## Thursday, 18 August 2016

### On This Day in Math - August 19

Let us weigh the gain and the loss in wagering that God is. Let us consider the two possibilities. If you gain, you gain all; if you lose, you lose nothing. Hesitate not, then, to wager that He is.

Blaise Pascal,Pensees (1670)

The 232nd day of the year; 232 is the maximum number of regions that the plane can be divided into with 21 lines (how many of the regions would be of infinite area?)

And from Derek Orr
232 is sum of the cubes of the factorials of its digits,
232 = (2!)3 + (3!)3 + (2!)3
and the sum of the first 11 Fibonacci numbers
232 = 1+1+2+3+5+8+13+21+34+55+89

If you add up all the proper divisors of a number, n, they can be less than n(deficient), equal to n (perfect, like 6 or 28) or abundant. 12 is the smallest abundant number. Nicomachus wrote only of even numbers because he thought all odd numbers were deficient, but he was wrong. The 232nd abundant number is odd, 945.

EVENTS
1577 " On August 19, his new book is put to printing (one hundred copies) at John Day's press in Aldersgate. " The printing of John Dee's 'General and rare memorials...' begins.
ht  ‏@RCPmuseum

1758 Etienne Montucla received the approval from the censors for his Histoire des mathematiques. Often called the first true history of mathematics. *VFR

1791 "On this day in 1791, Benjamin Banneker (free African American scientist & almanac author) published his 1st Almanac."
*Bibliophilia ‏@Libroantiguo

1819 the first bicycle in the U.S. were seen in New York City. Such bicycle velocipedes or "swift walkers" had been imported that same year. Shortly thereafter, on 19 Aug 1819, the city's Common Council passed a law to "prevent the use of velocipedes in the public places and on the sidewalks of the city of New York."*TIS (Skateborders take note, you are not the first to be banned from the sidewalks)

In 1887, Dmitri Ivanovich Mendeleev (1834-1907) used a balloon to ascend above the cloud cover to an altitude of 11,500 feet (3.5 km) to observe an eclipse in Russia. He made the solo ascent above Klin without any prior experience. While his family was rather concerned, he paid no attention to controlling the balloon until after he had completed his observations, at which time he worked out how to land it. Mendeleev is the Russian chemist known for the ordering of the Periodic Table of the Elements. Yet, he was interested in many fields of science. He studied problems associated with Russia's natural resources, such as coal, salt, metals, and the petroleum industry. In 1876, he visited the U.S. to observe the Pennsylvania oil fields. *TIS

1888 Irving Stringham, after a few years at the newly formed University of California at Berkeley, writes Felix Klein, his old professor, to complain that, "I impatiently await the time when it will be possible to bring some important researchers in the field of mathematics to the California coast." *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

BIRTHS

1584 Pierre Vernier born (19 August 1580 at Ornans, Franche-Comté, Spanish Habsburgs (now France) – 14 September 1637 same location). He developed an accurate scale for the astrolabe. The Vernier scale that he invented in 1631 is still common on precision instruments. First described in English by John Barrow in 1750 in his Navigatio Britannica. It is sometimes called a nonius after Pedro Nunes, the Portuguese mathematician and instrument maker, who designed a precursor to the vernier scale in 1542. A nice illustration of how the Vernier alignment method works is at this Wikipedia site. *Wik
Clavius originated a way of dividing a scale for precise measurements. His idea was adopted by Vernier 42 years later.

1646 John Flamsteed (19 Aug 1646; 31 Dec 1719)English astronomer who established the Greenwich Observatory. Science Historian/blogger Thony Christie writes
"the observational astronomer John Flamsteed Observational astronomy only produced three significant star catalogues in the two thousand years leading up to the 18th century. The first, the Greek catalogue from Hipparchus and Ptolemaeus published by Ptolemaeus in the 2nd century CE, which contained just over 1000 stars mapped with an accuracy that was astounding for the conditions under which it was produced. The second, containing somewhat more that 700 stars plus another 300 borrowed from the Ptolemaeus catalogue, was produced by the Danish astronomer Tycho Brahe in the last quarter of the 16th century, with an accuracy many factors better than his Greek predecessors. Both of these catalogues were produced with naked eye observations. The first catalogue to be produced using telescopic sights on the measuring instruments was that of John Flamsteed published posthumously in 1725, which contains more than 3000 stars measured to a much higher degree of accuracy than that of Tycho."
He then goes on to correct some misconceptions about Flamsteed's life that are commonly repeated, (he did NOT take part in talking Charles II into creating the observatory) and gives a nice description of a complex man. *Renaissance Mathematicus

1739 Georg Simon Klügel (August 19, 1739 – August 4, 1812) made an exceptional contribution to trigonometry, unifying formulae and introducing the concept of trigonometric function, in his Analytische Trigonometrie. Euler, who studied similar problems 9 years later, in some respects achieved less than Klügel in this area. Folta writes:"Klügel's trigonometry was very modern for its time and was exceptional among the contemporary textbooks. "
It was his mathematical dictionary, however, which led to his fame. This was a three volume work which appeared between 1803 and 1808. In 1808 Klügel became seriously ill and could do no further work on the project. Another three volumes were added between 1823 and 1836 by Mollweide and Grunert and the dictionary was widely used for several generations making Klügel's name widely known. *SAU

