Selected problems and theorems on elementary mathematics. Geometry. Stereometry. (Izbrannye zadachi i teoremy elementarnoj matematiki. Geometriya. Stereometriya). (Q2709814)

This book represents a book of problems made on the material of the mathematical circle at Moscow State University in 1940-1950. NEWLINENEWLINENEWLINEThe book contains more then 100 problems on stereometry, on section and folding of figures on the plane and in the space. The book consists of the settings of problems, answers and instructions and, at last, solutions given to all problems of the book. Besides, where it is necessary, the settings of problems are supplied by explanations. NEWLINENEWLINENEWLINEThe contents of book is rather diverse. It consists of four sections nearly not connected among themselves. NEWLINENEWLINENEWLINESection 1 assembles the problems of increased difficulty on the school course of stereometry. Many from these problems were offered on the Moscow mathematical olympiads in 1941-1953. The problems on the geometry of tetrahedron finish this section. NEWLINENEWLINENEWLINESection 2 is devoted to the general theory of polyhedrons. It includes also the problems on the measurement of polyhedral angles. NEWLINENEWLINENEWLINEThe problems on the regular polyhedrons are allocated in Section 3. Here the regular star-like polyhedrons are considered. NEWLINENEWLINENEWLINESome peculiar is section 4 which contains both planimetric and stereometrical problems. Some problems of this section are devoted to the homogeneity of isometric polygons, to the partition of rectangles on squares and to the theory of zonehedrons -- convex polyhedrons with centrally symmetric faces. The problems are not equivalent on the difficulty. Alongside with easy problems, more difficult and very difficult problems are included in the book. The book is intended for teachers and schoolboys of senior classes.