## Friday, 12 August 2011

### On This Day in Math - Aug 12

I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them.
~Erwin Schrodinger

The 224th day of the year; 224 is the sum of the cubes of 4 consecutive integers:

224 = 23 + 33 + 43 + 53

EVENTS

1269 A letter written on this day by Master Peter de Maricourt (Perigrinus) indicates that he had a knowledge of magnetic polarity, knew that opposites attract, understood that splitting a bar magnet preserved two poles in each part, and was aware that a weaker magnet could have its polarity reversed by a stronger one.  *A history of physics in its elementary branches  By Florian Cajori

1755 19 year old Joseph Louis Lagrange sends a letter to Euler where he described his "method of variations". *Optimal Control and Forecasting,  Euler responded promptly and with great fervor and the two began a long series of correspondence. Euler also promoted the admission of Lagrange to the Berlin Academy.

1877 Asaph Hall discovered Deimos, outer satellite of Mars. It is named after Deimos, a figure representing dread or terror in Greek Mythology. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik
In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars. " *assorted

1883 Fragmented Comet Nearly Hits The Earth:  On 12th and 13th August 1883, an astronomer at a small observatory in Zacatecas in Mexico made an extraordinary observation. José Bonilla counted some 450 objects, each surrounded by a kind of mist, passing across the face of the Sun.  Today, Hector Manterola at the National Autonomous University of Mexico in Mexico City,  gave a different interpretation. He thinks Bonilla must have been seeing fragments of a comet that had recently broken up. This explains the 'misty' appearance of the pieces and why they were so close together. Manterola and co end their paper by spelling out just how close Earth may have come to catastrophe that day. They point out that Bonilla observed these objects for about three and a half hours over two days. This implies an average of 131 objects per hour and a total of 3275 objects in the time between observations.
Each fragment was at least as big as the one thought to have hit Tunguska. Manterola and co end with this: "So if they had collided with Earth we would have had 3275 Tunguska events in two days, probably an extinction event." *MIT Technology Review,  (Many question the interpretation)

1949 On Aug. 12, 1949, time slowed briefly in London. Fifty starlings settled on Big Ben’s minute hand and delayed the striking of the hour by four and a half minutes. *Greg Ross, Futility Closet (A “murmuration” of starlings, as this phenomenon is known, must be one of the most magical, yet underrated, wildlife spectacles on display in winter. Impenetrable as the flock’s movements might seem to the human eye, the underlying maths is comparatively straightforward. Each bird strives to fly as close to its neighbors as possible, instantly copying any changes in speed or direction. As a result, tiny deviations by one bird are magnified and distorted by those surrounding it, creating rippling, swirling patterns. In other words, this is a classic case of mathematical chaos (larger shapes composed of infinitely varied smaller patterns). Whatever the science, however, it is difficult for the observer to think of it as anything other than some vast living entity. Until recently such sights were common over London. *Daniel Butler, Telegraph, 23 Feb 2009)

1985 Celebration of the centenary of the International Statistical Institute in Amsterdam begins. It lasted until August 22. *VFR

BIRTHS

1769 Johann Christian Martin Bartels (12 August 1769 – 7/20 December 1836) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan. *Wik

1862 Jules Antoine Richard born. Richard worked mainly on the foundations of mathematics and geometry, relating to works by Hilbert, von Staudt and Méray.
Further according to Richard, it is the aim of science to explain the material universe. And although non-Euclidean geometry had not found any applications (Albert Einstein finished his general theory of relativity only in 1915), Richard already stated clairvoyantly:"One sees that having admitted the notion of angle, one is free to choose the notion of straight line in such a way that one or another of the three geometries is true." *Wik

1887 Erwin Schrodinger, born. Austrian theoretical physicist who shared the 1933 Nobel Prize for Physics with the British physicist P.A.M. Dirac. Schrödinger took de Broglie's concept of atomic particles as having wave-like properties, and modified the earlier Bohr model of the atom to accommodate the wave nature of the electrons. This made a major contribution to the development of quantum mechanics. Schrödinger realized the possible orbits of an electron would be confined to those in which its matter waves close in an exact number of wavelengths. This condition, similar to a standing wave, would account for only certain orbits being possible, and none possible in between them. This provided an explanation for discrete lines in the spectrum of excited atoms. *TIS

DEATHS

1900 James Edward Keeler was an American astronomer who confirmed Maxwell's theory that the rings of Saturn were not solid (requiring uniform rotation), but composed of meteoric particles (with rotational velocity given by Kepler's 3rd law). His spectrogram of 9 Apr 1895 of the rings of Saturn showed the Doppler shift indicating variation of radial velocity along the slit. At the age of 21, he observed the solar eclipse of July, 1878, with the Naval Observatory expedition to Colorado. He directed the Allegheny Observatory (1891-8) and the Lick Observatory from 1898, where, working with the Crossley reflector, he observed large numbers of nebulae whose existence had never before been suspected. He died unexpectedly of a stroke, age 42.*TIS

1901 Ernest de Jonquières was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

1989 William B. Shockley English-American engineer and teacher, co-winner (with John Bardeen and Walter H. Brattain) of the Nobel Prize for Physics in 1956 for their development of the transistor, a device that largely replaced the bulkier and less-efficient vacuum tube and ushered in the age of microminiature electronics. *TIS

2004 Sir Godfrey Newbold Hounsfield English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS

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