國立高雄大學圖資館 |

Language: English

Back

Methods of solving solid geometry problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Methods of solving solid geometry problems by Ellina Grigorieva.
Author:	Grigorieva, Ellina.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xxi, 546 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Solid.
Online resource:	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

Methods of solving solid geometry problems
LDR:02938nmm a2200349 a 4500 001 688776
003 DE-He213
005 20250926130606.0
006 m d
007 cr nn 008maaau
008 260318s2025 sz s 0 eng d
020 $a 9783031869693$q(electronic bk.)
020 $a 9783031869686$q(paper)
024 7 $a 10.1007/978-3-031-86969-3 $2 doi
035 $a 978-3-031-86969-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA457
072 7 $a PBM $2 bicssc
072 7 $a PBD $2 bicssc
072 7 $a MAT012020 $2 bisacsh
072 7 $a PBM $2 thema
072 7 $a PBD $2 thema
082 0 4 $a 516.23 $2 23
090 $a QA457 $b .G857 2025
100 1 $a Grigorieva, Ellina. $3 731710
245 1 0 $a Methods of solving solid geometry problems $h [electronic resource] / $c by Ellina Grigorieva.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2025.
300 $a xxi, 546 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Introduction to Solid Geometry -- Polyhedra and their Properties -- Cross-Section of Polyhedra -- Spheres, Cones, Cylinders, and More -- References.
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.
650 0 $a Geometry, Solid. $3 1004012
650 1 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a General Mathematics. $3 929628
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-86969-3
950 $a Mathematics and Statistics (SpringerNature-11649)