After a break we being with our postings again. To start, we will see a title in the Little Mathematics Library which is a`natural continuation’ of last post, this one is called Induction in Geometry and the authors are L. I. Golovina and I. M. Yaglom. One of the authors, I. M Yaglom, has written many excellent books in mathematics, we will maybe try to cover them in the future.
The preface says:
This little book is intended primarily for high school pupils, teachers of mathematics and students in teachers training colleges majoring in physics or mathematics. It deals with various applications of the method of mathematical induction to solving geometric problems and was intended by the authors as a natural continuation of I. S. Sominsky’s booklet The Method of Mathematical Induction published (in English) by Mir Publishers in1975. Our book contains 38 worked examples and 45 problems accompanied by brief hints. Various aspects of the method of mathematical induction are treated in them in a most instructive way. Some of the examples and problems may be of independent interest as well.
The book was translated from the Russian by Leonid Levant and was first published by Mir in 1979. This was also published in the Topics in Mathematics series in 1963, and was translated by A.W. Goodman and Olga A. Titelbaum.
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The book contains following sections:
Introduction: The Method of Mathematical Induction 7
Sec. 1. Calculation by Induction 12
Sec. 2. Proof by Induction 20
Map Colouring 33
Sec. 3. Construction by Induction 63
Sec. 4. Finding Loci by Induction 73
Sec. 5. Definition by Induction 80
Sec. 6. Induction on the Number of Dimensions 98
1. Calculation bv Induction on the Number of Dimensions 106
2. Proof by Induction on the Number of Dimensions 109
3. Finding Loci by Induction on the Number of Dimensions 126
4. Definition by Induction on the Number of Dimensions 130