CHALLENGES IN GEOMETRY - FOR MATHEMATICAL OLYMPIANS PAST AND PRESENT

One way to get into shape is to stay in shape, and Bradley (mathematics, Oxford U.) writes on behalf of Mathematical Olympians who are just staring on their way to gold or who remember their triumphs in the dim past. He includes a wealth of exercises in integer-sided triangles, circles and triangles, lattices, rational points on curves, shapes and numbers, quadrilaterals and triangles, touching circles and spheres, solids, circles and conics and finite geometries, and provides an appendix on areal coordinates. Fortunately for the armchair Olympians amongst us, he also provides the answers.