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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 a Dutch botanist who posed the problem in 1930 while studying the distribution of pores on pollen grains. It can be viewed as a particular special case of the generalized Thomson problem.
See also

Spherical code
Kissing number problem
Cylinder sphere packings

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" (PDF). Journal of Physics A: Mathematical and General. 24: Ll369–Ll377. Bibcode:1991JPhA...24L1369E. doi:10.1088/0305-4470/24/23/008.
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" (PDF). Physical Review Letters. 90 (24): 248101–1–248101–4. arXiv:cond-mat/0211390. Bibcode:2003PhRvL..90x8101B. doi:10.1103/PhysRevLett.90.248101. Archived from the original (PDF) on 2007-09-15.

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. pp. 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).

Mathematics Encyclopedia

Hellenica World - Scientific Library

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