A mathematical gift, II. The interplay between topology, functions, geometry, and algebra. (English)

American Mathematical Society, Providence, RI (ISBN 0-8218-3283-2). 128 p. (2004).

This is the second of three volumes originated from a series of lectures in mathematics given by professors of Kyoto University (Japan) for high school students. The first chapter of the book talks about the theory of trigonometric and elliptic functions. It includes such aspects of this theory as power series expansions, addition and multiple-angle formulas, and arithmetic-geometric mean. The second chapter discusses various aspects of the Poncelet Closure Theorem. This discussion illustrates to the reader the idea of algebraic geometry as a method of studying geometric properties of figures using algebra as a tool.