## Tuesday, 30 August 2016

### On This Day in Math - August 30

Frustra fit per plura, quod fieri potest per pauciora.

It is vain to do with more what can be done with less.

~William of Ockham

The 243rd day of the year; 243 is the largest three digit number that can be expressed as a fifth power (35).

243 is also the sum of five consecutive prime numbers (41 + 43 + 47 + 53 + 59).

Venus' day is 243 Earth days. *Derek Orr

EVENTS

In 1831, Charles Darwin replied to the letter from Revd. Henslow telling him of the offer to sail on the H.M.S. Beagle. Darwin's had learned natural history from Henslow, who had recommended him for the unpaid position as a naturalist. Darwin told Henslow that his father would not permit him to leave on such a voyage. Meanwhile, his father had written to his brother-in-law, Josiah Wedgwood II, about his concerns regarding the proposed two-year jaunt. This afternoon Darwin prepared to join the Wedgwoods for the next day's beginning of the shooting season by riding to Maer Hall, the Wedgwood home. The Darwin family was related to the Wedgwood family through the marriage of Darwin's father to the daughter of the first Josiah Wedgwood, the famous potter. *TIS

1791 Thomas Jefferson sends a letter to Benjamin Banneker after receiving his almanac and a letter announcing that, "Sir, I freely and cheerfully acknowledge, that I am of the African race, and in that color which is natural to them of the deepest dye". Jefferson responds that, " I thank you sincerely for your letter of the 19th. instant and for the Almanac it contained. no body wishes more than I do to see such proofs as you exhibit, that nature has given to our black brethren, talents equal to those of the other colours of men, that the appearance of a want of them is owing merely to the degraded condition of their existence both in Africa and America. I can add with truth that no body wishes more ardently to see a good system commenced for raising the condition both of their body & mind to what it ought to be, as fast as the imbecillity of their present existence, and other circumstance which cannot be neglected, will admit. I have taken the liberty of sending your almanac to Monsieur de Condorcet, Secretary of the Academy of sciences at Paris, and member of the Philanthropic society because I considered it as a document to which your whole colour had a right for their justification against the doubts which have been entertained of them. I am with great esteem, Sir, Your most obedt. humble servt. Th. Jefferson" *Mathematicians of the African Diaspora, SUNY at Buffalo

In 1831, Michael Faraday demonstrated the first electrical transformer.*TIS

1908 A committee appointed by the Swiss society of naturalists reported its willingness, provided sufficient ﬁnancial assistance could be secured, to publish the complete works of Euler in about 40 volumes. Today 80 volumes of Euler’s Opera Omnia have been published, and the end is hardly in sight.*VFR

In 1963, the "Hot Line" communications link between the White House, Washington D.C. and the Kremlin, Moscow, went into operation to provide a direct two-way communications channel between the American and Soviet governments in the event of an international crisis. This was one year after the Cuban Missile Crisis. It consisted of one full-time duplex wire telegraph circuit, routed Washington- London- Copenhagen- Stockholm- Helsinki- Moscow, used for the transmission of messages and one full-time duplex radiotelegraph circuit, routed Washington- Tangier- Moscow used for service communications and for coordination of operations between the two terminal points. Note, this was not a telephone voice link.*TIS

In 1979, Comet Howard-Koomen-Michels (SOLWIND I) collided with the Sun, the first recorded comet to collide with Sun and the first discovered by a spacecraft. The coronographs taken on 30 and 31 Aug 1979 from the satellite P78-1 used to monitor solar corona activity were not inspected until Sep 1981, by Russ Howard. The recording instruments were designed and operated by Martin Koomen and Don Michels. The remarkable series of images showed the comet heading around the Sun. Its perihelion distance was too small, and the head did not reappear from behind the Sun, presumably disintegrated by the heat of the sun. The decapitated comet's tail continued, becoming fan-like, brightening the corona, until dissipated and blown away from the Sun*TIS

BIRTHS

1804 Ernst Wilhelm Grebe (30 August, 1804 - 14 January, 1874) is remembered only for a thoughtful paper that appeared in 1847 concerning some interesting properties of the triangle: If on each side of a given (arbitrary) triangle ABC one describes a square ( exterior to ABC ), then the extended outside sides of the squares, thus obtained, form a similar triangle A'B'C'. The center of similarity of both triangles is the meeting point of the straight lines AA', BB', CC'. In German this point was first called _Grebe'schen Punkt_ [Grebe's point], a TERM which seems to have been first referred to by E. Hain as early as 1875, in his paper "Ueber den Grebe'schen Punkt" [ _Archiv der Mathematik und Physik_ (= Grunert's _Archive_) volume LVIII (1876), pp. 84-89 ] *Julio Gonzalez Cabillon , Posting to the Historia Matematica discussion group
He also named the Vecten point.

