ABSTRACT
Tammes was interested in the number and locations of exit points in pollen grains and he compared many types. He found 4, 6, 8, and 12 common; 5 never occurs; and 7, 9, and 10 occur less frequently. Very rarely does 11 occur.2 He discovered that the distances between exit points were consistent within a type and their distribution on the grain was highly regular. These recurring numbers are no accident; they are optimal solutions to point distributions on the sphere. The similarity of pollen exits to circle packing lies in finding the optimal arrangement of a given set of points on the sphere. To measure how evenly distributed the points are, they are all surrounded by congruent circles large enough for two closest ones to be tangent but not overlap. Other circles will not be tangent, and the challenge is to make them as even as possible and minimize the total uncovered area outside the circles. Today, this optimization problem is called Tammes problem in his honor.
