with repeating drawn images in small increments of motion on one and regularly spaced slits in the other. He called this device of 1832 the phenakistoscope.
Plateau has often been termed a "martyr for science". . In many (popular) publications the blindness of Plateau is ascribed to his experiment of 1829 in which he looked directly into the sun for 25 seconds. Recent research definitely refutes this. The exact date of the blindness is difficult to formulate simply. It was a gradual process during the year 1843 and early 1844. Plateau publishes two papers in which he painstakingly describes the scientific observations of his own blindness. After 40 years of blindness he still has subjective visual sensations. For his experiments, as well as for the related deskwork colleagues and family help him. *Wik

1868 Alessandro Padoa​ (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.*Wik

1890 Birth of Dwight D. Eisenhower. In high school, the math teacher took away Ike’s geometry book, telling him to work out the problems without beneﬁt of the book. Eisenhower was told that unless the experiment was terminated by the teacher, he would receive an A+ in the course. “Strangely enough, I got along fairly well.” Wrote Eisenhower later. [From In Review: Pictures I’ve Kept by Dwight D. Eisenhower, 1969, p. 7]. (Morris Bishop, in a footnote to his biography of Pascal, makes an even stronger claim; he says Eisenhower was told to “construct his own geometry”.) *VFR

1900 W. Edwards Deming (14 Oct 1900; died 20 Dec 1993) was an American statistician, the father of "Total Quality Management." After WW II, he contributed to Japan's economic recovery by recommending statistical methods of quality control in industrial production. His method embraced carefully tallying product defects, examining their causes, correcting the problems, and then tracking the results of these changes on subsequent product quality. In his career before the war, he had developed statistical sampling techniques that were first used in the 1940 U.S. census. From the 1980's in the U.S. Deming taught quality control through the statistical control of manufacturing processes for companies such as Ford, Xerox, and GM.*TIS

DEATHS
1940 Heinrich Kayser (16 Mar 1853, 14 Oct 1940) Heinrich (Gustav Johannes) Kayser was a German physicist who discovered the presence of helium in the Earth's atmosphere. Prior to that scientists had detected helium only in the sun and in some minerals. Kayser's early research work was on the properties of sound. In collaboration with the physicist and mathematician Carl D.T. Runge, Kayser carefully mapped the spectra of a large number of elements. He wrote a handbook of spectroscopy (1901–12) and a treatise on the electron theory (1905).*TIS

1956 Jules Richard (12 August 1862 in Blet, France- 14 October 1956 in Châteauroux) worked on Geometry but is best known for Richard's paradox involving the set of real numbers which can be defined in a finite number of words.*SAU
Kurt Gödel considered his incompleteness theorem as analogous to Richard's paradox which, in the original version runs as follows:
Let E be the set of real numbers that can be defined by a finite number of words. This set is denumerable. Let p be the nth decimal of the nth number of the set E; we form a number N having zero for the integral part and p + 1 for the nth decimal, if p is not equal either to 8 or 9, and unity in the contrary case. This number N does not belong to the set E because it differs from any number of this set, namely from the nth number by the nth digit. But N has been defined by a finite number of words. It should therefore belong to the set E. That is a contradiction.
Richard never presented his paradox in another form, but meanwhile there exist several different versions, some of which being only very loosely connected to the original. For the sake of completeness they may be stated here.

1982 Edward Hubert Linfoot (8 June 1905, 14 Oct 1982)was a British mathematician, primarily known for his work on optics, but also noted for his work in pure mathematics. Linfoot's mathematical papers cover the period 1926–1939, all his subsequent work being on optics. These papers cover a wide range of areas in Fourier analysis, number theory, and probability, the first of these being applied later to his optical studies. His optics work was primarily concerned with synthesis, error balancing, assessment and testing. In particular he used his prodigious mathematical background to determine ways to improve and invent new optical configurations. *Wik

1984 Sir Martin Ryle (27 Sep 1918, 14 Oct 1984) British radio astronomer who developed revolutionary radio telescope systems and used them for accurate location of weak radio sources. With improved equipment, he observed the most distant known galaxies of the universe. Ryle and Antony Hewish shared the Nobel Prize for Physics in 1974, the first Nobel prize in the field of astronomy. Ryle helped develop radar for British defense during WW II. Afterward, he was a leader in the development of radio astronomy. Using interferometry he and his team located radio-emitting regions on the sun and pinpointed other radio sources so that they could be studied in visible light. Ryle’s catalogues of radio sources led to the discovery of numerous radio galaxies and quasars. He was Astronomer Royal 1972 to 1982.

