Tammes problem
Encyclopedia
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
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, Tammes problem is a problem in packing a given number of circles
Circle packing
In geometry, circle packing is the study of the arrangement of circles on a given surface such that no overlapping occurs and so that all circles touch another. The associated "packing density", η of an arrangement is the proportion of the surface covered by the 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
Pollen
Pollen is a fine to coarse powder containing the microgametophytes of seed plants, which produce the male gametes . Pollen grains have a hard coat that protects the sperm cells during the process of their movement from the stamens to the pistil of flowering plants or from the male cone to the...
grains. It can be viewed as a specialization of the generalized Thomson problem
Thomson problem
The Thomson problem is to determine the minimum energy configuration of N electrons on the surface of a sphere that repel each other with a force given by Coulomb's law. The physicist J. J...
.
External links
- How to Stay Away from Each Other in a Spherical Universe (PDFPortable Document FormatPortable Document Format is an open standard for document exchange. This file format, created by Adobe Systems in 1993, is used for representing documents in a manner independent of application software, hardware, and operating systems....
). - Packing and Covering of Congruent Spherical Caps on a Sphere.
- Talk on the Tammes problem (PDF).
- Science of Spherical Arrangements (PPTMicrosoft PowerPointMicrosoft PowerPoint, usually just called PowerPoint, is a non-free commercial presentation program developed by Microsoft. It is part of the Microsoft Office suite, and runs on Microsoft Windows and Apple's Mac OS X operating system...
). - General discussion of packing points on surfaces, with focus on toriTorusIn geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...
(PDF).