1819 Joseph Alfred Serret (30 Aug 1819 in Paris, France - 2 March 1885 in Versailles, France) He was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve. In 1860 Serret succeeded Poinsot in the Académie des Sciences. In 1871 he retired to Versailles as his health began to deteriorate.
Serret also worked in number theory, calculus and mechanics. He edited the works of Lagrange which were published in 14 volumes between 1867 and 1892. He also edited the 5th edition of Monge in 1850.*SAU

1856 Carl David Tolmé Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements. *SAU In numerical analysis, the Runge–Kutta methods that are named for him are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were developed around 1900  Runge and M.W. Kutta.*Wik When  your regular walking partners include Felix Klein, David Hilbert, and Hermann Minkowski, you can't count on easily impressing them with your mental math skills, but it seems that Runge did so frequently.  Once on their regular walks Klein brought up some departmental event that required them to know what date Easter would occur the next year.  The group immediately turned to the idea of where they might acquire a calendar for the following year along the walk; all that is, except Runge who fell silent for a few yards, and then announced the date.

1871 Sir Ernest Rutherford (30 Aug 1871; 19 Oct 1937). (baron) New Zealand-born British physicist who laid the groundwork for the development of nuclear physics. He worked under Sir J. J. Thomson at Cambridge University (1895-98). Then he collaborated with Frederick Soddy in studying radioactivity. In 1899 he discovered alpha particles and beta particles, followed by the discovery of gamma radiation the following year. In 1905, with Soddy, he announced that radioactive decay involves a series of transformations. In 1907, with Hans Geiger and Ernest Marsden, he devised the alpha-particle scattering experiment that led in 1911 to the discovery of the atomic nucleus. In 1919 he achieved the artificial splitting of light atoms. In 1908 he was awarded the Nobel Prize for Chemistry. *TIS A story is told by A.. V. Hill that Rutherford had told him once, "I've just been reading some of my early papers, and when I had read them for a bit I said to myself, "Ernest my boy, you used to be a darn clever fellow.'" *Walter Gratzer, Eurekas and Euphorias, pg 27
[I love this quote from a few years before his death. "The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine."]

1906 Olga Taussky-Todd She received her Ph.D. in 1930 under Philip Furtwangler at Vienna in number theory. Her ﬁrst job involved editing Hilbert’s papers on number theory.*VFR

1907 John Mauchly (30 Aug 1907; 8 Jan 1980) American physicist and engineer, who with John P. Eckert invented (1946) the Electronic Numerical Integrator and Computer (ENIAC), the first general-purpose electronic computer. Mauchly initially conceived of the computer's architecture, and Eckert possessed the engineering skills to bring the idea to life. ENIAC was developed (1946) for the US Army Ordnance Department as what was probably the first general-purpose electronic computer. It was a vast machine, consuming 100 kW of electric power and containing 18,000 electronic valves. Their successful UNIVAC computer (1951) was the first commercial computer, and introduced magnetic tape for programming.*TIS

1907 Gordon Brown founded the Servomechanisms Laboratory at MIT, which pioneered the development of feedback-control theory, computer technology, and automatic control of machine tools and had many famous graduate students who went on to become major contributors in the fields of Electrical Engineering and Computer Science. *CHM

1912 E.M. Purcell (30 Aug 1912; 7 Mar 1997) American physicist who shared, with Felix Bloch of the United States, the Nobel Prize for Physics in 1952 for his independent discovery (1946) of nuclear magnetic resonance in liquids and in solids. Nuclear magnetic resonance (NMR) has become widely used to study the molecular structure of pure materials and the composition of mixtures. The method detects and measures the magnetic fields of atomic nuclei. *TIS

DEATHS

1621 Baha' ad-Din al-Amili (27 Feb 1547 in Baalbek, now in Lebanon - 30 Aug 1621 in Isfahan, Iran) was a Lebanese-born mathematician who wrote influential works on arithmetic, astronomy and grammar. Perhaps his most famous mathematical work was Quintessence of Calculation which was a treatise in ten sections, strongly influenced by The Key to Arithmetic (1427) by Jamshid al-Kashi. *SAU