1991 Walter M. Elsasser (20 Mar 1904, 14 Oct 1991) German-born American physicist notable for a variety of contributions to science. He is known for his explanation of the origin and properties of the Earth's magnetic field using a "dynamo model." Trained as a theoretical physicist, he made several important contributions to fundamental problems of atomic physics, including interpretation of the experiments on electron scattering by Davisson and Germer as an effect of de Broglie's electron waves and recognition of the shell structure of atomic nuclei. Circumstances later turned his interests to geophysics, where he had important insights about the radiative transfer of heat in the atmosphere and fathered the generally accepted dynamo theory of the earth's magnetism. *TIS

2010 Benoit Mandelbrot (20 November 1924 – 14 October 2010) was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.*SAU He was a French American mathematician.
Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot also wrote books and gave lectures aimed at the general public.
Mandelbrot spent most of his career at IBM's Thomas J. Watson Research Center, and was appointed as an IBM Fellow. He later became a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique.
Mandelbrot died in a hospice in Cambridge, Massachusetts, on 14 October 2010 from pancreatic cancer, at the age of 85. Reacting to news of his death, mathematician Heinz-Otto Peitgen said "if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years." *Wik

2010 Wilhelm Paul Albert Klingenberg (28 January 1924 Rostock, Mecklenburg, Germany – 14 October 2010 Röttgen, Bonn) was a German mathematician who worked on differential geometry and in particular on closed geodesics. One of his major achievements is the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to the sphere. *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

## Friday, 13 October 2017

### On This Day in Math - October 13

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
~George Boole

The 286th day of the year; 286 is a tetrahedral number (a triangular pyramid, note that 285 was a square pyramidal number, how often can they occur in sequence?) It is the sum of the first eleven triangular numbers, 286 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66

And to top yesterday's curiosity, here are four squares with the same digits 2862=81796, 1372=18769, 1332 = 17 689, 2812 =78961

EVENTS

2128 B.C. In China the earliest record of solar eclipse was made.*VFR (This date seems to have been computed back by a Buddhist astronomer,I-Hang in about 720 AD based on the year of the Dynasty for which it was recorded.)

1597 Kepler replied to Galileo’s letter of 4 August 1597 urging him to be bold and proceed openly in his advocacy of Copernicanism. [Eves, Circles, 159◦] *VFR

1729 Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. [Cajori, History of Mathematical Notations, vol. 2, p. 271] (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.)
In this same letter, Euler gives the relation we would now write as $\frac{1}{2}! = \frac{\sqrt {\pi}}{2}$ and points out many other fractional relations. *Detlef Gronau Why the Gamma Function So As It Is

 Sketch of M51 by Lord Rosse in 1845, *Wik
1773 What later became known as the Whirlpool Galaxy was discovered on October 13, 1773 by Charles Messier while hunting for objects that could confuse comet hunters, and was designated in Messier's catalogue as M51. *David Dickinson ‏@Astroguyz

1860 The earliest surviving aerial photograph is titled 'Boston, as the Eagle and the Wild Goose See It.' Taken by James Wallace Black and Samuel Archer King on October 13, 1860, it depicts Boston from a height of 630m. Aerial photography was first practiced by the French photographer and balloonist Gaspard-Félix Tournachon, known as "Nadar", in 1858 over Paris, France. The photographs he produced no longer exist. *Smithsonian *Wik

1884 An international conference in Washington D. C. decided “to adopt the meridian passing through the center of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.” Greenwich Mean Time, or GMT, was born. If someone ever asked you what President Chester Arthur did for us (don't say "Who?") simply say he pushed for the International Meridian Conference in Washington.

