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Kiselev's Geometry / Book II. Stereometry Hardcover – September 1, 2008

by A. P. Kiselev (Author), Alexander Givental (Author)

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The book is an English adaptation of a classical Russian grade school-level text in solid Euclidean geometry. It contains the chapters Lines and Planes, Polyhedra, Round Solids, which include the traditional material about dihedral and polyhedral angles, Platonic solids, symmetry and similarity of space figures, volumes and surface areas of prisms, pyramids, cylinders, cones and balls. The English edition also contains a new chapter Vectors and Foundations (written by A. Givental) about vectors, their applications, vector foundations of Euclidean geometry, and introduction to spherical and hyperbolic geometries. This volume completes the English adaptation of Kiselev's Geometry whose 1st part ( Book I. Planimetry ), dedicated to plane geometry, was published by Sumizdat in 2006 as ISBN 0977985202.

Both volumes of Kiselev's Geometry are praised for precision, simplicity and clarity of exposition, and excellent collection of exercises. They dominated Russian math education for several decades, were reprinted in dozens of millions of copies, influenced geometry education in Eastern Europe and China, and are still active as textbooks for 7-11 grades. The books are adapted to the modern US curricula by a professor of mathematics from UC Berkeley.

Kiselev's Geometry / Book II. Stereometry

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Product Details

Hardcover: 180 pages
Publisher: Sumizdat (September 1, 2008)
Language: English
ISBN-10: 0977985210
ISBN-13: 978-0977985210
Product Dimensions: 8.6 x 5.7 x 0.7 inches
Shipping Weight: 11.2 ounces (View shipping rates and policies)
Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
Amazon Best Sellers Rank: #411,078 in Books (See Top 100 in Books)

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9 of 10 people found the following review helpful

Solid book

By Basilik on December 21, 2011

Format: Hardcover

Kiselev's Stereometry is a sequel to the first book and deals with solid geometry - a subject that should not be overlooked. Solid geometry (or stereometry) is the generalization of plane geometry to three dimensions and deals with such things as planes, dihedral angles, polyhedral angles, surface area, volume, polyhedrons, prisms, parallelepipeds, pyramids, 5 regular polyhedra, cylinders, cones, and spheres. The treatment is very terse but fully rigorous and slick proofs are provided for most theorems. The questions are quite difficult and there are ~200 of them spread throughout the different sections. What I found unique in this book is that explicit construction of the 5 regular polyhedra is actually discussed. There is a final section on vectors and their applications to geometry and a brief introduction to non-Euclidean geometries, with a set of ~100 questions; I skipped this section entirely so my review is confined largely to the bulk of the book dealing with actual geometry.

Overall a great book with an excellent set of exercises. Be warned however it is very difficult and will require time and dedication to plough through. For a more gentle exposition to this same subject check out Wentworth's Plane and Solid Geometry.

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6 of 6 people found the following review helpful

A Little More Than Necessary, But Terse

By Cory Dean on August 5, 2013

Format: Hardcover Verified Purchase

Following the classic Kiselev text on geometry, this second book covers 3-D geometry. Of particular note is the material on some of the more exotic solids (as opposed to boring pyramids and cubes), which is placed at a level easily graspable by the average high school geometry student. This is a good start, as it provides a strong basis and proves everything, if one wants to BEGIN and HAS NOT STARTED contest level geometry.

I like to show this book to possible math majors, because of the terseness of the book. Definition is followed by theorem is followed by proof is followed by corollaries, and then all of that is repeated. There is little fluff or motivational material, and there are not so much "examples" as there are proofs of smaller, insignificant (relatively speaking) theorems. Being able to trudge through such material is necessary for anyone who plans on taking higher mathematics, particularly anything above Calc I at the university level. For this reason, though, I would hesitate to recommend this as a self-study text to all but the brightest of students, and I would hesitate to use this in the classroom unless I knew all the students were taking wonderful notes.

There is also material on vector geometry that is of some use for SAT Math Subject Tests Level I&II but this is above the level of geometry required for the math sections of the SAT.

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