1844 Francis Baily   (28 Apr 1774, 30 Aug 1844)English astronomer who detected the phenomenon called "Baily's beads" during an annular eclipse of the Sun on 15 May 1836. His vivid description aroused new interest in the study of eclipses. After retiring in 1825 from a successful business career, Baily turned to science. Baily revised several star catalogs, repeated Henry Cavendish's experiments to determine the density of the Earth, and measured its elliptical shape. His protests regarding the British Nautical Almanac, then notorious for its errors, were instrumental in bringing about its reform.*TIS  A really nice discussion of the many contributions of Baily is in this post at The Renaissance Mathematicus, To whet your appetite, " Baily’s Flamsteed memoir had a major influence on the history and the  historiography of science; he had succeeded in pricking Newton’s  hagiographic bubble. St Isaac had been taken down a peg or two. Baily’s  work marks a turning point in our understanding of Newton moving him  along the road from plastic saint to real, if somewhat unpleasant, human  being. Sometimes editing star catalogues can lead to unexpected results  for the history of science."

1901 Biquard Pierre, (30 August 1901 in Paris - 28 April 1992 in Paris)In 1932, He discovered light diffraction by ultrasonic waves: Pierre Biquard, born 30 Aug 1901, friend of Frédéric Joliot Curie *Arjen Dijksman ‏@materion

1928 Wilhelm Wien  (13 Jan 1864, 30 Aug 1928)German physicist who received the Nobel Prize for Physics in 1911 for his displacement law concerning the radiation emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it). While studying streams of ionized gas Wien, in 1898, identified a positive particle equal in mass to the hydrogen atom. Wien, with this work, laid the foundation of mass spectroscopy. J J Thomson refined Wien's apparatus and conducted further experiments in 1913 then, after work by E Rutherford in 1919, Wien's particle was accepted and named the proton. Wien also made important contributions to the study of cathode rays, X-rays and canal rays.*TIS [I find it curiously interesting that all three of  the  great physicists mentioned here either were born or died this day]

1940 Sir J(oseph) J(ohn) Thomson (born 18 Dec 1856, 30 Aug 1940 )was an English physicist who helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908. Thomson experimented with currents of  electricity inside empty glass tubes, investigating a long-standing puzzle known as "cathode rays." His experiments prompted him to make a bold proposal: these mysterious rays are streams of particles much smaller than atoms. He called these particles "corpuscles," and suggested that they might make up all of the matter in atoms. It was startling to imagine a particles inside the atom at a time when most people thought that the atom was indivisible, the most fundamental unit of matter.*TIS

1995 Fischer Sheffey Black (January 11, 1938, August 30, 1995) was an American economist, best known as one of the authors of the famous Black–Scholes equation.In 1973, Black, along with Myron Scholes, published the paper 'The Pricing of Options and Corporate Liabilities' in 'The Journal of Political Economy'. This was his most famous work and included the Black–Scholes equation. The Nobel Prize is not given posthumously, so it was not awarded to Black in 1997 when his co-author Myron Scholes received the honor for their landmark work on option pricing along with Robert C. Merton, another pioneer in the development of valuation of stock options. In the announcement of the award that year, the Nobel committee prominently mentioned Black's key role.*Wik

2004 Fred Lawrence Whipple  (5 Nov 1906, 30 Aug 2004) was an American astronomer who proposed the "dirty snowball" model for comet nuclei. In the 1930s, using a new, two-station method of photography, he determined meteor trajectories and found that nearly all visible meteors are made up of fragile material from comets, and that none come from beyond the solar system. Whipple suggested (1950) that comets have icy cores inside thin insulating layers of dirt, and that jets of material ejected as a result of solar heating were the cause of orbital changes. This model was confirmed in 1986 when spacecraft flew past comet Halley. Whipple’s work on tracking artificial satellites led to improved knowledge of the shape of the earth and greatly improved positions on earth. *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

## Monday, 29 August 2016

### On This Day in Math - August 29

 Jeannie at VLA

In most sciences one generation tears down what another has built,
and what one has established, another undoes.
In mathematics alone each generation adds a new storey to the old structure.
~Hermann Hankel

The 242nd day of the year; 242 has six divisors...but 243, 244, and 245 also each has six divisors. 242 is the smallest integer to begin a run of four consecutive integers all of which have the same number of divisors. (What is the smallest integer that begins a run of three consecutive integers with an equal number of divisors?)

242 is not only a palindrome in base ten, it is also a palindrome in base 3 and base 7.  (What palindrome in base ten is also a palindrome in the most other bases 2-9?)

