Induction in Geometry

Induction in Geometry discusses the application of the method of mathematical induction to the solution of geometric problems, some of which are quite intricate. The book contains 37 examples with detailed solutions and 40 for which only brief hints are provided. Most of the material requires only a background in high school algebra and plane geometry; chapter six assumes some knowledge of solid geometry, and the text occasionally employs formulas from trigonometry. Chapters are self-contained, so readers may omit those for which they are unprepared.

To provide additional background, this volume incorporates the concise text, The Method of Mathematical Induction. This approach introduces this technique of mathematical proof via many examples from algebra, geometry, and trigonometry, and in greater detail than standard texts. A background in high school algebra will largely suffice; later problems require some knowledge of trigonometry. The combination of solved problems within the text and those left for readers to work on, with solutions provided at the end, makes this volume especially practical for independent study.

About the Authors

L. I. Golovina was on the faculty of Moscow State University.

I. M. Yaglom (1921–88) was affiliated with Moscow State Pedagogical Institute. He wrote several popular books on mathematics, including these Dover publications: Challenging Mathematical Problems with Elementary Solutions (with A. M. Yaglom) in two volumes, and The U.S.S.R. Olympiad Problem Book (with D. O. Shklarsky and N. N. Chentzov).

I. S. Sominskii was on the faculty of the Novgorod Pedagogical Institute.