1790 Edward John Dent (19 Aug 1790 - 8 Mar 1853).English clockmaker and inventor whose chronometers were noted for high accuracy. His patents in this field included compasses for navigation and surveying. He experimented with springs made of steel, gold and glass, and devices for counteracting the effects of temperature change upon timepiece mechanisms. As clockmaker to Queen Victoria, he was commissioned to build the Great Clock for the clock tower of the Houses of Parliament (known as Big Ben, although that is actually the nickname of its hour bell) which he began in the year he died. His son, Frederick Dent, completed the work the following year and it was installed in the tower in 1859. It continues to be recognised for its great accuracy of 4 seconds in a year.*TIS

1830 (Julius) Lothar Meyer (19 Aug 1830; 12 Apr 1895) was a German chemist who discovered the Periodic Law, independently of Dmitry Mendeleyev, at about the same time (1869). However, he did not develop the periodic classification of the chemical elements as thoroughly as Mendeleyev. Meyer trained originally in medicine and chemistry. He examined the effect of carbon monoxide on blood. In 1879, Meyer compared atomic volume to atomic weight. Plotted on a graph, the curve showed the periodicity of the elements. He also established the concept of valency by indicating that a given element combined with a characteristic number of hydrogen atoms, and coined the terms like univalent, bivalent, and trivalent, based on that number.*TIS

1872 Théophile Ernest de Donder (19 August 1872 – 11 May 1957) was a Belgian mathematician and physicist famous for his 1923 work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy.
He received his doctorate in physics and mathematics from the Université Libre de Bruxelles in 1899, for a thesis entitled Sur la Théorie des Invariants Intégraux (On the Theory of Integral Invariants).
He was professor between 1911 and 1942, at the Université Libre de Bruxelles. Initially he continued the work of Henri Poincaré and Élie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity. He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy.
He is considered the father of thermodynamics of irreversible processes. De Donder’s work was later developed further by Ilya Prigogine. De Donder was an associate and friend of Albert Einstein. *Wik

1934 Gordon Bell (August 19, 1934 - ) is born Digital Equipment Corporation​ (DEC) innovator . In his 23 years at DEC, Bell developed several of the company's most successful minicomputers as well as its well-known VAX machine. One the world's top computer architects, Bell is considered by many to be the father of the minicomputer and is also an authority on supercomputing. The author of several books, Bell's awards include the National Medal of Technology and the IEEE Von Neumann Medal. *CHM

1939 Alan Baker born in London (19 August 1939 - ). In 1970 he received a Fields Medal for his work on Hilbert’s seventh problem which dealt with transcendental numbers. *VFR In mathematics, a transcendental number is a number (possibly a complex number) that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e. The word transcendental seems to have been created by Liebniz. In 1900, David Hilbert posed an influential question about transcendental numbers, Hilbert's seventh problem: If a is an algebraic number, that is not zero or one, and b is an irrational algebraic number, is ab necessarily transcendental? The affirmative answer was provided in 1934 by the Gelfond–Schneider theorem. This work was extended by Alan Baker in the 1960s in his work on lower bounds for linear forms in any number of logarithms (of algebraic numbers). *Wik

1973 Olga Holtz (August 19, 1973 - ) is a Russian mathematician specializing in numerical analysis. She received the Sofia Kovalevskaya Award in 2006 and the European Mathematical Society Prize (2008). Since 2008, she is a member of the Young Academy of Germany.

Holtz's early mathematical development was largely due to her parents, who were both programmers.

After winning a €1,000,000 Sofia Kovalevskaya Award in 2006, Holtz built her research group at the Technical University Berlin, [ where she became a Professor of applied mathematics while concurrently serving as an Associate, then Full Professor of Mathematics at University of California, Berkeley. Since then, Holtz has garnered additional honors. The European Mathematical Society awarded her its 2008 prize, and the European Research Council awarded her €880,000 Starting Grant in August 2010. In 2015 she was elected as a fellow of the American Mathematical Society "for contributions to numerical linear algebra, numerical analysis, approximation theory, theoretical computer science, and algebra".

Holtz, who considered a career in music before deciding on mathematics, performs with the Berlin Philharmonic Choir and practices ballroom dancing, (in her spare time????)*Wik

DEATHS

1662 Blaise Pascal died (19 June 1623 – 19 August 1662). I can not be brief about a life that contained so much in such a short time, so I mention his death. Sickly for most of his life (autopsies showed he had a deformed skull), he grew much worse in 1662. Pascal was also in a severe depression after his sister's death the year. On the night before his death he went into convulsions and received the sacraments. His last words were "May God never abandon me." He was thirty-nine years old at the time of his death. He is buried in the cemetery of Saint-Étienne, the little church where he worshiped regularly in the fifth district of Paris, near the Parthenon. There is a simple small marker near the front of the church. While frequently overlooked today, it was a prestigious church during Pascal's life. *Wik Among Pascal's lesser known inventions, it seems that he may have established the first commercial bus line in Paris.  The profits were all to go to the monastery in Port Royal.*Peter L. Bernstein, Against the Gods

1703 John Wallis (23 Nov 1616, 19 Aug 1703) British mathematician who introduced the infinity math symbol. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS In addition to the infinity sign, and the use of it's reciprocal for infinitesimals, he also is credited with the idea of number line. He also probably originated the terms "mantissa" and "continued fraction". The commonly repeated idea that he refused to believe negative numbers were "less than zero" is dispelled by his use of the number line to show 5 - 8 = -3 in his "Treatise on Algebra", in 1685. *personal correspondence from Professor Phillip Beeley, Wallis Project, Oxford Univ.