EVENTS

1609 Galileo writes to his brother in Florence to tell him about his telescope presentation to the Doge on the 24th of August.

1654 Fermat to Pascal Saturday, August 29, 1654
Monsieur,
Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Trait´e du triangle arithmetique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would he of the nature of a Compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of the parliament augments my duties and I hope that out of your goodness you will allow me due and almost necessary respite.
In the same letter he states that, "Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity [I.e. 22n+1] are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number;The square of the square makes 16 which, when unity is added makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true)and I assure you that I have not yet been able to find it fully." * York University Maths Dept

1692 For his services to the field of astronomy, Johann Philipp von Wurzelbauer was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. *Wik

1831 Michael Faraday discovered electrical induction. *VFR In 1831, Michael Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. He found that upon closing the battery circuit, there was a deflection of the galvanometer in the second circuit. Then he was astonished to see the galvanometer needle jump in the opposite direction when the battery circuit was opened. He had discovered that a current was induced in the secondary when a current in the primary was connected and an induced current in the opposite direction when the primary current was disconnected.*TIS

1899 Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem (Let A and B be sets. If there is a 1-1 correspondence from A to B and a 1-1 corespondence from B to A, then the sets have the same cardinality.) *Cantorian Set Theory and Limitation of Size By Michael Hallett

In 1940, Sir Henry Tizard led a mission of leading British and Canadian scientists to the USA to brief official American representatives on devices under active development for war use and to enlist the support of American scientists. Thus began a close cooperation of Anglo-American scientists in such fields as aeronautics and rocketry. His influence probably made the difference between defeat or victory at the Battle of Britain in 1940. *TIS

1949 the USSR tested their first atomic device, "First Lightning." It was an an implosive type plutonium bomb, detonated at the Semipalatinsk test range, giving up to a 20 kiloton yield. In the U.S. it was calledJoe No. 1 ("Joe" was nickname for Y. Stalin.) This event came five years earlier than anyone in the West had predicted, largely due to one man, the spy Klaus Fuchs. As a Los Alamos physicist, Fuchs had passed detailed blue prints of the original American Trinity bomb design to the Russians. With the emergence of the USSR as a nuclear rival, America's monopoly of atomic weaponry was ended giving the U.S. strong motivation for intensifying its program of nuclear testing. Thus the Cold War was launched.*TIS

1970 Oscar Morgenstern writes in his diary that Gödel would NOT publish his ontological proof for the existence of God. The first version of the ontological proof in Gödel's papers is dated "around 1941". Gödel is not known to have told anyone about his work on the proof until 1970, when he thought he was dying. In February, he allowed Dana Scott to copy out a version of the proof, which circulated privately. In August 1970, Gödel told Oskar Morgenstern that he was "satisfied" with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions (completeness, etc.) correspondingly axiomatized, is possible) *Wik

1990 The British Computer Misuse Act goes into effect One of the earliest laws anywhere designed to address computer fraud, the Act resulted from a long debate in the 1980s over failed prosecutions of hackers -- in one well-publicized case, two men hacked into a British Telecom computer leaving messages in the Duke of Edinburgh's private mailbox. *CHM

BIRTHS

1756 Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer at the turn of the 18th and 19th centuries.
Born in Żnin, Śniadecki studied at Kraków University and in Paris. He was rector of the Imperial University of Vilnius, a member of the Commission of National Education, and director of astronomical observatories at Kraków and Vilnius. He died at Jašiūnai Manor near Vilnius.
Śniadecki published many works, including his observations on recently discovered planetoids. His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability. *Wik He is considered as the best Polish mathematician born in the 18th century.

1876 Charles F. Kettering (29 Aug 1876; 25 Nov 1958) was an American engineer whose 140 patents included the electric starter, car lighting and ignition systems. In his early career, with the National Cash Register Co., Dayton (1904-09), he created the first electric cash register with an electric motor that opened the drawer. When he co-founded the Dayton Engineering Laboratories Company (DELCO, with Edward A. Deeds) he invented the key-operated self-starting motor for the Cadillac (1912) and it spread to nearly all new cars by the 1920's. As vice president and director of research for General Motors Corp. (1920-47) he developed engines, quick-drying lacquer finishes, anti-knock fuels, and variable-speed transmissions.*TIS

1881 Ferdinand Springer born, The founder of an important publishing house,. Today Springer-Verlag is one of the most important publishers of advanced work on mathematics. *VFR

1904 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) British Mathematician who worked primarily in Algebraic Geometry. *SAU

