## Saturday, 9 July 2011

### On This Day in Math - July 9

Epitaph (by Kepler, for himself)
Mensus eram coelos, nunc Terrae metior umbras.
Mens coelestis erat, corporis umbra jacet.

I used to measure the Heavens, now I measure the shadows of Earth.
The mind belonged to Heaven, the body's shadow lies here.

EVENTS
1595 Kepler gets the inspiration for his first model of the universe.. when the 23 year old Kepler, while teaching, made the first of a profound series of discoveries. Kepler fully elaborates this discovery in his Mysterium Cosmographicum, published less than a year later. It appeared to him that the respective radii of the orbits of the planets corresponded to the lengths determined by a specific sequence in which the five regular solids were placed within one another, with a sphere separating each solid from the other. The sphere (orbit) of Saturn enveloped a cube which in turn enveloped another sphere, the orbit of Jupiter. This circumscribed a tetrahedron, a sphere (the orbit of Mars), a dodecahedron, a sphere (the orbit of earth), an icosahedron, a sphere (the orbit of Venus), an octahedron, and the smallest sphere (the orbit of Mercury). The idea was the main theme of his Mysterium cosmographicum (1596). *Dave Richeson, Euler’s Gem

On that day, while standing at the blackboard drawing a geometrical figure for his class, Kepler had an epiphany. He believed it was a divine inspiration. Kepler had drawn a triangle with a circle circumscribed around it, which meant that each of the triangle's corners touched the rim of the circle. Then he inscribed another circle inside the triangle, which meant that the center of each side of the triangle touched the inner circle.
When Kepler stepped back and looked at what he had drawn, he realized with a shock that the ratios of the two circles were the same as the ratios of the orbits of Saturn and Jupiter. And with that realization, inspiration struck. Jupiter and Saturn were the outermost planets of the solar system, and the triangle was the simplest polygon. Kepler wondered whether you could fit the orbits of the other planets around other geometric figures, and tried his best inscribing circles in squares and pentagons. But the planetary orbits refused to fit.
Then Kepler had a second epiphany. The solar system was three dimensional – so why would he think that its governing pattern would be found in two dimensional figures? Kepler turned to three dimensional objects, and found his answer in the five perfect solids. A perfect solid is a three dimensional figure, such as a cube, whose sides are all identical. Conveniently for Kepler, there are only five perfect solids: the tetrahedron (which has four triangular sides), cube (six square sides), octahedron (eight triangular sides), dodecahedron (twelve pentagonal sides), and icosahedron (twenty triangular sides). Each perfect solid can be inscribed in and circumscribed around a sphere. *Spark Notes

1814 Gauss
made the 146th and last entry in his scientiﬁc diary. He observed a connection between biquadradic residues and the lemniscate functions. This has become the most famous entry in the diary as it led to the Weil conjectures. See Gray, Expositions Mathematicae, 2(1984), 97–130. *VFR

1857 Weierstrass, in his inaugural speech at the Berlin Academy, stated that mathematics occupies an especially high place because only through its aid can a truly satisfying understanding of natural phenomena be obtained. *VFR

1953 France issued a stamp picturing Gaspard Monge. [Scott #279].

BIRTHS

1845 Birthdate of George Howard Darwin, ﬁfth child of the evolutionist Charles Darwin. After graduating second wrangler and Smith’s prizeman at Cambridge in 1866 he studied law before settling down to his life work in mathematical astronomy. He addressed the Fifth International Congress of Mathematicians at Cambridge in 1912 on his work on the three body problem. *VFR  He championed a theory (no longer accepted) that the Moon was once part of the Earth, in what is now the Pacific Ocean. His was the first mathematical analysis of the evolution of Earth's Moon. He suggested that since the effect of the tides has been to slow the Earth's rotation and to cause the Moon to recede from the Earth, then by extrapolating back 4.5 billion years ago the Moon and the Earth would have been very close, with a day being less than five hours. Before this time the two bodies would actually have been one, until the Moon was torn away from the Earth by powerful solar tides that would have deformed the Earth every 2.5 hours. *TIS

John Archibald Wheeler (July 9, 1911 – April 13, 2008) was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission. One of the later collaborators of Albert Einstein, he tried to achieve Einstein's vision of a unified field theory. He is also known for having coined the terms black hole, quantum foam and wormhole and the phrase "it from bit". For most of his career, Wheeler was a professor at Princeton University and was influential in mentoring a generation of physicists who made notable contributions to quantum mechanics and gravitation.*Wik

1931 Valentina Mikhailovna Borok (9 July 1931, Kharkiv, Ukraine, USSR–4 February 2004, Haifa, Israel) was a Soviet Ukrainian mathematician. She is mainly known for her work on partial differential equations.*Wik
DEATHS
1856 Count Amedeo Avogadro  Italian chemist and physicist who found that at the same temperature and pressure equal volumes of all perfect gases contain the same number of particles,  known as Avogadro's Law (1811) leading to the Avogadro's constant being 6.022 x 1023 units per mole of a substance. He realized the particules could be either atoms, or more often, combinations of atoms, for which he coined the word "molecule." This explained Gay-Lussac's law of combining volumes (1809). Further, Avogadro determined from the electrolysis of water that it contained molecules formed from two hydrogen atoms for each atom of oxygen, by which the individual oxygen atom was 16 times heavier than one hydrogen atom (not 8 times as suggested earlier by Dalton.) The Italian, Romano Amadeo Carlo Avogadro, had suggested [in 1811] that all gases have the same number of molecules in a given volume. Loschmidt figured out [in 1865] how many molecules that would be which is the number now known as Avogadro's constant. John D. Cook suggested that maybe it should be called Loschmidt's constant, and pointed out three interesting coincidences involving Avogadro's Constant:
NA is approximately 24! (i.e., 24 factorial.)
The mass of the earth is approximately 10 NA kilograms.
The number of stars in the observable universe is 0.5 NA.
*John D. Cook, The Endeavour Blog

1953  Henri Padé made important contributions to the theory of continued fractions *SAU

1980  Arend Heyting is important in the development of intuitionistic logic and algebra. (try saying that three times really fast)*SAU

1984 Edna Ernestine Kramer Lassar died of pneumonia at her home in Manhattan. She graduated magna cum laude from Hunter College and earned a Ph.D. at Columbia in 1930. She is best known for her book The Nature and Growth of Modern Mathematics, which is an excellent exposition of much of modern mathematics. It is very accessible to undergraduates. For more about her, see Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise
S. Grinstein and Paul J. Campbell. *VFR

1996  Douglas George Chapman was a Canadian-born U.S. mathematical statistician  and an expert on wildlife statistics. He was one of the scientific advisors to the International Whaling Commission that warned in the 1960s that the number of whales being taken by the whaling industry was far in excess of what the population could stand, and proposed annual fin whale catch quotas that would permit the depleted populations of this species to recover. His later research on fish farming expanded to include mollusk aquaculture and he directed a program to develop quantitative methods to aid in the management of fisheries resources.*TIS

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