Friday, 5 August 2011

On This Day in Math - Aug 5

Mathematics is like checkers in being suitable for the young,
not too difficult, amusing, and without peril to the state. 

This is the 217th day of the year;  217 is both the sum of two positive cubes and the difference of two positive consecutive cubes in exactly one way: 217 = 63 + 13 = 93 − 83. (How frequently would the difference of two consecutive cubes also be expressible as the sum of two cubes?)

1775 Montucla, who was the anonymous editor, served as Royal Censur for a new edition of Jacques Ozanam’s book on mathematical recreations (the first edition was written in Ozanam’s spare time during war time and published in 1694). *VFR The book was later published in English by Charles Hutton in 1803.

In 1864, Giovanni Batista Donati (1827-73) made the first spectroscopic observations of a comet tail (from the small comet, Tempel, 1864 II). At a distance from the Sun the spectrum of a comet is identical to that of the Sun, and its visibility is due only to reflected sunlight. Donati showed that comet tail formed close to the Sun contains luminous gas. In the spectrum of light from the comet tail, Donati saw three absorption lines bands superimposed on a continuous spectrum, which he named alpha, beta and gamma, and are now known as the Swan bands. These bands were also seen in a comet tail viewed by Pietro Secchi in 1866. Sir William Huggins (1868) identified that these were due to the presence of carbon (molecular carbon, C2).*TIS

1935 Institute of Mathematical Statistics founded.*VFR The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world. Beginning in 2005, the institute started offering joint membership with the Bernoulli Society for Mathematical Statistics and Probability as well as with the International Statistical Institute.

1962 a lunar occultation on August 5 enabled Australian radio astronomers to more precisely fix the location of the previously known radio source 3C 273, in Virgo. In 1963 this became the first member of a new class of object eventually to be called quasars or "quasi-stellar radio sources." Maarten Schmidt, using the Hale optical telescope, saw it as a faint star-like object with a visible jet. Its spectrum featured unusual emission lines, which he identified as ordinary hydrogen lines shifted toward longer wavelengths (redshifted) by 16%. If the shift is due to velocity, it is moving away at one-sixth the speed of light and one of the most distant objects visible. Quasars radiate as much energy per second as a hundred or more galaxies. 3C273 is the brightest quasar known.*TIS

1798 John Wrottesley, 2nd Baron Wrottesley, was an English astronomer, who published Catalogue Of The RA Of 1318 Stars. He was a founder member of the Royal Astronomical Society. From his first Observatory in Blackheath, London, he recorded over 12,000 observations. After he inherited the title and the Staffordshire family estate at Wrottesley in 1841, he built an observatory there. In 1855, the city of Wolverhampton nearby decreed that if any ... furnace chimney ...was built ... within three miles of the observatory, it shall be constructed on the best and approved principles "for consuming the smoke arising ... therefrom". This of course was so that observations from the observatory would not be hampered by smoke pollution.*TIS

1802 Neils Henrik Abel was born at Fomm¨oy, a small island near Stavanger in Norway. Before going to the university in 1821 he attacked, with the vigor and immodesty of youth, the problem of the solution of the quintic equation. He submitted a solution for publication but found an error before it was published. In 1823 he proved the impossibility of a solution involving radicals that solves fifth or higher degree equations. *VFR He developed the concept of elliptic functions independently of Carl Gustav Jacobi, and the theory of Abelian integrals and functions became a central theme of later 19th-century analysis. He had difficulty finding an academic position, was troubled by poverty, and died in poverty in his late twenties.*TIS  I love Abel's commet on Gauss' writing style, "He is like the fox, who effaces his tracks in the sand with his tail." 

1855 William Henry Dines was an English meterologist and inventor of related measurement instruments such as the Dines pressure tube anemometer (the first instrument to measure both the velocity and direction of wind, 1901), a very lightweight meteorograph, and a radiometer (1920). He joined the Royal Meteorological Society study of the cause of the disastrous Tay Bridge collapse of 1879. His measurements of upper air conditions, first with kites and later by balloon ascents (1907), brought an understanding of cyclones from dynamic processes in the lower stratosphere rather than thermal effects nearer to the ground.*TIS

1855  Alfredo Capelli (5 Aug 1855, Milan, Italy – 28 Jan 1910, Naples, Italy) was an Italian mathematician who discovered Capelli's identity.
Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati. In 1881 he became a professor at the University of Palermo, replacing Cesare Arzelà who had recently moved to Bologna. In 1886, he moved again to the University of Naples, where he held the chair in algebra. He remained at Naples until his death in 1910. As well as being a professor there, he was editor of the Giornale di Matematiche di Battaglini from 1894 to 1910, and was elected to the Accademia dei Lincei.*Wik

