Sunday, 14 August 2011

On This Day in Math - Aug 14

Nothing is difficult to him who would be learned.
~Giovanni Battista Benedetti

The 226th day of the year; The iteration of the sum of the squares of the digits leads to one (a happy number). What percentage of numbers have this property?

EVENTS
1612 Galileo explains his new method of observing the sun in his second letter to Marc Welser:
… I shall now describe the method of drawing the spots with complete accuracy. This was discovered, as I hinted in my other letter, by a pupil of mine, a monk of Cassino named Benedetto Castelli. …
The method is this: Direct the telescope upon the sun as if you were going to observe that body. Having focused and steadied it, expose a flat white sheet of paper about a foot from the concave lens; upon this will fall a circular image of the sun's disk, with all the spots that are on it arranged and disposed with exactly the same symmetry as in the sun. The more the paper is moved away from the tube, the larger this image will become, and the better the spots will be depicted. Thus they will be seen without damage to the eye, even the smallest of them — which, when observed through the telescope, can scarcely be perceived, and only with fatigue and injury to the eyes.”
Previously he had only observed the sun directly near sunrise or sunset. *Galileo's Sunspot Letters at http://mintaka.sdsu.edu/

1894 “The ﬁrst summer meeting of the American Mathematical Society was held in one of the lecture-rooms of the Polytechnic Institute in Brooklyn, N.Y.” Only ten papers were presented! The meeting lasted two days; August 15 was the second. *VFR
This was on a Tuesday and Wednesday of the week to immediately precede the dates of the meeting of The American Association for the Advancement of Science. Thomas Friske's papers indicate this was not only the first summer meeting, it was the first meeting ever under the AMS name. The New York Association had dissolved and reformed itself into the AMS.
The following papers were presented :
1. Theorems in the calculus of enlargement. Dr. Emory
McOlintock, New York, N. Y.
2. A method for calculating simultaneously all the roots of
an equation. Dr. Emory McOlintock, New York, N. Y.
3. Elliptic functions and the Cartesian curve. Professor
Frank Morley, Haver ford, Pa.
4. Concerning the definition by a system of functional
properties of the function f\z) = sin 7tz . Professor E. Hastings
Moore, Chicago, 111.
5. Bertrand's paradox and the non-euclidean geometry»
Professor George Bruce Halsted, Austin, Texas.
6. Analytical theory of the errors of interpolated values
from numerical tables. Professor R. S. Woodward, New
York, N. Y.
7. Upon the problem of the minimum sum of the distances
of a point from given points. Professor V. Schlegel, Hagen,
Germany.
8. On the fundamental laws of algebra. Professor Alexander
Macfarlane, Austin, Texas.
9. About cube numbers whose sum is a cube number. Dr.
Artemas Martin, Washington, D.O.
10. Reduction of the resultant of a binary quadric and w-ic
by virtue of its semicombinant property. Professor Henry S.
White, Evanston, 111.
In the absence of their authors, paper No. 7 was presented
by Professor Hyde, paper No. 9 by the Secretary, and No. 10
by Professor Ziwet.
*Bulletin of the American Mathematical Society

In 1894, the first wireless transmission of information using Morse code was demonstrated by Oliver Lodge during a meeting of the British Association at Oxford. A message was transmitted about 150 yards (50-m) from the old Clarendon Laboratory to the University Museum. However, as he later wrote in his Work of Hertz and Some of his Successors, the idea did not occur to Lodge at the time that this might be developed into long-distance telegraphy. "Stupidly enough, no attempt was made to apply any but the feeblest power, so as to test how far the disturbance could really be detected." Nevertheless this demonstration predated the work of Guglielmo Marconi, who began his experiments in 1896.*TIS

