Convex Figures (library of the mathematical circle-volume 4)
This book has been written for pupils of the higher classes in secondary schools and for students in the first semester of universities, as well as for all those who love mathematics. It can be used for study in mathematical work groups in secondary schools as well as universities. The presentation assumes nothing beyond high school mathematics, and the largest part of the book can be understood with the background acquired by the eighth grade in a secondary school. Moreover, we have striven in presenting the material to present even an inexperienced reader with as few difficulties as possible, although at some places, in the interest of ready comprehension, we were forced to give up complete rigor. We believe that all necessary steps toward precision can be carried out independently by any student in the middle semester in mathematics at a university or teachers college. To make this work easier, we intro duce at the end of the book the rigorous definition of the concept of a plane figure as used in this book
Before reading the book, it is advisable to read through carefully the instructions for using it.
By studying Convex Figures a high school teacher will greatly increase his insight and, if the expression is permissible, his pride in Euclidean geometry, while an undergraduate who is a prospective research mathematician will obtain excellent training of his intuition. When he meets the inescapable graduate student who looks down condescendingly on plane geometry, he can easily confound him with a series of nontrivial and appealing facts for whose proof abstract algebra, say, provides no help at all. The mathematically interested under graduate who does not plan to pursue mathematics beyond his A.B. degree will derive lots of fun from a course or seminar based on the book, and even many mature mathematicians will enjoy perusing it.
However, the book does not fit any pattern familiar in the United States. The translators, Professors Paul J. Kelly and Lewis F. Walton, therefore thought that Convex Figures needed to be introduced to the public. It gives me great pleasure to do the honors, because I am con vinced that the reader will not be disappointed.
Translated from the Russian by Paul J. Kelly and Lewis F. Walton
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