Geometry Through Problems: A Book for Teachers
by S. I. Shokhor-Trotsky
Translated by Valery Manokhin, PhD
A complete school course in plane and solid geometry, written for the teacher and built from graded problems rather than ready-made theorems, in first faithful English translation from the original Russian edition. It opens with the author’s essay “To the Attention of the Teacher” on teaching by expedient problems, then runs in six chapters and eighteen numbered sections: the straight line, the angle and the arc; triangles, parallel lines and polygons, the length of the circumference and construction problems; areas of rectilinear figures and of the circle; the lateral surfaces of cylinders and cones and the surface of the sphere; lines and planes in space, dihedral and polyhedral angles, and projections of figures and solids onto a plane; and the volumes of prisms, cylinders, pyramids, cones and the sphere. 439 numbered problems with 251 lettered sub-problems, each with the teacher’s notes on how the class works it, answers given in the text, 398 drawings, the author’s alphabetical index and a selection of reviews. The numbers missing from the sequence belong to the companion pupils’ book, as the author explains.
6 chapters · 18 numbered articles · 439 exercises · 363 pages
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | 6–10 | Teacher's guide: Grade 6–8 geometry and measurement → Geometry, plane and solid |
|---|---|---|
| United Kingdom | Years 7–11 | Teaching KS3 → GCSE; projections cover GCSE plans and elevations |
| Canada | Ontario 6–10 | teaching Grade 6–8 math · MTH1W · MPM2D measurement and geometry |
Not covered in this book
coordinate geometry · transformations on a grid · vectors · statistics and data handling · probability · metric units — some problems use old Russian measures (versts, sazhens, arshins, poods)
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Problems to work alongside it
- Elementary Geometry$69.95
- Kiselev's Planimetry$59.95
- Kiselev's Stereometry$49.95
Table of contents
19 section headings — the printed contents page in full.
Translator's Preface
Author's Preface
To the Attention of the Teacher
Chapter 1. The straight line, the angle, and the arc of a circle3 sections
- § 1. The straight line
- § 2. The linear angle
- § 3. The circumference of a circle and the measurement of angles
Chapter 2. Triangles, parallel lines, and polygons5 sections
- § 4. Triangles, their elements, equality, and similarity
- § 5. Parallel and nonparallel straight lines
- § 6. Quadrilaterals and polygons, their equality and similarity, the sum of their angles and the length of their perimeters
- § 7. Calculation of the length of the circumference
- § 8. Solution of certain construction problems
Chapter 3. Areas of rectilinear figures and of the circle2 sections
- § 9. Areas of rectilinear figures
- § 10. The area of a circle
Chapter 4. Surfaces of round solids2 sections
- § 11. Lateral surfaces of right cylinders and cones
- § 12. The surface of a sphere
Chapter 5. Lines and planes in space3 sections
- § 13. The straight line and the plane
- § 14. Dihedral and polyhedral angles
- § 15. Projections of figures and solids onto a plane
Chapter 6. Computation of the volumes of certain solids4 sections
- § 16. Volumes of prisms and right cylinders
- § 17. Volumes of pyramids and of a right cone
- § 18. The volume of a sphere
- Conclusion
Alphabetical Index
From Reviews of Certain Books and Manuals
About the Author
About the Translator
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $39.95 | — | Gumroad · Instant download | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 363 pages
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
More in This Series
Rachinsky's 1001 Problems
by S. A. Rachinsky
US grades 4–8 · UK Years 5–9
1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."
Perelman's Entertaining Arithmetic
by Ya. I. Perelman
US grades 4+ · UK Year 5+
The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.
Markov: Probabilities
by Andrei A. Markov
US grades 12 and university · UK Year 13 and university
The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.