1940 John Atanasoff finishes a paper describing the Atanasoff Berry Computer, or ABC, the computer he designed with Clifford Berry to solve simultaneous linear equations. Atanasoff was only able to claim credit for this paper and title of inventor of the electronic digital computer after a long court battle that ended in 1972. The case - initiated on a charge by Honeywell Inc. that Sperry Rand​. Corp. had enforced a fraudulent patent - involved lengthy testimony by Atanasoff and ENIAC inventors Presper Eckert​ and John Mauchly​, who held the patent under review. A judge's ruling that Atanasoff was the true inventor led to invalidation of the ENIAC patent.
A working replica of the original ABC was completed in 1997 by staff and volunteers at Iowa State University at Ames. *CHM

BIRTHS
1530 Giovanni Battista Benedetti (died 20 June 1598) He was taught only by his father, by Tartaglia, and as he says in his writing, "N Tartaglia taught me only the first four books of Euclid, all the rest I learned by myself with great care and study. Nothing is difficult to him who would be learned." (A poster for every teachers wall). He demonstrated the classic constructions using only a "broken compass"; a compass of a fixed opening. Interestingly this was a challenge problem from Tartaglia to Cardan and Ferrari. Benedetti had a very low opinion of Tartaglia, perhaps because he had been his student during the loss of face duel with Ferrarri in which he left before the problems were finished. He also wrote before Galileo on the mechanics of free-fall.

1737 Charles Hutton was an English mathematician who wrote arithmetic textbooks. A textbook he wrote while at the Royal Military Academy, Woolwich was later adopted as the first math text by the USMA in West Point, NY and served as the principal math text for two decades.

1777 Hans Christian Oersted (14 Aug 1777, 9 Mar 1851 at age 73) Danish physicist and chemist whose discovery (1820) that an electric current in a wire causes a nearby magnetized compass needle to deflect, indicating the electric current in a wire induces a magnetic field around it, marks the starting point for the development of electromagnetic theory. For this, he can be called “the father of electromagnetism,” for which his name was adopted for the magnetic field strength in the CGS system of units (for which the SI system now uses the henry unit). Philosophically, he had believed nature's forces had a common origin. Oersted was the first to isolate aluminum as a metal (1825). He also made the first accurate determination of the compressibility of water (1822). Late in his career, he researched diamagnetism. In his final years, he turned back to philosophy, and started writing The Soul in Nature. *TIS

1842 Jean-Gaston Darboux, born . French mathematician whose work on partial differential equations introduced a new method of integration (the Darboux integral) and contributed to infinitesimal geometry. He wrote a paper in 1870 on differential equations of the second order in which he presented the Darboux integral. In 1873, Darboux wrote a paper on cyclides and between 1887-96 he produced four volumes on infinitesimal geometry, including a discussion of one surface rolling on another surface. In particular he studied the geometrical configuration generated by points and lines which are fixed on the rolling surface. He also studied the problem of finding the shortest path between two points on a surface. *TIS

1850 Walter William Rouse Ball born in London. (14 August 1850 – 4 April 1925) a British mathematician, lawyer and a fellow at Trinity College, Cambridge from 1878 to 1905. He was also a keen amateur magician, and the founding president of the Cambridge Pentacle Club in 1919, one of the world's oldest such societies.*Wik Rouse Ball wrote A short account of the history of mathematics (1888) which provided a very readable and popular account of the subject. The fourth edition of 1908 was reprinted in 1960. He was also the author of the very popular Mathematical Recreations and Essays first published in 1892 which has run to fourteen editions (the last four being revised by H S M Coxeter).*SAU

1865 Guido Castelnuovo, (14 August 1865 – 27 April 1952) Italian algebraic geometer born. When Jewish students were barred from the state universities in the 1930’s, Castelnuovo organized courses for them. *VFR His father, Enrico Castelnuovo, was a novelist and campaigner for the unification of Italy. Castelnuovo is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability are also significant.*Wik He studied under Veronese and followed Cremona as the Advanced Geometry teacher in Rome.