Addendum: I have been gently corrected by Rebekah Higgitt ‏@beckyfh and Thony Christie ‏@rmathematicus that in fact "The resolutions from the conference were only proposals – it was up to the respective governments to show political will and implement them ..." and that happened slowly. I am also aware that GMT was widely used in the UK before this conference to standardize railway time tables. A good source on a little more detail is at the Greenwich Meridian Org

1893 The term "Diophantine equation" appears in English in 1893 in Eliakim Hastings Moore (1862-1932), "A Doubly-Infinite System of Simple Groups," Bulletin of the New York Mathematical Society, *Jef Miller, Earliest Known Uses of Some of the Words of Mathematics

1904 Clever Hans, The horse that could do math is investigated by Oskar Pfungst. The investigation will continue for six weeks.
Hans was a horse owned by Wilhelm von Osten, who was a gymnasium mathematics teacher, an amateur horse trainer, phrenologist, and something of a mystic. Hans was said to have been taught to add, subtract, multiply, divide, work with fractions, tell time, keep track of the calendar, differentiate musical tones, and read, spell, and understand German. Von Osten would ask Hans, "If the eighth day of the month comes on a Tuesday, what is the date of the following Friday?” Hans would answer by tapping his hoof. Questions could be asked both orally, and in written form. Von Osten exhibited Hans throughout Germany, and never charged admission. Hans's abilities were reported in The New York Times in 1904. After von Osten died in 1909, Hans was acquired by several owners. After 1916, there is no record of him and his fate remains unknown.
psychologist Oskar Pfungst demonstrated that the horse was not actually performing these mental tasks, but was watching the reaction of his human observers.*Wik

1915 "Precision Computer" - The issue of the Engineering and Contracting journal for this date, in addition to details of a new three-ton worm drive contractors truck, advised of the availability of the new Ross Precision Computer. This circular slide rule consists of a silver-colored metal dial, 8-1/2" wide, mounted on a silver-colored metal disc. Three oblong holes on the base disc permit the reading of trigonometric scales on a white celluloid and cardboard disc that is between the metal discs. (HT to JF Ptak ‏@ptak)

In 1985, at the Fermi National Accelerator Laboratory in Illinois, the first observation was made of proton-antiproton collisions by the Collider Detector at Fermilab (CDF) with 1.6 TeV center-of-mass energy. In all, 23 of collisions were detected in Oct 1985. The Tevatron, four miles in circumference (originally named the Energy Doubler), is the world's highest-energy particle accelerator. Its low-temperature cooling system was the largest ever built when it was placed in operation in 1983. Its 1,000 superconducting magnets are cooled by liquid helium to -268 deg C (-450 deg F). Fermilab (originally named the National Accelerator Laboratory) was commissioned by the U.S. Atomic Energy Commission, in a bill signed by President Johnson on 21 Nov 1967.  *TIS

BIRTHS

1734 William Small (13 October 1734; Carmyllie, Angus, Scotland – 25 February 1775; Birmingham, England). He attended Dundee Grammar School, and Marischal College, Aberdeen where he received an MA in 1755. In 1758, he was appointed Professor of Natural Philosophy at the College of William and Mary in Virginia, then one of Britain’s American colonies.
Small is known for being Thomas Jefferson's professor at William and Mary, and for having an influence on the young Jefferson. Small introduced him to members of Virginia society who were to have an important role in Jefferson's life, including George Wythe a leading jurist in the colonies and Francis Fauquier, the Governor of Virginia.
Recalling his years as a student, Thomas Jefferson described Small as:
"a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and a large and liberal mind... from his conversation I got my first views of the expansion of science and of the system of things in which we are placed."
In 1764 Small returned to Britain, with a letter of introduction to Matthew Boulton from Benjamin Franklin. Through this connection Small was elected to the Lunar Society, a prestigious club of scientists and industrialists.
In 1765 he received his MD and established a medical practice in Birmingham, and shared a house with John Ash, a leading physician in the city. Small was Boulton's doctor and became a close friend of Erasmus Darwin, Thomas Day, James Keir, James Watt, Anna Seward and others connected with the Lunar Society. He was one of the best-liked members of the society and an active contributor to their debates.
Small died in Birmingham on 25 February 1775 from malaria contracted during his stay in Virginia. He is buried in St. Philips Church Yard, Birmingham.
The William Small Physical Laboratory, which houses the Physics department at the College of William & Mary, is named in his honor. *Wik

