Tammes problem

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Some natural systems such as this coral require approximate solutions to problems similar to the Tammes problem

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.[1] 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.[citation needed]

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.[2] Thus far, solutions have been proven only for small numbers of circles: 3 through 14, and 24.[3] There are conjectured solutions for many other cases, including those in higher dimensions.[4]

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References[edit]

  1. ^ Pieter Merkus Lambertus Tammes (1930): On the number and arrangements of the places of exit on the surface of pollen-grains, University of Groningen
  2. ^ Batagelj, Vladimir; Plestenjak, Bor. "Optimal arrangements of n points on a sphere and in a circle" (PDF). IMFM/TCS. Archived from the original (PDF) on 25 June 2018.
  3. ^ Musin, Oleg R.; Tarasov, Alexey S. (2015). "The Tammes Problem for N = 14". Experimental Mathematics. 24: 460–468. doi:10.1080/10586458.2015.1022842.
  4. ^ Sloane, N. J. A. "Spherical Codes: Nice arrangements of points on a sphere in various dimensions".

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