Tammes problem

File:Tammes cropped.png

12 points in an optimal arrangement around a sphere, which also are the points of a regular icosahedron.

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.

Unsolved problem in mathematics

What is the optimal packing of circles on the surface of a sphere for every possible amount of circles?

More unsolved problems in mathematics

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.

File:Coral Sphere Flynn Reef.jpg

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

See also

• Spherical code
• Kissing number problem
• Cylinder sphere packings

References

Bibliography

Journal articles

Books

External links

• .
• Packing and Covering of Congruent Spherical Caps on a Sphere.
• Science of Spherical Arrangements (PPT).
• General discussion of packing points on surfaces, with focus on tori (PDF).