1776 Peter Barlow (13 Oct 1776; 1 Mar 1862) English mathematician and engineer who invented two varieties of achromatic (non-colour-distorting) telescope lenses. In 1819, Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal. In 1822, he built a device which is to be considered one of the first models of an electric motor supplied by continuous current. He also worked on the design of bridges, in particular working (1819-26) with Thomas Telford on the design of the bridge over the Menai Strait, the first major modern suspension bridge. Barlow was active during the period of railway building in Britain.*TIS

1885 Viggo Brun (13 October 1885, Lier – 15 August 1978, Drøbak) was a Norwegian mathematician.
He studied at the University of Oslo and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors (9-almost primes); and that all large even integers are the sum of two 9 (or smaller)-almost primes.
In 1919 Brun proved that the sum of the reciprocals of the twin primes converges to Brun’s constant:
1⁄3  +  1 ⁄5  +  1⁄ 5 + 1⁄7 + 1 ⁄11 + 1⁄ 13 + 1⁄17 + 1 ⁄19 + . . . = 1.9021605 . . .by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946.
It was in 1994, while he was trying to calculate Brun’s constant,
that Thomas R. Nicely discovered a famous flaw in the Intel Pentium
microprocessor. The Pentium chip occasionally gave wrong answers
to a floating-point (decimal) division calculations due to errors in five
entries in a lookup table on the chip. Intel spent millions of dollars
replacing the faulty chips.
More recently, Nicely has calculated that the value of Brun’s constant
1s 1.902160582582 _ 0.000000001620.
*Wik

1890 Georg Feigel born in Homburg, Germany. At the University of Berlin he developed an intro¬ductory course, Einf¨uhrung in die H¨ohere Mathematik (published, posthumeously, 1953) which was responsible for introducing the new fundamental concepts of mathematics based on axioms and structures into the universities. *VFR

1893 Kurt Werner Friedrich Reidemeister (13 Oct 1893, 8 July 1971) Reidemeister was a pioneer of knot theory and his work had a great influence on Group Theory. Reidemeister's other interests included the philosophy and the foundations of mathematics. He also wrote about poets and was a poet himself. He translated Mallarmé. *SAU

1915  Arthur Burks​, a principal designer of the ENIAC, was born. Burks -- who was born in Duluth, Minn., and educated at DePauw University and the University of Michigan -- did extensive work on the ENIAC, the machine designed at the University of Pennsylvania​’s Moore School and completed in 1946. After working with J. Presper Eckert​ and John Mauchly on the ENIAC, Burks moved on to Princeton University, where he helped John von Neumann develop his computer at the Institute for Advanced Studies.*CHM

1932 John Griggs Thompson (13 Oct 1932, )American mathematician who was awarded the Fields Medal in 1970 for his work in group theory, solving (with Walter Feit) one of its thorniest problems, the so-called "odd order" problem. (Group theory is a branch of mathematics that focuses on the study of symmetries - such as the symmetries of a geometric figure, or symmetries that arise in solutions to algebraic equations.) Thompson's proof, with 253 pages of equations, filled an entire issue of the Pacific Journal of Mathematics. It stands out as one of math’s longest and most complex. Thompson also collaborated on the classification of the finite simple groups, the building blocks of more general groups. Group theory has important applications in physics, chemistry and other fields.*TIS

