Methods of Solving Solid Geometry Problems
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 8 October 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031869686
- Binding Hardback
- No. of pages540 pages
- Size 235x155 mm
- Language English
- Illustrations XXI, 540 p. 393 illus., 383 illus. in color. Illustrations, black & white 700
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Long description:
"
This textbook completes the author’s series of books on solving complex math problems and is aimed at developing readers' geometric thinking to master the skills of solving solid geometry problems. Written in a friendly manner, it discusses many important and sometimes overlooked topics about polyhedra such as their cross sections, unfolding, inscribed and circumscribed solids, and figures of revolution. Over 350 unique problems with detailed solutions and hints are presented throughout the text, many of which are solved in multiple ways to aid readers with different mathematical backgrounds. If the problem is of historical significance or can be related to a similar problem solved in ancient times, its original solution, historical information about its creation and origin of its methods are also included.
Various applications of stereometry are also explored, including those to chemistry, molecular structures, and crystallography. For example, using Euler's formula for a convex polyhedron, the reader will learn how to explain the structure of various chemical compounds, such as how to predict the shape of the truncated icosahedron for the C60 fullerene molecule (the most powerful antioxidant known today) and to prove why the surface of any fullerene C2n consists of n -10 regular hexagons and always only 12 regular pentagons.
Demonstrating the connections between different areas of mathematics, Methods of Solving Solid Geometry Problems will be of interest to students who want to excel in math competitions and to those who aspire for greater mastery in linear algebra, analytic geometry, calculus, and more advanced topics. It can also be used by teachers to stimulate abstract thinking and bring out the originality of their students.
" MoreTable of Contents:
Introduction to Solid Geometry.- Polyhedra and their Properties.- Cross-Section of Polyhedra.- Spheres, Cones, Cylinders, and More.- References.
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