DEATHS

1873 Hermann Hankel (14 February 1839 - 29 August 1873) He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 1867 exposition on complex numbers and quaternions is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by respecting the law of distributivity to the left and the right is that which conforms to the rule of signs." *Wik

1930 James Bolam (1839 in Newcastle, England - 29 Aug 1930 in St Helen's, Drumchapel, Dumbartonshire, Scotland) was educated at Newcastle. He became head of the Government Navigation School (later the Leith Nautical College). He was a founder member of the EMS and became an honorary member in 1923. *SAU

1937 Otto Ludwig Hölder (December 22, 1859 – August 29, 1937) worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. *SAU

1967 Charles Brace Darrow (10 Aug 1889, 29 Aug 1967) was an American inventor who designed the board game Monopoly. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. On 31 Dec 1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. *TIS

1975 Éamon de Valera (14 October 1882, 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government of the Irish Free State and head of government and head of state of Ireland. He also introduced the Constitution of Ireland.
De Valera was a leader of Ireland's struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
In his youth he had trained as a mathematician and taught mathematics prior to the Easter Rising. Throughout his life he maintained an interest in mathematics and returned to it with a passion in his later life. *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

## Sunday, 28 August 2016

### On This Day in Math - August 28

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
~Joseph Louis Lagrange

The 241st day of the year; 241 is the larger of a pair of twin primes. The larger of a pair of twin primes is always one more than a multiple of six; the smaller is always one less than a multiple of six.

2+4+1 is prime. 241 is the 53rd prime. (53 is also prime) *Derek Orr

241 is also The smallest prime p such that p plus the reversal of p equals a palindromic prime.  241 + 142 = 383; which is a prime palindrome.

And it is the largest known prime p such that the reversal of (p! + p) is prime.  (241! + 241 ends with a string of fifty-five zeros, and then 241 :
980360372638941007038951797078339359751464353463061342202811
188548638347461066010066193275864531994024640834549254693776
854464608509281547718518965382728677985343589672835884994580
815417004715718468026937051493675623385569404900262441027874
255428340399091926993707625233667755768320823071062785275404
107485450075779940944580451919726756974354635829128751944137
27644867102380111026020691554782580923999494640500736
0000000000000000000000000000000000000000000000000000000241....
and if you write the reversal of that, it's prime.

EVENTS

412 BC The ancient city of Syracuse suffered heavily under siege by the Athenians during the Peloponnesian War. A turn of events occurred during the Second Battle of Syracuse: on Aug. 28, 41.C. a lunar eclipse occurred, causing the superstitious Athenians to delay departure. The Syracuseans took advantage of Athenian indecision and decisively defeated the unprotected Athenian expedition as it sat exposed in the harbor. *listosaur.com

1666 John Evelyn Records in his diary: "to the Royal Society, where one Mercator, an excellent mathematician, produced his rare clock and new motion to perform the equations, and Mr. Rooke, his new pendulum." The Mercator is Nicholas Mercator who taught mathematics in London (1658–1682). He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles. Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668 in which he described the Mercator series, also independently discovered by Gregory Saint-Vincent $\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots.$
I suspect the "Mr Rooke" should have been Hooke who is mentioned at the meeting in Pepys' Diary. *Wik, *John Evelyn Diary

1730 Murder by Unicorn Horn on a Holborn skittle-ground : On the 28th of August 1730, Joseph Hastings died after receiving “several mortal Bruises with an Unicorn’s Horn”, wielded by John Williams of St. Andrew’s Holborn eleven days earlier. The assault occurred on a Holborn skittle-ground, witnessed by several local men.
Williams was angered by Hastings response to his offer to purchase the (probably Narwhale) horn and an argument ensued which led to the beating. More detail at Sloan Letters

In 1789, Enceladus, the sixth-largest moon of Saturn, was discovered by Fredrick William Herschel on August 28, 1789, during the first use of his new 1.2 m (47 in) telescope, then the largest in the world. Little was known about Enceladus until the two Voyager spacecraft passed near it in the early 1980s.
Enceladus is named after the giant Enceladus of Greek mythology.[14] The name Enceladus—like the names of each of the first seven satellites of Saturn to be discovered—was suggested by William Herschel's son John Herschel in his 1847 publication Results of Astronomical Observations made at the Cape of Good Hope.[30] He chose these names because Saturn, known in Greek mythology as Cronus, was the leader of the Titans. *Wik

