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Mathematics & Computation IV
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Sonia Kovalevskaya (1850-1891) was born into a noble Russian family and due to her gender had to overcome many obstacles in order to pursue her interest in mathematics. Barred from matriculating at Heidelberg, she audited lectures and later studied privately with Weierstrass, receiving a doctorate (in absentia) from Goettingen for an important paper on partial differential equations. Still, academic appointments eluded her. In 1884 she did obtain a position in Stockholm, thereafter winning honors and prizes, including the Prix Bordin in France. (Detail) |
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Pafnuty Lvovich Chebyshev (1821-1894) was a Russian mathematician working in number theory, particularly with prime numbers. (Detail) |
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Srinivasa Ramanujan (1887-1920) was an Indian mathematician who was largely self-taught, deriving independently some work of Gauss and Riemann. G.H. Hardy at Cambridge sponsored the brilliant young mathematician, whose notebooks of original discoveries are being published and are a source of inspiration to other mathematicians. (Detail) |
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Some of its illustrious members included in a set with Sierpinski are Stanislaw Zaremba (1863-1942), Stefan Banach (1892-1945), and Zygmunt Janiszewski (1888-1920). |
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Waclaw Sierpinski (1882-1969), a Polish mathematician working in number theory and set theory, described the self-repeating, or fractal design shown on the Macau and Finnish stamps at left. Sierpinski triangles are created by connecting the the midpoints of the sides of a triangle to form four smaller, interior triangles, and then repeating this process for each of the outside three triangles, ad infinitum. A Hungarian stamp commemorating a mathematical congress shows a design of Sierpinski pyramids, with Michelangelo's hand of God from the Sistine Chapel ceiling thrown in for good measure. A full description of the Polish School of Mathematics appears  |
Stamps commemorating mathematical congresses often use eye-catching figures to draw attention. The Austrian stamp shows Escher's impossible cube. The German stamp issued for the International Congress of Mathematicians held in Berlin in 1998 shows the constant pi calculated to ever increasing accuracy and spiraling outward. (Detail) |  |
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The World Mathematical Year 2000 was observed in many countries with postage stamps picturing significant theorems or relationships of a mathematical nature. The Belgian stamp at left shows a circle, the bell shape of the Gaussian distribution, Stokes' theorem, Fermat's last theorem valid for n=2, and some white scratch marks at the bottom the stamp which should not be ignored. They are marks found on the Bone of Ishango, a 6,000 to 30,000 year old artifact discovered in the 30's by a geologist in Congo. The numbers of the notches display certain mathematical relationships, such as multiplication by 2, as well as addition. The bone now resides in the Belgian Museum of Natural Sciences in Brussels, and was considered significant enough in the history of mathematics to be included on the Belgian stamp. |
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 One example of a fractal is the "snowflake" curve constructed by taking an equilateral triangle and repeatedly erecting smaller equilateral triangles on the middle third of the progressively smaller sides. Theoretically, the result would be a figure of finite area but with a perimeter of infinite length, consisting of an infinite number of vertices. In mathematical terms, such a curve cannot be differentiated. The Swedish mathematician Helge von Koch created this curve 100 years ago. Four such iterations are shown on the right snowflake (three on the left) but cannot be distinguished with this low magnification. (Encarta) The Macau stamp is part of a set on chaos and fractals. |
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