Problems in Geometry – Modenov

In this post, we will see the book Problems in Geometry by P. S. Modenov.

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About the book

This text offers certain general methods of solving problems in elemen­tary geometry and is designed for teachers of mathematics in secondary schools and also for senior students.
The present text includes material that goes beyond the scope of mathe­matics curricula for secondary schools (the use of complex numbers in plane geometry, inversion, pencils of circles and others).
The book consists of five chapters. The first four chapters deal with the application of vector algebra, analytic geometry, complex numbers and the inversion transformation to geometric problems. Chapter V contains a list of the basic definitions and formulas used in the first four chapters. Before starting a new chapter, the reader is advised to refresh his memory with the appropriate material of Chapter V. Some of the derivations of formulas given in Chapter V are familiar to senior students of secondary school. More detailed theoretical material can be found in the bibliography at the end of the book.
The book was translated from the Russian by George Yankovsky and published by Mir 1981.
Contents
PREFACE 7

CHAPTER I. VECTOR ALGEBRA

Sec. 1. Vectors in the plane (solved problems) 11
Sec. 2. Vectors in space (solved problems) 14
Sec. 3. Vectors in the plane and in space (problems with hints and
answers) 30

CHAPTER II. ANALYTIC GEOMETRY

Sec. 1. Application of analytic geometry(solved problems) 44
Sec. 2. Application of analytic geometry(problems with hints and answers) 66
1. Plane geometry 66
2. Solid geometry 78

CHAPTER III. THE USE OF COMPLEX NUMBERS IN PLANE GEOMETRY

Sec. 1. Solved problems 82
Sec. 2. Problems with hints and answers 253

CHAPTER IV. INVERSION

Sec. 1. Inversion defined. Properties of inversion 281
Sec. 2. Problems involving inversion 285
Sec. 3. Mapping of regions under inversion 297
Sec. 4. Mechanical inversors: the Peaucellier cell and the Hart cell 308
Sec. 5. The geometry of Mascheroni 309
Sec. 6. Inversion of space 313

CHAPTER V. BASIC DEFINITIONS, THEOREMS AND FORMULAS
Sec. 1. Determinants of order three 334
Sec. 2. Vector algebra 373
Sec. 3. Analytic geometry 347
Sec. 4. Complex numbers 377

LIST OF SYMBOLS 387
APPENDIX. LIST OF BASIC FORMULAS FOR REFERENCES 390
BIBLIOGRAPHY 394
NAME INDEX 395
SUBJECT INDEX 396

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2 Responses to Problems in Geometry – Modenov

  1. Bleti says:

    Hello!
    I need help.
    Im imterested for some geoemtry books for university(dep.of mathematics) with full detailed solutions.
    Can anyone help me? Thanks in advance 😊

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