Sunday, 17 July 2011

On This Day in Math - July 17

Science is built up with facts, as a house is with stones. 
But a collection of facts is no more a science
than a heap of stones is a house.
~Henri Poincaré

The 198th day of the year; 198 is a Harshad number, divisible by the sum of its digits. A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997.
(Students might try to find the a pair of consecutive numbers greater than 10 which are harshad numbers)

In 709 BC, the earliest record of a confirmed total solar eclipse was written in China. From: Ch'un-ch'iu, book I: "Duke Huan, 3rd year, 7th month, day jen-ch'en, the first day (of the month). The Sun was eclipsed and it was total." This is the earliest direct allusion to a complete obscuration of the Sun in any civilisation. The recorded date, when reduced to the Julian calendar, agrees exactly with that of a computed solar eclipse. Reference to the same eclipse appears in the Han-shu ('History of the Former Han Dynasty') (Chinese, 1st century AD): "...the eclipse threaded centrally through the Sun; above and below it was yellow." Earlier Chinese writings that refer to an eclipse do so without noting totality.*TIS

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS
Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion. Travelling through France ten years later, " in 1788, he noticed peasants near Nancy ploughing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)." Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches. Jefferson is believed to be the first person ever to use the term "catenary" in English.
1850 Vega became the first star (other than the Sun) to be photographed, when it was imaged by William Bond and John Adams Whipple at the Harvard College Observatory. The photo was a daguerreotype. *Wik
1879 It was announced in Nature that Kempe had proved the four-color conjecture. A correct proof, based on Kempe’s ideas, had to wait another century. [N. L. Biggs, et al., Graph Theory 1736–1936, p. 94] *VFR

1935 The first problem was entered into the Scottish Book, a large bound notebook that Stefan Banach brought to the Scottish Cafe in LLw´ow for mathematicians to record research problems. Many of the problems offered prizes to the solver. They ranged from “5 small beers” to “100 grammes of caviar.” This book has been translated into English and edited by R. D. Mauldin. (below) *VFR .. in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and
topology. Stanislaw Ulam recounts that the tables of the café had marble tops, so they could write in pencil, directly on the table, during their discussions. To keep the results from being lost, and after becoming annoyed with their writing directly on the table tops, Stefan Banach's wife provided the mathematicians with a large notebook, which was used for writing the problems and answers and eventually became known as the Scottish Book. The book—a collection of solved, unsolved, and even probably unsolvable problems—could be borrowed by any of the guests of the café. For problem 153, which was later recognized as being closely related to Stefan Banach 's "basis problem", Stanislaw Mazur offered the prize of a live goose. This problem was solved only in 1972 by Per Enflo, who was presented with the live goose in a ceremony that was broadcast throughout Poland.
The café building now houses the Universal Bank at the street address of 27 Taras Shevchenko Prospekt.*Wik

1997 "You DON'T have mail"... A programming error temporarily threw the Internet into disarray in a preview of the difficulties that inevitably accompany a world dependent on e-mail, the World Wide Web, and other electronic communications.
At 2:30 a.m. Eastern Daylight Time, a computer operator in Virginia ignored alarms on the computer that updated Internet address information, leading to problems at several other computers with similar responsibilities. The corruption meant most Internet addresses could not be accessed, resulting in millions of unsent e-mail message. *This Day in History, Computer History Museum

2011  NASA's Dawn Spacecraft Enters Orbit Around Vesta
NASA's Dawn spacecraft on Saturday became the first probe ever to enter orbit around an object in the main asteroid belt between Mars and Jupiter. *NASA

1698 Birthdate of Pierre Louis de Maupertuis, developer of the principle of least action. *VFR a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great.
Maupertuis made an expedition to Lapland to determine the shape of the earth. He is often credited with having invented the principle of least action; a version is known as Maupertuis' principle – an integral equation that determines the path followed by a physical system. His work in natural history has its interesting points, since he touched on aspects of heredity and the struggle for life.*Wik (he died in the home of Johann II Bernoulli, whose death occurred on this same date, (see Deaths)

1831 Victor Mayer Amédée Mannheim (17 July 1831 – 11 December 1906) was the inventor of the modern slide rule. Around 1850, he introduced a new scale system that used a runner to perform calculations. This type of slide rule became known under the name of its inventor: the Mannheim.*Wik

1837 Wilhelm Lexis studied data presented as a series over time thus initiating the study of time series.*SAU  Although the author of an Allgemeine Volkswirtschaftslehre (general economics book) (1910) and certainly a distinguished economist, even a pioneer of Law and Economics thinking and of the study of consumption and crises, Lexis is today primarily known as a statistician, partially due to his creation of the Lexis ratio. His reputation as a demographer is underlined by the ubiquity of Lexis Diagrams, which are named for him, although primary credit for their invention belongs to Gustav Zeuner and O. Brasche (a notable example of Stigler's law of eponymy). He is also one of the founding fathers of the interdisciplinary, professional study of insurance. A Kathedersozialist, he was closely affiliated with academic policy makers in Prussia and one of Friedrich Althoff’s experts and the editor of important works on German higher education, most famously the six-volume Das Unterrichtswesen im Deutschen Reich, compiled for the St. Louis World's Fair of that year and still the key reference work for that time. *Wik

1863 Herbert Richmond studied at Cambridge and spent his whole career there, His main interest was in Algebraic Geometry. He became an honorary member of the EMS in 1930.*SAU

1868 Peter Comrie graduated from St Andrews and after a series of teaching posts became Rector of Leith Academy. He was much involved in the EMS, becoming Secretary in 1911 and President in 1916 and 1917.*SAU

1909 Geoffrey Walker studied at Oxford and Edinburgh. He taught at Imperial College London, Liverpool and Sheffield before returning to Liverpool as Professor of Pure Mathematics. He worked on Differential Geometry, Relativity and Cosmology.*SAU

1920 Gordon Gould American physicist who coined the word "laser" from the initial letters of "Light Amplification by Stimulated Emission of Radiation." Gould was inspired from his youth to be an inventor, wishing to emulate Marconi, Bell, and Edison. He contributed to the WWII Manhattan Project, working on the separation of uranium isotopes. On 9 Nov 1957, during a sleepless Saturday night, he had the inventor's inspiration and began to write down the principles of what he called a laser in his notebook Although Charles Townes and Arthur Schawlow, also successfully developed the laser, eventually Gould gained his long-denied patent rights. *TIS

1790 Johann II Bernoulli died *VFR Johann II Bernoulli (Basel 18 May 1710–1790; also known as Jean), the youngest of the three sons of Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five years professor of eloquence in the university of his native city. In 1736 awarded the prize of the French Academy for his suggestive studies of Aether[1] [2].On the death of his father he succeeded him as professor of mathematics. He was thrice a successful competitor for the prizes of the Academy of Sciences of Paris. His prize subjects were, the capstan, the propagation of light, and the magnet. He enjoyed the friendship of P. L. M. de Maupertuis, who died under his roof (July 27, 1759) while on his way to Berlin. He himself died in 1790. His two sons, Johann and Jakob, are the last noted mathematicians of the Bernoulli family. *Wik

1912 Jules Henri Poincare died very suddenly from an embolism while dressing, in his 59th year. *VFR French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity.
The Poincaré group used in physics and mathematics was named after him.*Wik
His Poincaré Conjecture holds that if any loop in a given three-dimensional space can be shrunk to a point, the space is equivalent to a sphere. Its proof remains an unsolved problem in topology.*TIS
His family gravestone at Cimetière de Montparnasse in Paris is covered with coins, flowers, and notes.  One telling him that "It has been proven."

1917 Giuseppe Veronese Although his work was severely criticised as unsound by Peano, he is now recognised as having priority on many ideas that have since become parts of transfinite numbers and model theory, and as one of the respected authorities of the time, his work served to focus Peano and others on the need for greater rigor.
He is particularly noted for his hypothesis of relative continuity which was the foundation for his development of the first non-archimedean linear continuum.*SAU

1944 William James Sidis(April 1, 1898 – July 17, 1944) an American child prodigy with exceptional mathematical and linguistic abilities. He became famous first for his precocity, and later for his eccentricity and withdrawal from the public eye. He avoided mathematics entirely in later life, writing on other subjects under a number of pseudonyms. The difficulties Sidis encountered in dealing with the social structure of a collegiate setting may have shaped opinion against allowing such children to rapidly advance through higher education in his day.*Wik

1963 Bevan Braithwaite Baker graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London.*SAU

1998 Sir Michael James Lighthill was a British mathematician who contributed to supersonic aerofoil theory and, aeroacoustics which became relevant in the design of the Concorde supersonic jet, and reduction of jet engine noise. Lighthill's eighth power law which states that the acoustic power radiated by a jet is proportional to the eighth power of the jet speed. His work in nonlinear acoutics found application in the lithotripsy machine used to break up kidney stones, the study of flood waves in rivers and road traffic flow. Lighthill also introduced the field of mathematical biofluiddynamics. Lighthill followed Paul Dirac as Lucasian professor of Mathematics (1969) and was succeeded by Stephen Hawking *TIS

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