DEATHS

1715 Nicolas Malebranche was a major French philosopher and follower of Descartes whose ideas he developed to bring them more in line with standard Roman Catholic orthodox belief.*SAU

1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker.
Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700-800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter.
He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge.
There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik

1913 Gyula Vályi (5 January 1855 - 13 October 1913) was a Hungarian mathematician and theoretical physicist, a member of the Hungarian Academy of Sciences, known for his work on mathematical analysis, geometry, and number theory.*Wik

1987 Walter H. Brattain (10 Feb 1902, 13 Oct 1987) Walter Houser Brattain was an American scientist born in China who, with John Bardeen and William B. Shockley, won the Nobel Prize for Physics in 1956 for investigating semiconductors (materials of which transistors are made) and for the development of the transistor. At college, he said, he majored in physics and math because they were the only subjects he was good at. He became a solid physicist with a good understanding of theory, but his strength was in physically constructing experiments. Working with the ideas of  Shockley and Bardeen, Brattain's hands built the first transistor. Shortly, the transistor replaced the bulkier vacuum tube for many uses and was the forerunner of microminiature electronic parts.*TIS

1990 Hans Freudenthal, . *VFR   (September 17, 1905, Luckenwalde, Brandenburg – October 13, 1990) was a Dutch mathematician. He was Professor Emeritus at Utrecht University when he died at age 85. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education. *Wik

2001 Olga Arsenevna Oleinik (2 July 1925, 13 Oct 2001) Oleinik wrote over 370 published papers and eight books. Her main research was concerned with algebraic geometry, partial differential equations, and mathematical physics. Winner of numerous prizes including the 1952 Chebotarev Prize for her research on elliptic equations with a small parameter in the highest derivative, the 1964 Lomonosov Prize for research on asymptotic properties of the solutions of problems of mathematical physics, and the 1988 State Prize for her series of papers on the investigation of boundary-value problems for differential operators and theirs applications in mathematical physics. In 1985 she was awarded the honorary title of Honored Scientist of the Russian Federation for her achievements in research and teaching, and in 1995 was awarded the Order of Honor by the president of the Russian Federation. She was also the 1996 AWM Noether Lecturer.*Agnes Scott College,

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

## Thursday, 12 October 2017

### On This Day in Math - October 12

"Yet I exist in the hope that these memoirs ...
may find their way to the minds of humanity in Some Dimensions,
and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality."
~ Edwin Abbott Abbott, Flatland

The 285th day of the year, 285 is a square pyramidal number (like a stack of cannonballs, or oranges with the base in a square)... Or.. the sum of the first nine squares. $285 = \sum _{i=1} ^ 9 (i^2)$

285 is 555 in base 7.

Not sure how rare this is, but just saw it on MAA's Number a Day and was intrigued, 285^2 = 81225 uses the same digits as 135^2 (18225) and 159^2 (25281).

EVENTS

1793 At the University of North Carolina, the cornerstone was laid for “Old East,” the oldest state university building in the U.S.*VFR

1810 the German festival Oktoberfest was first held in Munich.  Reaaly good ideas WILL spread.

1850, classes began at the Women's Medical College of Pennsylvania, the first medical school entirely for women.*TIS

1884 George Bruce Halsted presented his inaugural address before the Texas Academy of Science. He spoke of his teacher at Johns Hopkins, J. J. Sylvester, and related how the rumor started that Sylvester killed a student when he was at the university of Virginia. [Science, 22 February 1885; vol. 1, no. 8, p. 265] *VFR

1988 Steve Jobs unveiled the NeXT, the computer he designed after moving on from Apple Computer Inc., which he had founded with Steve Wozniak. Although the NeXT ultimately failed, it introduced several features new to personal computers, including an optical storage disk, a built-in digital signal processor that allowed voice recognition, and object-oriented languages that simplified programming. On a microprocessor with 8 megabytes of RAM, however, the NeXT ran too slowly to be popular. NeXT Computer Inc. eventually became NeXT Software Inc. and then was bought by Apple in 1997.

