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Methods of solving solid geometry problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Methods of solving solid geometry problems by Ellina Grigorieva.
作者:	Grigorieva, Ellina.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xxi, 546 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometry, Solid.
電子資源:	https://doi.org/10.1007/978-3-031-86969-3
ISBN:	9783031869693$q(electronic bk.)

Methods of solving solid geometry problems
Grigorieva, Ellina.

Methods of solving solid geometry problems [electronic resource] /by Ellina Grigorieva. - Cham :Springer Nature Switzerland :2025. - xxi, 546 p. :ill. (some col.), digital ;24 cm.

Introduction to Solid Geometry -- Polyhedra and their Properties -- Cross-Section of Polyhedra -- Spheres, Cones, Cylinders, and More -- References.

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.

ISBN: 9783031869693$q(electronic bk.)

Standard No.: 10.1007/978-3-031-86969-3doiSubjects--Topical Terms:

1004012
Geometry, Solid.

LC Class. No.: QA457

Dewey Class. No.: 516.23

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520 $a 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.
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