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Many problems in discrete geometry are simply stated and can be used in teaching to make certain concepts easier to understand. Searching for points with integer coordinates on a line naturally leads to applications of theorems from number theory.
One of the arts and pleasures of mathematics is finding different ways to represent problems. Some problems in dynamics can profitably be replaced by the study of trajectories on a billiard table, revealing hidden structures—and hence hidden logical beauty.
The algorithm for computing the GCD dates back at least to Euclid. It was subsequently refined over the centuries.
Many arithmetic problems can be solved using standard methods, whether elementary or advanced. But some puzzles call for a basic concept—divisibility—and a little ingenuity.
