Customer Reviews

Kiselev's Geometry / Book II. Stereometry

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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.