## Sunday, 21 August 2011

### On This Day in Math - Aug 21

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
~Augustin-Louis Cauchy

The 233rd day of the year; 233 is the only three digit prime that is also a Fibonacci number.

EVENTS
1560 The occurrence at the predicted time of a solar eclipse in Copenhagen turned Tycho Brahe toward a life of observational astronomy. *VFR

1609 Galileo demonstrates his telescope to the aristocrats of Venice. *Renaissance Mathematicus,

1706 Jakob Hermann writes to Leibniz about proof that Machin's series converges to pi. In 1706 William Jones published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sense it is now used)  This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated, "... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin."
No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π so when de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details. Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.  *VFR

1776 First recorded use of dollar symbol $. (see cajori, vol II pg 24) but for much longer, it would not be common.. many textbooks used D, d, c for Dollar, Dime and Cents. *VFR Ezra l'Hommedieu, a member of the New York Provencial Assembly had over a dozen different symbols in his diary beginning with a single vertical bar and proceeding to two vertical bars. *F Carjori 1888 William Seward Burroughs of St. Louis obtained a patent for his adding machine, the ﬁrst successfully marketed. In January, 1886, he incorporated as the American Arithmometer Corporation. *VFR He received patents on four adding machine applications (No. 388,116-388,119), the first U.S. patents for a "Calculating-Machine" that the inventor would continue to improve and successfully market. One year after making his first patent application on 10 Jan 1885, he incorporated his business as the American Arithmometer Corporation of St. Louis, in Jan 1886, with an authorized capitalization of $100,000.$ After Burrough's early death in 1898, after moving from St. Louis to Detroit, Michigan, that company reorganized as the Burroughs Adding Machine Co., incorporated in Jan 1905, with a capital of$5 million. The new name was in tribute to the inventor.*TIS

1893 The zeroeth International Mathematical Congress with representatives of seven countries was held in conjunction with the Chicago World’s Fair on August 21–25. William E. Story of Clark University was president of the Congress. Felix Klein of Germany came at Kaiser Wilhelm’s personal request. Klein brought nearly all of the mathematical papers published by his countrymen and a superb collection of mathematic models. [AMS Semicentennial Publishers, vol 1, p. 74]. *VFR I have read that Klein's models led to more frequent use of them in American Education.

1949 John Mauchly and J. Presper Eckert, Jr. demonstrate BINAC, a computer capable of calculating 12,000 times faster than a human being.*VFR (I wonder how they decided how fast a human being could calculate?)

1972 Peru issued a Air Post Stamp picturing a Quipu. [Scott #C341]. *VFR

BIRTHS

1757 Josiah Beigs, meteorologist and mathematician, born. This freethinking Democrat left his professorship at Yale for political reasons and became president of the University of Georgia. He applied Galileo’s formula for fallen bodies to the nine day’s fall of Lucifer and his angels, to determine that Hell was 1,832,308,363 miles deep. [Struik, Origins of American Science, p. 370] *VFR

1789 Augustin-Louis Cauchy (21 Aug 1789;23 May 1857) French mathematician who pioneered in analysis and the theory of substitution groups (groups whose elements are ordered sequences of a set of things). He was one of the greatest of modern mathematicians. *TIS

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

1932 Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges' theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.*SAU

1940 Endre Szemerédi (August 21, 1940, ) is a Hungarian mathematician, working in the field of combinatorics and theoretical computer science. He is the State of New Jersey Professor of computer science at Rutgers University since 1986. He received his PhD from Moscow State University. His adviser was the late mathematician Israel Gelfand. He has published over 200 scientific articles in the fields of Discrete Mathematics, Theoretical Computer Science, Arithmetic Combinatorics and Discrete Geometry. He is best known for his proof from 1975 of an old conjecture of Paul Erdős and Paul Turán: if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions. This is now known as Szemerédi's theorem. One of the key tools introduced in his proof is now known as the Szemerédi regularity lemma, which has become a very important tool in combinatorics, being used for instance in property testing for graphs and in the theory of graph limits.
He is also known for the Szemerédi-Trotter theorem in incidence geometry and the Hajnal-Szemerédi theorem in graph theory. Ajtai and Szemerédi proved the corners theorem, an important step toward higher dimensional generalizations of the Szemerédi theorem. With Ajtai and Komlós he proved the ct2 /log t upper bound for the Ramsey number R(3,t), and constructed a sorting network of optimal depth. With Ajtai, Chvátal, and M. M. Newborn, Szemerédi proved the famous Crossing Lemma, that a graph with n vertices and m edges, where m greater than 4n has at least m3 / 64n2 crossings. With Paul Erdős, he proved the Erdős-Szemerédi theorem on the number of sums and products in a finite set. With Wolfgang Paul, Nick Pippenger, and William Trotter, he established a separation between nondeterministic linear time and deterministic linear time, in the spirit of the infamous P versus NP problem. With William Trotter, he established the Szemerédi–Trotter theorem obtaining an optimal bound on the number of incidences between finite collections of points and lines in the plane.*Wik

DEATHS

1757 Samuel König was a German mathematician who is best remembered for his part in a dispute with Maupertuis over the Principle of Least Action.*SAU In the 17th century Pierre de Fermat postulated that "light travels between two given points along the path of shortest time," which is known as the principle of least time or Fermat's principle.
Credit for the formulation of the principle of least action is commonly given to Pierre Louis Maupertuis, who wrote about it in 1744 and 1746. Maupertuis felt that "Nature is thrifty in all its actions", and applied the principle broadly. *Wik

1814 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS

1836 Claude-Louis Navier was a French mathematician best known for the Navier-Stokes equations describing the behaviour of a incompressible fluid. *SAU

1927 William Burnside wrote the first treatise on groups in English and was the first to develop the theory of groups from a modern abstract point of view. *SAU

1957 Harald Ulrik Sverdrup ( 15 Nov 1888; 21 Aug 1957)was a Norwegian meteorologist and oceanographer known for his studies of the physics, chemistry, and biology of the oceans. He explained the equatorial countercurrents and helped develop the method of predicting surf and breakers. As scientific director of Roald Amundsen's polar expedition on Maud (1918-1925), Sverdrup worked extensively on meteorology, magnetics, atmospheric electricity, physical oceanography, and tidal dynamics on the Siberian shelf, and even on the anthropology of Chukchi natives. In 1953, Sverdrup quantified the concept of "critical depth", explaining the onset of the spring phytoplankton bloom in newly stratified water columns.*TIS

1995 Subrahmanyan Chandrasekhar (19 Oct 1910, 21 Aug 1995) Indian-born U.S. astrophysicist who shared with William A. Fowler the 1983 Nobel Prize for Physics for formulating the currently accepted theory on the later evolutionary stages of massive stars, work that subsequently led to the discovery of neutron stars and black holes. *TIS

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum