## Wednesday, 20 July 2011

### On This Day in Math - July 20

The greatest discoveries of science have always been
those that forced us to rethink our beliefs
about the universe and our place in it.

-Robert L. Park

EVENTS
Today is the 201st day of the year. 201 is a harshad number... 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. (Can you find the string of three consecutive harshad numbers smaller than 201?) On a leap year it is the 202nd day of the year: In an alphabetical listing of the first one-thousand numbers, 202 is last

1632 Pierre de Carcavi became a member of the parliament of Toulouse. His friendship with Fermat dates from this time.*VFR

1714 Just twelve days before her death, Queen Anne signs "An Act for Providing a Publick Reward for such Person or Persons as shall Discover the Longitude at Sea". *Derek Howse, Britain's Board of Longitude:the Finances 1714-1828

1798 The Battle of the Pyramids during Napoleon’s Egyptian campaign. It is a myth that his troops damaged the Sphinx by using it for target practice. *VFR (I'm afraid it is a myth I have shared, sorry kids!)

1959 The ﬁrst “International Mathematical Olympiad” began in Bucharest, Romania. It lasted until 30 July and involved teams from seven Eastern Euroean countries. [The College Mathematics Journal, 16 (1985), p. 333] *VFR

1969 Neil Armstrong, now of Lebanon, OH, was the ﬁrst man on the moon; Edwin Aldrin was a close second. Armstrong all but quoted what D. T. Whiteside wrote two years earlier about Isaac Newton: “May this present edition be a small step towards that long-overdue monument to a man who in so many areas of human thought himself took a giant’s leap.” See The Mathematical Papers of Isaac Newton, I, xxxvi and VIII, xxix. *VFR In 1969, Apollo XI astronauts Neil Armstrong and Edwin "Buzz" Aldrin became the first men to walk on the moon, after their lunar module separated from the command module and landed on the lunar surface at 09:18 GMT/4:18 EDT on the Sea of Tranquillity. Neil Armstrong and Edwin Aldrin establish Tranquility Base while Michael Collins orbited above. Armstrong stepped on the lunar surface at 10:56 ET and proclaimed, "That's one small step for a man, one giant leap for mankind." Internationally, nearly 700 million television viewers witnessed the event live as it happened.*TIS
1969 The mineral armalcolite was found on the moon, before it was known to exist on the earth. Named for the first letters of the Apollo 11 astronauts who found it, ARMstrong, COLlins, and ALDrin, the mineral was later found in Montana, South Africa, Greenland, and the Ukraine. *FFF pg 220

BIRTHS
1873 Alberto Santos-Dumont was a Brazilian aviation pioneer, deemed the Father of Aviation by his countrymen. At the age of 18, Santos-Dumont was sent by his father to Paris where he devoted his time to the study of chemistry, physics, astronomy and mechanics. His first spherical balloon made its first ascension in Paris on 4 July 1898. He developed steering capabilities, and in his sixth dirigible on 19 Oct 1901 won the "Deutsch Prize," awarded to the balloonist who circumnavigated the Eiffel Tower. He turned to heavier-than-air flight, and on 12 Nov 1906 his 14-BIS airplane flew a distance of 220 meters, height of 6 m. and speed of 37 km/h. to win the "Archdecon Prize." In 1909, he produced his famous "Demoiselle" or "Grasshopper" monoplanes, the forerunners of the modern light plane. *TIS

1894 Errett Lobban Cord U.S. automobile manufacturer, advocate of front-wheel-drive vehicles. Cord, still in his twenties when he arrived at the Auburn Automobile Company, had a talent for seeking and hiring young, innovative minds, full of drive and ambition. Cord was a brilliant, complex industrialist who helped personal and public transportation come of age. He is best known today for Auburn, Cord and Duesenberg automobiles, Cord's greatest talent may have been his unparalleled ability to construct an automotive empire durable enough to thrive during the darkest years of the Great Depression. Photo: 1929 Cord L-29 Sedan, America's first front-drive production car. Built by the Auburn Automobile Company, Auburn, Indiana. *TIS

1924  Robert D. Maurer was born  Maurer is an American physicist who co-invented the optical fiber with Donald Keck and Peter Schultz . Optical fiber is a fiber made of glass or plastic that can carry light along its length. They are used in telecommunications and information technology or even illumination. They work as a waveguide because the core keeps the light by total internal reflection. The light bounces off the edges and is reflected back into the fiber without any loss out the side.*Today in History

1947 Gerd Binnig German-born physicist who co-invented the scanning tunneling microscope with Heinrich Rohrer. They shared the 1986 Nobel Prize for Physics with Ernst Ruska, who designed the first electron microscope. This instrument is not a true microscope ( i.e. an instrument that gives a direct image of an object) since it is based on the principle that the structure of a surface can be studied using a stylus that scans the surface at a fixed distance from it. Vertical adjustment of the stylus is controlled by means of what is termed the tunnel effect - hence the name of the instrument.*TIS

DEATHS
1819 John Playfair Scottish mathematician, physicist, and geologist who is remembered for his axiom that two intersecting straight lines cannot both be parallel to a third straight line. His Illustrations of the Huttonian Theory of the Earth (1802) gave strong support to James Hutton's principle of uniformitarianism, essential to a proper understanding of geology. Playfair was the first scientist to recognise that a river cuts its own valley, and he cited British examples of the gradual, fluvial origins of valleys, to challenge the catastrophic theory (based on the Biblical Flood in Genesis) that was still widely accepted. He was also the first to link the relocation of loose rocks to the movement of glaciers. Playfair published texts on geometry, physics, and astronomy. *TIS

1866 Georg Friedrich Bernhard Riemann died in Bolzano, Italy, at age 39. The inscription on his tombstone (translated from the German) reads: “All things work together for good to them that love the Lord.” *VFR Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.
Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral.
He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis. (The actual manuscript had been digitized by the Clay institute.)
He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.*Wik

1937 Guglielmo Marconi Italian inventor, born in Bologna. He was a physicist, who invented the wireless telegraph in 1935 known today as radio. Nobel laureate (1909). In 1894, Marconi began experimenting on the "Hertzian Waves" (the radio waves Hertz first produced in his laboratory a few years earlier). Lacking support from the Italian Ministry of Posts and Telegraphs, Marconi turned to the British Post Office. Encouraging demonstrations in London and on Salisbury Plain followed. Marconi obtained the world's first patent for a system of wireless telegraphy, in 1897, and opened the world's first radio factory at Chelmsford, England in 1898. In 1900 he took out his famous patent No. 7777 for "tuned or syntonic telegraphy."*TIS

1922 Andrey Andreyevich Markov Russian mathematician who helped to develop the theory of stochastic processes, especially those called Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. (For example, the probability of winning at the game of Monopoly can be determined using Markov chains.) His work based on the study of the probability of mutually dependent events has been developed and widely applied to the biological and social sciences.*TIS (Another who died within six weeks of their birthdate.)  Simple Markov chain problem for students, The probability of Events A, B and C are 1/2, 1/3, and 1/6 respectively.  If one of these events occurs on each trial, what is the probability that it takes six trials to get all three outcomes?

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