1930 Neil Alden Armstrong, U.S. astronaut, was the first man to walk on the moon (20 Jul 1969, Apollo 11). He served as a Navy pilot during the Korean War, then joined the National Advisory Committee for Aeronautics (which became NASA), as a civilian test pilot. In 1962, he was the first civilian to enter the astronaut-training program. He gained experience as command pilot of the Gemini 8 mission, which accomplished the first physical joining of two orbiting spacecraft. Later he was commander of the Apollo 11 lunar mission. From 1971, he worked as professor of aerospace engineering at the University of Cincinnati. He was a member of the commission that investigated the 1986 Challenger space shuttle disaster.*TIS

1729 Thomas Newcomen, inventor of the atmospheric steam engine, died in London. His invention of c.1711 came into use to pump water out of coal mines by 1725. It had a piston connected to one end of a large crossbeam; the other end was connected to a very heavy pump piston. On each stroke, water chilled and condensed the steam in the cylinder, dropping the piston thus moving the crossbeam and operating the pump. This was wasteful of fuel needed to reheat the cylinder for the next stroke. Although it was slow and inefficient, Newcomen's engine was relied on for the first 60 years of the new steam age it began. *TIS
1853 Théodore Olivier (21 Jan 1793 in France - 5 Aug 1853 in France) From the 1840's Olivier wrote textbooks. His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry. Some of the models were of ruled surfaces, with moving parts to illustrate to students how the ruled surfaces were generated. Others were designed to illustrate the curves of intersection of certain surfaces. In fact Olivier earned quite a good income from selling these models, particularly in the United States.
The United States Military Academy at West Point had 23 mathematical models made for them by Olivier to use as teaching aids:=
These models are built on wooden boxes as bases, have metal supports, and consist of strings suspended from movable arms and arranged to form a variety of geometrical figures. The strings are held in place by lead weights that are concealed by the bases. The models illustrate such things as the intersection of two half cones, the intersection of a plane, hyperbolic paraboloid and a hyperboloid of one sheet, and the intersection of two half cylinders.
Other institutions in the United States such as the Columbia School of Mines also purchased models from Olivier while Princeton had copies of Olivier's models made for them. In 1849 Olivier presented a full set of the range of models he had created to the Conservatoire National des Arts et Métiers. The models had been manufactured by the firm of Pixii, Père et Fils, and later by the firm of Fabre de Lagrange which took over their manufacture. In 1857, four years after Olivier died, Harvard University purchased 24 of Olivier's models from Fabre de Lagrange and after the university received the order Benjamin Peirce gave a series of lectures on the mathematics which they illustrated. These models are still in Harvard's collection of scientific instruments.
Even after giving a complete set of his models to the Conservatoire National des Arts et Métiers, forty models were still in Olivier's possession at the time of his death. These were sold in 1869 to William Gillispie from Union College in Schenectady, east-central New York, United States. Gillispie exhibited the models at Union College which was appropriate since, twenty years earlier, Union College had became one of the first liberal arts colleges in the United States to give engineering courses. When Gillispie died Olivier's models were sold to the college. *SAU
1872 Charles-Eugène Delaunay French mathematician and astronomer whose theory of lunar motion advanced the development of planetary-motion theories. After 20 years of work, he published two volumes on lunar theory, La Théorie du mouvement de la lune (1860,1867). This is an important case of the three body problem. Delaunay found the longitude, latitude and parallax of the Moon as infinite series. These gave results correct to 1 second of arc but were not too practical as the series converged slowly. However this work was important in the beginnings of functional analysis. Delaunay succeeded Le Verrier as director of the Paris Observatory in 1870 but two years later he and three companions drowned in a boating accident.*TIS

1853 Théodore Olivier was a French geometer who made string models of ruled surfaces. *SAU

1910 Julius Petersen was a Danish mathematician who worked on geometry and graph theory. He is best remembered for the Petersen graph. *SAU  In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by A. B. Kempe (1886). Donald Knuth states that the Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general."  *Wik

1981 Jerzy Neyman, in a paper with his long-time friend and colleague Elizabeth Scott, wrote:
Each morning before breakfast every single one of us approaches an urn filled with white and black balls. We draw a ball. If it is white, we survive the day. If it is black, we die. The proportion of black balls in the urn is not the same for each day, but grows as we become older ... Still there are always some white balls present, and some of us continue to draw them day after day for many years.
On this date, Neyman, age 87, drew a black ball. As he wished of many of his friends, “May the earth rest lightly on him.” [From a review, by Robert V. Hogg, of Neyman—From Life, by Constance Reid (Springer, 1983), in the The College Mathematics Journal, 15(1984), 82–84]*VFR
Neyman was a Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS

1985 Mary P. Dolciani Halloran, noted writer of several High School texts, of Hunter College died at the age of 62. The MAA book series Dolciani Mathematical Expositions is named in her honor. *VFR

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

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