## Configuration Theorems – Argunov, Skornyakov

In this post, we will see the book Configuration Theorems by B. I. Argunov, L. A. Skornyakov. The book is a part of Topics in Mathematics series. We will see some more books in this series in the future.

This booklet presents several important configuration theorems, along with their applications to the study of the properties of figures and to the solutions of several practical problems. In doing this, the authors introduce the reader to some fundamental concepts of projective geometry-central projection and ideal elements of space. Only the most elementary knowledge of plane and solid geometry is presupposed.

Chapters 2 and 3 are devoted to the two most important configuration theorems, the Pappus-Pascal theorem and that of Desargues. The chapters which follow present applications of these theorems. Chapter 6 touches upon the algebraic interpretation of configuration theorems and the general method of arriving at such theorems.

The book was translated from Russian by Edgar E. Enochs and Robert B. Brown and was published in 1963.

You can get the book here.

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Contents

Introduction 1

1. What is a configuration theorem? 1
2. Example of a configuration theorem 2

Chapter 1 Central Projection and Ideal Elements 4

3. Central projection in a plane; ideal elements
4. Elimination of exceptional cases
5. Basic theorems about projective lines
6. Central projection in space

Chapter 2 Theorem of Pappus and Pascal

7. The Pappus-Pascal Theorem 9
8. Introduction to the proof of Pappus-Pascal Theorem 11
9. Completion of the proof of Pappus-Pascal Theorem 13
10. Brianchon’s Theorem 14

Chapter 3 Desargue’s Theorem 16

11. Desargue’s Theorem 16
12. Alternative proofs of Desargues’s theorem 19
13. The converse of Desargue’s Theorem 23

Chapter 4 Some Properties of Polygons 24

14. Some properties of quadrilaterals 24
15. Some properties of pentagons 25
16. More properties of quadrilaterals 26

Chapter 5. Problems 29

17. Inaccessible points or lines 29
18. Constructions involving inaccessible points or lines30
19. Problems for solutions by the reader 34

Chapter 6. The Algebraic Meaning of Configuration Theorems 37

20. Algebraic Identities as Configuration Theorems 37
21. Schematic notation of Configuration Theorems 38

Bibliography 41