1822 Jean Baptiste Joseph chevalier Delambre (19 September 1749, Amiens – 19 August 1822, Paris) was a French mathematician and astronomer. He was also director of the Paris Observatory, and author of well-known books on the history of astronomy from ancient times to the 18th century. Delambre was one of the first astronomers to derive astronomical equations from analytical formulas. His name is also one of the 72 names inscribed on the Eiffel tower. Delambre died in 1822 and was interred in the Père Lachaise Cemetery in Paris.

1887 Alvan Clark (8 Mar 1804, 19 Aug 1887)American astronomer whose family became the first significant manufacturers of astronomical instruments in the U.S. His company manufactured apparatus for most American observatories of the era, including Lick and Pulkovo, and others in Europe. In 1862, while testing a telescope, Clark discovered the companion star to Sirius, which had previously been predicted but until then never sighted. The 18½-in objective telescope he used was subsequently delivered to the Dearborn Observatory, Chicago. His sons, Alvan Graham Clark and George Bassett Clark, continued the business. The unexcelled 40-in refractor telescopes for the 40-in Yerkes observatory was made by Alvan Graham Clark*TIS

1910 Eugène Rouché (18 August 1832 at Sommières, Hérault, France - 19 August 1910 at Lunel, Hérault) died on the day following his seventy-eighth birthday. A French Geometer who edited Laguerre's "Collected Works". He also is known for Rouche's Theorem on Complex functions. *SAU

1957 Maurice Kraitchik (April 21, 1882, Minsk - August 19, 1957, Bruxelles) was a Belgian mathematician, author, and game designer. His main interests were the theory of numbers and recreational mathematics.
He is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:
Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favorable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man?

Kraitchik wrote several books on number theory during 1922-1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics.

During World War II, Kraïtchik emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." *Wik

1951 Michael H. Freedman (21 April 1951 in Los Angeles, California, ). In 1986 he received a Fields Medal for his proof of the four-dimensional Poincar´e conjecture. *VFR [The Poincaré conjecture, one of the famous problems of 20th-century mathematics, asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere. The higher dimensional Poincaré conjecture claims that any closed n-manifold which is homotopy equivalent to the n-sphere must be the n-sphere. When n = 3 this is equivalent to the Poincaré conjecture. Smale proved the higher dimensional Poincaré conjecture in 1961 for n at least 5. Freedman proved the conjecture for n = 4 in 1982 but the original conjecture remained open until settled by G Perelman who was offered the 2006 Fields medal for his proof. ] *Wik

1957 Carl-Gustaf Arvid Rossby (28 Dec 1898, 19 Aug 1957) Swedish-U.S. meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. His work contributed to developing meteorology as a science. Rossby first theorized about the existence of the jet stream in 1939, and that it governs the easterly movement of most weather. U.S. Army Air Corps pilots flying B-29 bombing missions across the Pacific Ocean during World War II proved the jet stream's existence. The pilots found that when they flew from east to west, they experienced slower arrival times and fuel shortage problems. When flying from west to east, however, they found the opposite to be true. Rossby created mathematical models (Rossby equations) for computerized weather prediction (1950).*TIS

1964 Hugo Gernsback (August 16, 1884 – August 19, 1967), born Hugo Gernsbacher, was a Luxembourgish-American inventor, writer, editor, and magazine publisher, best known for publications including the first science fiction magazine. His contributions to the genre as publisher were so significant that, along with the novelists H. G. Wells and Jules Verne, he is sometimes called "The Father of Science Fiction". In his honour, annual awards presented at the World Science Fiction Convention are named the "Hugos" *Wik

1968 George Gamow (4 Mar 1904,19 Aug 1968) Russian-born American nuclear physicist, cosmologist and writer who was one of the foremost advocates of the big-bang theory, which desribes the origin of the universe as a colossal explosion that took place billions of years ago. In 1954, he expanded his interests into biochemistry and his work on deoxyribonucleic acid (DNA) made a basic contribution to modern genetic theory. *TIS
Einstein is often quoted as saying that his use of a "cosmological constant" in his equations for the General Theory of Relativity was his "greatest blunder".  Recently (2013) I read that Mario Livio suspected that the quote had been made up by Gamow and first appears in a Scientific American article in 1956.  He quotes Gamow's history of "antics" and a quote from his wife that  ""In more than twenty years together, Geo has never been happier than when perpetuating a practical joke." *Rebecca J Rosen, The Atlantic

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