Tammes problem
Some natural systems such as this coral require approximate solutions to problems similar to the Tammes problem
In geometry, 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 a Dutch botanist who posed the problem in 1930 while studying the distribution of pores on pollen grains. It can be viewed as a specialization of the generalized Thomson problem.
See also
Bibliography
- Journal articles
- Tammes PML (1930). "On the origin of number and arrangement of the places of exit on pollen grains". Diss. Groningen.
- Tarnai T, Gáspár Zs (1987). "Multi-symmetric close packings of equal spheres on the spherical surface". Acta Crystallographica A43: 612–616. doi:10.1107/S0108767387098842.
- Erber T, Hockney GM (1991). "Equilibrium configurations of N equal charges on a sphere". Journal of Physics A: Math. Gen. 24: Ll369–Ll377.
- Melissen JBM (1998). "How Different Can Colours Be? Maximum Separation of Points on a Spherical Octant". Proceedings of the Royal Society A 454 (1973): 1499–1508. Bibcode:1998RSPSA.454.1499M. doi:10.1098/rspa.1998.0218.
- Bruinsma RF, Gelbart WM, Reguera D, Rudnick J, Zandi R (2003). "Viral Self-Assembly as a Thermodynamic Process". Physical Review Letters 90 (24): 248101–1–248101–4. arXiv:cond-mat/0211390. Bibcode:2003PhRvL..90x8101B. doi:10.1103/PhysRevLett.90.248101.
- Books
- Aste T, Weaire DL (2000). The Pursuit of Perfect Packing. Taylor and Francis. pp. 108–110. ISBN 978-0-7503-0648-5.
- Wells D (1991). The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin Books. p. 31. ISBN 0-14-011813-6.
External links
- How to Stay Away from Each Other in a Spherical Universe (PDF).
- Packing and Covering of Congruent Spherical Caps on a Sphere.
- Talk on the Tammes problem (PDF).
- Science of Spherical Arrangements (PPT).
- General discussion of packing points on surfaces, with focus on tori (PDF).
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