Collection of Problems in Geometry: Stereometry: Classical Russian Mathematics problems book (Russian Math Classics — English Editions)

838 problems in solid geometry, in one graded sequence from the first page to the last.

Spatial reasoning is not learned by reading about it. It is learned by drawing the figure, turning it in your head, and proving what you claim to see. This book is a sustained programme for doing exactly that.

Thirty-three sections carry 838 numbered problems in an unbroken run from 1 to 838. Each section opens with short questions that can be answered mentally and closes with multi-step constructions and computations, so the difficulty climbs inside every topic and not only across the book. By the sections on spheres and inscribed solids you are using the tools from the opening pages on lines and planes, only used harder.

THE GROUND COVERED

- Axioms of stereometry; relative position and parallelism of lines and planes
- Parallel projection, orthogonal projection, angles of inclination
- Dihedral and polyhedral angles; perpendicularity
- Prisms, pyramids, truncated pyramids, regular polyhedra
- Cylinders, cones, truncated cones, spheres
- Surface area and volume for every solid above
- Solids of revolution; inscribed and circumscribed solids
- A closing mixed section that draws on all of it

HOW IT IS BUILT TO BE USED

The 54 figures sit with the problems they belong to, close enough to reason from instead of flipping back and forth. Five sections - prism, pyramid, truncated pyramid, cone and truncated cone - close with practical exercises calling for measurement and physical models. Many problems are set in real situations: sections through beams, pontoons, quantities of material.

An answer key gives the answers for the keyed problems. Proofs and constructions are left to the reader, which is the point of them.

WHO IT IS FOR

Teachers assembling a problem set that does not run out. Students preparing for examinations that test spatial reasoning rather than recall. Homeschooling families who want a structured year of solid geometry. Anyone returning to the subject who wants a programme instead of a survey.

142 pages. 33 sections. 838 problems. One sequence, start to finish.

Pairs with Kiselev’s Stereometry and Rybkin’s Geometry Part II.

Part of Northern Star Mathematics Translations - classic mathematics textbooks and problem books in careful English editions. Browse the series at russianmathbooks.com