 Scientific American ‏@sciam
1845 the first issue of the Scientific American was published by Rufus Porter (1792-1884), a versatile if eccentric Yankee, who was by turns a portrait-painter, schoolmaster, inventor and editor. While the paper was still a small weekly journal with a circulation less than 300, he offered it for sale. It was bought for $800 in July 1846 by 20-year-old Alfred Ely Beach (1826-1896) as editor, and Orson Desaix Munn (1824-1907). Together, they built it over the years into a great and unique periodical. Their circulation reached 10,000 by 1848, 20,000 by 1852, and 30,000 by 1853.*TIS 1893 The first day of the Evanston Colloquial lectures by Felix Klein which would continue until 9 September. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900 1961 The Board of Governors of the MAA voted to name Dr. Mina S. Rees, (ﬁrst) Dean of Graduate Studies at the City University of New York, the ﬁrst recipient of their Award for Distinguished Service to Mathematics. From 1946 to 1953 she held several important positions at the Office of Naval Research and was instrumental in getting ONR to adopt the policy that mathematics was part of this country’s total scientiﬁc effort and should be properly supported by government-sponsored research programs. [AMM 69(1962), pp. 185-187]. *VFR 1974 Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string ﬁgure of a hyperbola. [Scott #1094]. *VFR HT to Emma L Bell, Storax Sedan, and Glen Carlson for image 1993, a picture was taken showing the first moon of an asteroid. The asteroid 243 Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach (within 2,400-km or 1,500 miles) to the asteroid. Ida is about 52 km (32 mi) in length and is irregularly shaped. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. Dactyl is only about 1.4-km in diameter, and it is spectrally different from Ida data. The picture was released on 26 Mar 1994. Galileo had encountered the first asteroid - 951 Gaspra - on 29 Oct 1991. Galileo continued on its mission to study Jupiter, beginning its orbit of the planet on 7 Dec 1995.*TIS 2009 The Australian Govt replies to a letter written "To A Top Scientist" by an Australian schoolboy shortly after the launch of Sputnik fifty-two years earlier with his suggested designs for a rocket ship. See all the details at this page from *Letters of Note BIRTHS 1796 Irénée-Jules Bienaymé (28 August 1796, 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik 1801 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS 1863 Andre-Eugene Blondel (28 Aug 1863; 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators.*TIS (Invention of the Oscillograph is also credited to William Du Bois Duddell.) 1867 Maxime Bˆochner born. After receiving his doctorate under Felix Klein in 1891 he returned to Harvard for a lifetime of teaching and research in differential equations. *VFR 1883 Jan A Schouten worked on tensor analysis and its applications.*SAU 1901 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*Wik 1911 Shizuo Kakutani (角谷 静夫 Kakutani Shizuo?, August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem. *Wik 1912 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000) George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder. In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her. Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA 1919 Sir Godfrey Newbold Hounsfield (28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS 1921 Ralph Asher Alpher (February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized. Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter). With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation. In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. *Wik 1919 Sir Godfrey Newbold Hounsfield (28 Aug 1919; 12 Aug 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built larger machines able to make a full body scan. *TIS 1939 John Frank Charles Kingman (28 August 1939, )worked in Statistics and made significant advances in queuing theory. He was N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by Sir David Wallace. He is famous for developing the mathematics of the coalescent, a theoretical model of inheritance, which is fundamental to modern population genetics. *Wik 1951 Edward Witten (born August 26, 1951) is an American theoretical physicist with a focus on mathematical physics who is a professor of Mathematical Physics at the Institute for Advanced Study at Princeton, New Jersey. Witten is a researcher in superstring theory, a theory of quantum gravity, supersymmetric quantum field theories and other areas of mathematical physics.[1] He has made contributions in mathematics and helped bridge gaps between fundamental physics and other areas of mathematics. In 1990 he became the first physicist to be awarded a Fields Medal by the International Union of Mathematics. In 2004, Time magazine stated that Witten was widely thought to be the world's greatest living theoretical physicist. *Wik DEATHS 2005 George Szekeres (29 May 1911 – 28 August 2005) was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics. *SAU Szekeres worked closely with many prominent mathematicians throughout his life, including Paul Erdős, Esther Szekeres (née Esther Klein), Paul Turán, Béla Bollobás, Ronald Graham, Alf van der Poorten, Miklós Laczkovich, and John Coates. The so-called Happy Ending problem is an example of how mathematics pervaded George's life. During 1933, George and several other students met frequently in Budapest to discuss mathematics. At one of these meetings, Esther Klein proposed the following problem: Given five points in the plane in general position, prove that four of them form a convex quadrilateral. After allowing George, Paul Erdős, and the other students to scratch their heads for some time, Esther explained her proof. Subsequently, George and Paul wrote a paper (1935) that generalizes this result; it is regarded as one of the foundational works in the field of combinatorial geometry. Erdős dubbed the original problem the "Happy Ending" problem because it resulted in George and Esther's marriage in 1937. George and Esther died within an hour of each other, on the same day, 28 August 2005, in Adelaide, Australia.*Wik 2005 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems. In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children. Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s. In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand. In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik 2007 Paul Beattie MacCready (29 Sep 1925, 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel. *TIS