1866 Charles-Jean Étienne Gustave Nicolas de la Vallée Poussin (14 August 1866 - 2 March 1962) was a Belgian mathematician. He is most well known for proving the Prime number theorem. This states that π(x), the number of primes ≤ x, tends to x/Lnx as x tends to infinity. (actually by this time the method of attack involved the use of Li(n), the logarithmic integral as described by Gauss).
The prime number theorem had been conjectured in the 18th century, but in 1896 two mathematicians independently proved the result, namely Hadamard (whose proof was much simpler) and Vallée Poussin. The first major contribution to proving the result was made by Chebyshev in 1848, then the proof was outlined by Riemann in 1851. The clue to two independent proofs being produced at the same time is that the necessary tools in complex analysis had not been developed until that time. In fact the solution of this major open problem was one of the major motivations for the development of complex analysis during the period from 1851 to 1896.
The king of Belgium ennobled him with the title of baron. *SAU

1886 Arthur Jeffrey Dempster (died 11 Mar 1950)Canadian-American physicist who in 1918 built the first mass spectrometer (based on the invention of Francis W. Aston) and discovered isotope uranium-235 (1935). The mass spectrometer is an instrument that uses electric and magnetic fields to separate and measure a sample's atoms according to their mass and relative quantity. In 1935, he discovered that naturally occurring uranium, though mostly uranium-238, contained 0.7% U-235 (later used as the primary fuel in atomic bombs and reactors after Niels Bohr predicted it could be used to produce a chain reaction releasing huge amounts of nuclear fission energy). During WW II, Dempster worked with the secret Manhattan Project that developed the world's first nuclear weapons.*TIS

1906 Eugene Lukacs (14 August 1906 – 21 December 1987) was a Hungarian statistician born in Szombathely, notable[1] for his work in characterization of distributions, stability theory, and being the author of Characteristic Functions[2], a classic textbook in the field.*Wik

DEATHS
1795 George Adams Jr. (1750– August 14, 1795), continued his father's work with his younger brother Dudley, publishing an Essay on Vision (1789) and Astronomical and Geometrical Essays (1789) and succeeding his father as Instrument Maker to King George II and the British East India Company. Born in Southampton he was later appointed Optician to the Prince of Wales. His instruments included barometers, microscopes, orreries, sectors, telescopes, and a variety of electrical appliances. He also made geographical globes.  Wik
*http://sciencemuseum.org.uk

1834 Edmond Nicolas Laguerre, studied approximation methods and is best remembered for the special functions: the Laguerre polynomials.*SAU

1858 George Combe (born 21 Oct 1788) Scottish lawyer who turned to the promotion of phrenology and published several works on the subject. He followed Johann Spurzheim who coined the word "phrenology" and promoted it in Europe and Britain, elaborating on "cranioscopy" he learned from Franz Josef Gall in Paris. Gall was a French physician who identified a number of areas on the surface of the head that he linked with specific localizations of cerebral functions and the underlying attributes of the human personality. Combe established the first infant school in Edinburgh and gave evening lectures. He studied the criminal classes and lunatic asylums wishing to reform them. Andrew Combe, physiologist, was his younger brother. *TIS

1930 Florian Cajori (born 28 Feb 1859)Swiss-born U.S. educator and mathematician whose works on the history of mathematics were among the most eminent of his time.*TIS at times Cajori's work lacked the scholarship which one would expect of such an eminent scientist, we must not give too negative an impression of this important figure. He almost single-handedly created the history of mathematics as an academic subject in the United States and, particularly with his book on the history of mathematical notation, he is still one of the most quoted historians of mathematics today. *SAU

1958 Frederic Joliot-Curie (born 19 Mar 1900) French physical chemist, husband of Irène Joliot-Curie, who were jointly awarded the 1935 Nobel Prize for Chemistry for their discovery of artificially prepared, radioactive isotopes of new elements. They were the son-in-law and daughter of Nobel Prize winners Pierre and Marie Curie.*TIS

1967 Jovan Karamata (February 1, 1902–August 14, 1967) was one of the greatest Serbian mathematicians of the 20th century. He is remembered for contributions to analysis, in particular, the Tauberian theory and the theory of slowly varying functions. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts in 1946. *Wik

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