geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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 Pollen is a powdery substance produced by seed plants. It consists of pollen grains (highly reduced microgametophytes), which produce male gametes (sperm cells). Pollen grains have a hard coat made of sporopollenin that protects the gametop ...

grains.Pieter Merkus Lambertus Tammes (1930): ''On the number and arrangements of the places of exit on the surface of pollen-grains'',

University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university of more than 30,000 students in the city of Groningen in the Netherlands. Founded in 1614, the university is the ...

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. It can be viewed as a particular special case of the generalized Thomson problem of minimizing the total

Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventio ...

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.

References

Bibliography

; Journal articles * * * * ; Books * *

External links

How to Stay Away from Each Other in a Spherical Universe
(

PDF Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ...

).
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). {{Packing problem Circle packing Spherical geometry Palynology

See also

References

Bibliography

External links