2011 Anthony Edgar Sale (or Tony Sale) (30 January 1931 - 28 August 2011) led the construction of a Colossus computer replica at Bletchley Park, completed in 2007 *Wik
In 1994, a team led by Tony Sale began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale (right) supervises the breaking of an enciphered message with the completed machine. *Wik Photo

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, 27 August 2016

### On This Day in Math - August 27

Questions that pertain to the foundations of mathematics,
although treated by many in recent times,
still lack a satisfactory solution.
The difficulty has its main source in the ambiguity of language.

Giuseppe Peano,
Opening of the paper Arithmetices principia in which he introduced axioms for the integers.

The 240th day of the year; 240 has more divisors (20 of them) than any previous number. What would be the next number that has more?

240 is the product of the first 6 Fibonacci numbers  240 = 1*1*2*3*5*8    *Derek Orr
These are often called Fibonacci factorials or fibonorials. 240 would be $6!_F$, also called the Fibonacci factorial

EVENTS

In 413 BC, a lunar eclipse caused panic among the sailors of the Athens fleet and thus affected the outcome of a battle in the Peloponnesian War. The Athenians were ready to move their forces from Syracuse when the Moon was eclipsed. The soldiers and sailors were frightened by this celestial omen and were reluctant to leave. Their commander, Nicias, consulted the soothsayers and postponed the departure for 27 days. This delay gave an advantage to their enemies, the Syracusans, who then defeated the entire Athenian fleet and army, and killed Nicias.*TIS

1666 John Evelyn makes an on-site visit to Old St. Pauls with Christopher Wren.  "We went about to survey the general decays of that ancient and venerable church, and to set down the particulars in writing, what was fit to be done.."  Five days later the reports would be rendered meaningless by the Great London Fire.  *Lisa Jardine, Ingenious Pursuits, pgs 69-70

1760 Leonhard Euler, in his Letters to a German Princess on various topics of physics and philosophy, explains how a surveyor uses a level. As an example he asks which end of the straight line between their homes is higher. He discusses the ﬂow of the rivers that connect their homes, but gives the wrong answer to his question. For discussion of this famous error, see Eves, Adieu, 34 *VFR

1771 Joseph Priestley finds a mint plant rejuvenates "spent" air. He had set out ten days earlier to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. On the 27th he would return to the experiment and relight the candle and find, "it burned perfectly well in it." *Steven Johnson, The Invention of Air

1776 Even in the onset of the American Revolution, (Nathan Hale was executed for treason only five days before) future President John Adams, wrote of a visit to the Princeton Orrery: "Here we saw a most beautiful machine--an Orrery or planetarium constructed by Mr. Rittenhouse of Philadelphia. It exhibits almost every motion in the astronomical world."
David Rittenhouse was a renowned American astronomer, clockmaker, mathematician, surveyor, scientific instrument craftsman, and public official. Rittenhouse was a president of the American Philosophical Society; Treausrer of Pennsylvania; & the first director of the United States Mint. *Barbara Wells Sarudy

1783 Jacques A. C. Charles (for whom Charles' Law is named) and the Robert brothers launched the world's first hydrogen filled balloon on August 27, 1783, from the Champ de Mars, (now the site of the Eiffel Tower) where Ben Franklin was among the crowd of onlookers. The balloon was comparatively small, a 35 cubic metre sphere of rubberised silk, and only capable of lifting circa 9 kg (20 lb). It was filled with hydrogen that had been made by pouring nearly a quarter of a tonne of sulphuric acid onto a half a tonne of scrap iron. The hydrogen gas was fed into the balloon via lead pipes; but as it was not passed through cold water, great difficulty was experienced in filling the balloon completely (the gas was hot when produced, but as it cooled in the balloon, it contracted).
Daily progress bulletins were issued on the inflation; and the crowd was so great that on the 26th the balloon was moved secretly by night to the Champ de Mars, a distance of 4 kilometres. (This may not have been very secret as another source says there were processions of torchlights along the route.)
The balloon flew northwards for 45 minutes, pursued by chasers on horseback, and landed 21 kilometers away in the village of Gonesse where the reportedly terrified local peasants destroyed it with pitchforks or knives. *Wik

