# Koch, Niels Fabian Helge von

Koch, Niels Fabian Helge von

▪ Swedish mathematician
born January 25, 1870, Stockholm, Sweden
died March 11, 1924, Stockholm
Swedish mathematician famous for his discovery of the von Koch snowflake curve, a continuous curve important in the study of fractal geometry.

Von Koch was a student of Gösta Mittag-Leffler and succeeded him as professor of mathematics at Stockholm University in 1911. His first work was on the theory of determinants of infinite matrices (matrix), a topic initiated by the French mathematician Henri Poincaré (Poincaré, Henri). This work now forms part of the theory of linear operators, which are fundamental in the study of quantum mechanics. He also worked on the Riemann hypothesis (see Riemann zeta function) and the prime number theorem.

Von Koch is remembered primarily, however, for a 1906 paper in which he gave a very attractive description of a continuous curve that never has a tangent. Continuous, “nowhere differentiable (differentiation)” functions had been rigorously introduced into mathematics by the German Karl Weierstrass (Weierstrass, Karl) in the 1870s, following suggestions by the German Bernhard Riemann (Riemann, Bernhard) and, even earlier, by the Bohemian Bernhard Bolzano (Bolzano, Bernhard), whose work was not well known. Von Koch's example is perhaps the simplest. Starting with an equilateral triangle, it replaces the middle third of each segment with an equilateral triangle having the deleted portion of the segment as its base (the base is erased). This replacement operation is continued indefinitely, with the result that the limiting curve is continuous but nowhere differentiable. If the new triangles always face outward, the resulting curve will have a striking resemblance to a snowflake, and so the curve is often called von Koch's snowflake.

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Universalium. 2010.

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• Helge Von Koch — Niels Fabian Helge von Koch, né le 25 janvier 1870 à Stockholm et mort le 11 mars 1924 à Danderyd, était un mathématicien suédois, qui a donné son nom à une des premières fractales : le flocon de Koch. Il a également… …   Wikipédia en Français

• Helge von koch — Niels Fabian Helge von Koch, né le 25 janvier 1870 à Stockholm et mort le 11 mars 1924 à Danderyd, était un mathématicien suédois, qui a donné son nom à une des premières fractales : le flocon de Koch. Il a également… …   Wikipédia en Français

• Helge von Koch — Curva Copo de nieve de Koch. Niels Fabian Helge von Koch (Estocolmo, 25 de enero de 1870 ibidem, 11 de marzo de 1924) fue un matemático sueco, cuyo nombre se ha asignado a una famosa curva fractal llamada curva Copo de nieve de Koch, una …   Wikipedia Español

• Helge von Koch — Niels Fabian Helge von Koch (January 25, 1870 March 11, 1924) was a Swedish mathematician, who gave his name to the famous fractal known as the Koch snowflake, which was one of the earliest fractal curves to have been described.He was born into a …   Wikipedia

• Helge von Koch — Pour les articles homonymes, voir Koch. Helge von Koch Helge von Koch Naissance 25 janvier …   Wikipédia en Français

• Helge von Koch — Niels Fabian Helge Hartmut von Koch (Aussprache: [ˌhɛlːgə fɔnˈkɔkː], * 25. Januar 1870 in Stockholm; † 11. März 1924 ebenda) war ein schwedischer Mathematiker. Er konstruierte die nach ihm benannte Koch Kurve, eines der ersten Fraktale, als… …   Deutsch Wikipedia

• Koch-Kurve — Kochsche Schneeflocke, Konstruktion. Die Koch Kurve oder kochsche Kurve ist ein von dem schwedischen Mathematiker Helge von Koch 1904 vorgestelltes Beispiel für eine überall stetige, aber nirgends differenzierbare Kurve. Es handelt sich bei ihr… …   Deutsch Wikipedia

• Helge (name) — Infobox Given Name Revised name = Helge imagesize= caption= pronunciation= gender = meaning = region = origin = related names = footnotes = Helge or Helgi is a Scandinavian name.The name is derived from Proto Norse * Hailaga [… …   Wikipedia

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