1996: A solar eclipse was broadcast live on the internet for the first time. * BBC Archive @BBCArchive

BIRTHS

1827 Josiah Parsons Cooke (October 12, 1827 – September 3, 1894) was an American scientist who worked at Harvard University and was instrumental in the measurement of atomic weights, inspiring America's first Nobel laureate in chemistry, Theodore Richards, to pursue similar research. Cooke's 1854 paper on atomic weights has been said to foreshadow the periodic law developed later by Mendeleev and others. Historian I. Bernard Cohen described Cooke "as the first university chemist to do truly distinguished work in the field of chemistry" in the United States. *Wik

1860 Elmer Sperry (12 Oct 1860; 16 Jun 1930) American electrical engineer and inventor of the gyrocompass. In the 1890's he made useful inventions in electric mining machinery, and patent electric brake and control system for street- or tramcars. In 1908, he patented the active gyrostabilizer which acted to stop a ship's roll as soon as it started. He patented the first gyrocompass designed expressly for the marine environment in 1910. This "spinning wheel" gyro was a significant improvement over the traditional magnetic compass of the day and changed the course of naval history. The first Sperry gyrocompass was tested at-sea aboard the USS Delaware in 1911 and established Sperry as a world leader in the manufacture of military gyrocompasses for the next 80 years. *TIS

DEATHS

1492 Piero della Francesca (June 1420, 12 Oct 1492) was an Italian artist who pioneered the use of perspective in Renaissance art and went on to write several mathematical treatises. In his own time he was also known as a highly competent mathematician. In his Lives of the most famous painters ... [13], Giorgio Vasari (1511-1572) says that Piero showed mathematical ability in his earliest youth and went on to write 'many' mathematical treatises. Of these, three are now known to survive. The titles by which they are known are: Abacus treatise (Trattato d'abaco), Short book on the five regular solids (Libellus de quinque corporibus regularibus) and On perspective for painting (De prospectiva pingendi). Piero almost certainly wrote all three works in the vernacular (his native dialect was Tuscan), and all three are in the style associated with the tradition of 'practical mathematics', that is, they consist largely of series of worked examples, with rather little discursive text.
The Abacus treatise is similar to works used for instructional purposes in 'Abacus schools'. It deals with arithmetic, starting with the use of fractions, and works through series of standard problems, then it turns to algebra, and works through similarly standard problems, then it turns to geometry and works through rather more problems than is standard before (without warning) coming up with some entirely original three-dimensional problems involving two of the 'Archimedean polyhedra' (those now known as the truncated tetrahedron and the cuboctahedron).
Four more Archimedeans appear in the Short book on the five regular solids: the truncated cube, the truncated octahedron, the truncated icosahedron and the truncated dodecahedron. (All these modern names are due to Johannes Kepler (1619).) Piero appears to have been the independent re-discoverer of these six solids. Moreover, the way he describes their properties makes it clear that he has in fact invented the notion of truncation in its modern mathematical sense.
On perspective for painting is the first treatise to deal with the mathematics of perspective, a technique for giving an appearance of the third dimension in two-dimensional works such as paintings or sculptured reliefs. Piero is determined to show that this technique is firmly based on the science of vision (as it was understood in his time). He accordingly starts with a series of mathematical theorems, some taken from the optical work of Euclid (possibly through medieval sources) but some original to Piero himself. Some of these theorems are of independent mathematical interest, but on the whole the work is conceived as a manual for teaching painters to draw in perspective, and the detailed drawing instructions are mind-numbing in their repetitiousness. There are many diagrams and illustrations, but unfortunately none of the known manuscripts has illustrations actually drawn by Piero himself.
None of Piero's mathematical work was published under his own name in the Renaissance, but it seems to have circulated quite widely in manuscript and became influential through its incorporation into the works of others. Much of Piero's algebra appears in Pacioli's Summa (1494), much of his work on the Archimedeans appears in Pacioli's De divina proportione (1509), and the simpler parts of Piero's perspective treatise were incorporated into almost all subsequent treatises on perspective addressed to painters. *SAU