1784 One year after the Charles Flight (above) James Tytler became the first person in Britain to fly by ascending in a hot air balloon (He had made a minimal flight on 25 August in Edinburgh when his balloon rose a few feet from the ground. On the 27th he managed to reach a height of some 350 feet, traveling for half a mile between Green House on the northern edge of what is now Holyrood Park to the nearby village of Restalrig. *Wik

1798 Egyptian Institute founded by Napoleon in imitation of the Institut de France *VFR

1911 A century ago, on August 27, 1911, headlines of the New York Times announced that Martians had completed stunning feats of engineering and construction: two 1000-mile-long canals built on Mars in a two-year period.  These canals had not only been seen and sketched by astronomers, but also had been captured photographically, appearing in the photos as “the most marked features on that part of the planet”. *The Renaissance Mathematicus

1947 China (there was only one until 1949) issued four stamps honoring Confucius. [Scott #741-4]. *VFR

1993 Compaq Computer Corp. announced its Presario family of personal computers, intended to be user friendly and cheap. For \$1,399, the Presario included a monitor, modem, and software to access the recently popularized online world through Prodigy and America Online. *CHM

BIRTHS
1850 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna.
Righi was the first person to generate microwaves,[citation needed] and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. *Wik

1858 Birthdate of Giuseppe Peano (27 Aug 1858; 20 Apr 1932) early contributor to symbolic logic. Through the use of symbols, equations are more easily understood by anyone regardless of their language. For example, Peano introduced symbols to represent "belongs to the set of" and "there exists." In Arithmetics principia (1889), a pamphlet he wrote in Latin, Peano published his first version of a system of mathematical logic, giving his Peano axioms defining the natural numbers in terms of sets. In 1903, Peano unsuccessfully proposed an international, artificial language he called "Latino sine flexione." It was based on Latin without grammar. Its vocabulary comprised words from English, French, German and Latin. *TIS Thony Christie maintains that this may overstate his contribution. "I've been here before. Peano made a substantial contribution to the history of symbolic logic, especially the fact that it was his work that inspired Russell. However I think Boole, Jevons, Demorgan, Venn, McColl, Frege, Peirce, Ladd-Franklin and quite a few others who were doing symbolic logic before Peano might object to him being called its founder. To say nothing of the Stoics! "

1915 Norman Foster Ramsey (27 Aug 1915, )American physicist who shared (with Wolfgang Paul and Hans Georg Dehmelt) the 1989 Nobel Prize for Physics in 1989 for "for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks." His work produced a more precise way to observe the transitions within an atom switching from one specific energy level to another. In the cesium atomic clock, his method enables observing the transitions between two very closely spaced levels (hyperfine levels). The accuracy of such a clock is about one part in ten thousand billion. In 1967, one second was defined as the time during which the cesium atom makes exactly 9,192,631,770 oscillations.*TIS

1923 Jacob Willem "Wim" Cohen (27 August 1923, 12 November 2000) was a Dutch mathematician, well known for over a hundred scientific publications and several books in queueing theory. *Wik

1926 Kristen Nygaard (August 27, 1926, August 10, 2002) was a Norwegian computer scientist, programming language pioneer and politician. He was born in Oslo and died of a heart attack in 2002. Internationally he is acknowledged as the co-inventor of object-oriented programming and the programming language Simula with Ole-Johan Dahl in the 1960s.

DEATHS

1898 John Hopkinson (27 Jul 1849, 27 Aug 1898)British physicist and electrical engineer who worked on the application of electricity and magnetism in devices like the dynamo and electromagnets. Hopkinson's law (the magnetic equivalent of Ohm's law) bears his name. In 1882, he patented his invention of the three-wire system (three phase) for electricity generation and distribution. He presented the principle the synchronous motors (1883), and designed electric generators with better efficiency. He also studied condensers and the phenomena of residual load. In his earlier career, he became (1872) engineering manager of Chance Brothers and Co., a glass manufacturer in Birmingham, where he studied lighthouse illumination, improving efficiency with flashing groups of lights.*TIS

1912 Mikhail Vashchenko-Zakharchenko worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.*SAU

1958 Ernest Orlando Lawrence (8 Aug 1901, 27 Aug 1958 ) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path, while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him. *TIS

1988 Max Black​ (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *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