Ingeometry, theTammes problem is a problem inpacking a given number of points on the surface of asphere such that the minimum distance between points is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanistJantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores onpollen grains.[1] If circles with diameter equal to the minimum distance are drawn around each point, they will not cross. Another equivalent way of phrasing the problem is to ask for the largest radius such that the given number of circles of that radius can be packed disjointly on the sphere.
It can be viewed as a particular special case of thegeneralized Thomson problem of minimizing the totalCoulomb energy ofelectrons in a spherical arrangement.[2] Thus far, solutions have beenproven only for small numbers of circles: 3 through 14, and 24.[3] There areconjectured solutions for many other cases, including those in higher dimensions.[4][5]
