Jump to content

Tammes problem

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Tamfang (talk | contribs) at 06:35, 6 August 2024 (packing != covering). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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 points on the surface of a sphere such that the minimum distance between points 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]

Unsolved problem in mathematics:
What is the optimal packing of circles on the surface of a sphere for every possible amount of circles?

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]

See also

References

  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 (4): 460–468. doi:10.1080/10586458.2015.1022842. S2CID 39429109.
  4. ^ Sloane, N. J. A. "Spherical Codes: Nice arrangements of points on a sphere in various dimensions".

Bibliography

Journal articles
Books