Project IV (MATH4072) 2012-13


Points on a Sphere

Paul Sutcliffe

Description

How should N points be placed on a sphere so that the smallest distance between any two points is as large as possible? This is known as the Tammes problem, named after the Dutch botanist who posed the problem in connection with the study of pores in spherical pollen grains. For very small values of N the problem can be solved (for example four points should be placed on the vertices of a tetrahedron) but the problem gets more difficult and interesting as N increases.

Suppose the N points represent the positions of N particles on a sphere that repel each other. How should the particles be arranged so that they are in equilibrium? How does the arrangement depend on the details of the force? Is the arrangement related to that of the Tammes problem? The most famous example of a problem like this is called the Thomson problem, which models the placement of electrons on a sphere.

It turns out that answers to these (and similar) questions have applications in a range of topics from carbon chemistry to modelling viruses and designing golf balls.

The project will involve understanding and investigating the above problems and their solutions.
It will require you to learn some very elementary computer programming to solve these problems.

Prerequisites

None.

Resources

There are many webpages dedicated to these kinds of issues.
Some examples are webpage1, webpage2.

email: Paul Sutcliffe


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