Yu. A. Shashkin

This booklet gives proofs of Euler's famous formula for convex polytopes and of its analogues for other figures (planes, spaces and polygons). The formulas bring the reader naturally to the notion of Euler's characteristic. Two definitions of the notion are given and their equivalence is proved. The part played by the Euler characteristic in different geometrical problems, i.e. in the decomposition of planes and spaces, in calculating areas, in covering of spheres, is discussed.
The book is intended for senior pupils, junior college and university students and all lovers of mathematics.… (mais)