In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanist Jantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores on pollen grains. Mathematicians independent of Tammes began studying circle packing on the sphere in the early 1940s; it was not until twenty years later that the problem became associated with his name.
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| - Tammesproblem (de)
- Problème de Tammes (fr)
- Tammes problem (en)
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| - Das Tammesproblem bezeichnet in der Mathematik die Anordnung von nicht-überlappenden Kreisen auf der Einheitskugel. Es ist nach dem Botaniker P. M. L. Tammes benannt, der in seiner Dissertation 1930 die Verteilung von runden Poren auf Pollenkörnern untersuchte. (de)
- In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanist Jantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores on pollen grains. Mathematicians independent of Tammes began studying circle packing on the sphere in the early 1940s; it was not until twenty years later that the problem became associated with his name. (en)
- En géométrie, le problème de Tammes, ou problème des dictateurs, consiste à rechercher la disposition d'un certain nombre de points répartis à la surface d'une sphère afin que la distance minimale entre deux points soit la plus grande possible. (fr)
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| - Das Tammesproblem bezeichnet in der Mathematik die Anordnung von nicht-überlappenden Kreisen auf der Einheitskugel. Es ist nach dem Botaniker P. M. L. Tammes benannt, der in seiner Dissertation 1930 die Verteilung von runden Poren auf Pollenkörnern untersuchte. Beim Tammesproblem soll der Minimalabstand zwischen den Kreisen auf der Kugel maximal werden. Bei diesem Packungsproblem handelt es sich also um ein Optimierungsproblem in der diskreten Geometrie. Für eine kleine Anzahl von Kreisen (N ≤ 14) ist das Problem gelöst. Auch für einige hochsymmetrische Fälle ist das Problem gelöst (N = 12, 24, 48, 60, 120). Wichtige Arbeiten auf diesem Gebiet stammen von László Fejes Tóth. (de)
- En géométrie, le problème de Tammes, ou problème des dictateurs, consiste à rechercher la disposition d'un certain nombre de points répartis à la surface d'une sphère afin que la distance minimale entre deux points soit la plus grande possible. Les applications de ce problème sont nombreuses : répartition de satellites artificiels, des creux à la surface d'une balle de golf, répartition de combustible sur des réacteurs nucléaires sphériques, étude d'atomes... Le surnom « problème des dictateurs » vient du fait que, si on laisse un certain nombre de dictateurs à la surface d'une planète, ceux-ci vont certainement chercher à s'éloigner le plus possible les uns des autres afin de pouvoir bénéficier du plus grand territoire (si on considère que le territoire d'un dictateur est constitué de tous les points de la sphère situés plus près de lui que de tout autre dictateur). (fr)
- In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanist Jantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores on pollen grains. Mathematicians independent of Tammes began studying circle packing on the sphere in the early 1940s; it was not until twenty years later that the problem became associated with his name. It can be viewed as a particular special case of the generalized Thomson problem of minimizing the total Coulomb force of electrons in a spherical arrangement. Thus far, solutions have been proven only for small numbers of circles: 3 through 14, and 24. There are conjectured solutions for many other cases, including those in higher dimensions. (en)
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