Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…

The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…

The origin, properties, and applications of various number systems are discussed. Among the 15 topics discussed are: tests for divisibility, the binary system, the game of Nim, computers, and infinite number representations. (MK)

Inversions are transformations of geometric figures, under which straight lines may be mapped to circles, and conversely. The use of such mapping allows development of a unified method of solution for many of the problems of elementary geometry, especially those concerning constructions and "pencils" of curves. This book discusses the inversion…

Presented is an elaboration of a course given at Moscow University for pupils in ninth and tenth grades. The development through abstraction of the general definition of distance is discussed and a class of spaces in which the notion of distance is defined, the so-called metric spaces, is introduced. The general concept of distance is related to a…

Pascal's Triangle is an important numerical table; with its help, a number of computation problems may be solved. Some of these problems are examined and the question of what"solving a problem" can mean is generally considered. (Author/MK)