Picard also travelled to Tycho Brahe's Danish observatory, Uraniborg, in order to assess its position accurately so that Tycho's readings could be compared to others'. Picard collaborated and corresponded with many scientists, including Isaac Newton, Christiaan Huygens, Ole Rømer, Rasmus Bartholin, Johann Hudde​, and even his main competitor, Giovanni Cassini, although Cassini was often less than willing to return the gesture. These correspondences led to Picard's contributions to areas of science outside the field of geodesy, such as the aberration of light he observed while in Uraniborg, or his discovery of mercurial phosphorescence upon his observance of the faint glowing of a barometer. This discovery led to Newton's studies of spectrometry.
Picard also developed what became the standard method for measuring the right ascension of a celestial object. In this method, the observer records the time at which the object crosses the observer's meridian. Picard made his observations using the precision pendulum clock that Dutch physicist Christiaan Huygens had recently developed. His book "Mesure de la Terre" was published in 1671.*Wik

1912 Lewis Boss (26 Oct 1846, 12 Oct 1912) American astronomer best known for his compilation of two catalogues of stars (1910, 1937). In 1882 he led an expedition to Chile to observe a transit of Venus. About 1895 Boss began to plan a general catalog of stars, giving their positions and motions. After 1906, the project had support from the Carnegie Institution, Washington, D.C. With an enlarged staff he observed the northern stars from Albany and the southern stars from Argentina. With the new data, he corrected catalogs that had been compiled in the past, and in 1910 he published the Preliminary General Catalogue of 6,188 Stars for the Epoch 1900. The work unfinished upon his death was completed by his son Benjamin in 1937*TIS

1926 Edwin Abbott Abbott (20 Dec 1838, 12 Oct 1926) His most famous work was Flatland: a romance of many dimensions (1884) which Abbott wrote under the pseudonym of A Square. The book has seen many editions, the sixth edition of 1953 being reprinted by Princeton University Press in 1991 with an introduction by Thomas Banchoff​. Flatland is an account of the adventures of A Square in Lineland and Spaceland. In it Abbott tries to popularise the notion of multidimensional geometry but the book is also a clever satire on the social, moral, and religious values of the period.
More recently, in 2002, an annotated version of Flatland has been produced with an introduction and notes by Ian Stewart who gives extensive discussion of mathematical topics related to passages in Abbott's text. *SAU The Kindle edition of Flatland is available for less than \$2.00 Flatland: A Romance of Many Dimensions [Illustrated] and the Stewart version is only a little more:

In a bold statement of personal opinion I add: This book should be read by every teacher and every student of mathematics.

1936 William Sheppard read Mathematics at Cambridge and then went on to study Law. He was appointed to the Department of Education. His mathematical interests were mainly in Statistics. *SAU

1984 Georgii Dmitrievic Suvorov (19 May 1919, 12 Oct 1984) made major contributions to the theory of functions. He worked, in particular, on the theory of topological and metric mappings on 2-dimensional space. Another area on which Suvorov worked was the theory of conformal mappings and quasi-formal mappings. His results in this area, mostly from the late 1960s when he was at Donetsk, are of particular significance. He extended Lavrentev's results in this area, in particular Lavrentev's stability and differentiability theorems, to more general classes of transformations. One of the many innovations in Suvorov's work was new methods which he introduced to help in the understanding of metric properties of mappings with bounded Dirichlet integral. *SAU

2011 Dennis MacAlistair Ritchie (September 9, 1941; found dead October 12, 2011), was an American computer scientist who "helped shape the digital era." He created the C programming language and, with long-time colleague Ken Thompson, the UNIX operating system. Ritchie and Thompson received the Turing Award from the ACM in 1983, the Hamming Medal from the IEEE in 1990 and the National Medal of Technology from President Clinton in 1999. Ritchie was the head of Lucent Technologies System Software Research Department when he retired in 2007. He was the 'R' in K&R C and commonly known by his username dmr. *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