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… Mehr zeigen 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 C 60 fullerene molecule (the most powerful antioxidant known today) and to prove why the surface of any fullerene C 2n 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. Weniger zeigen

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Produktinformationen

Technische Daten

Erscheinungsdatum

27.09.2025

Sprache

Englisch

EAN

9783031869686

Herausgeber

Springer International Publishing

Sonderedition

Nein

Autor

Ellina Grigorieva

Seitenanzahl

546

Einbandart

Gebundene Ausgabe

Schlagwörter

Solid Geometry, Analytic Geometry, Stereometry, Geometric problem solving, Math Olympiad problems

Thema-Inhalt

PBM - Geometrie PBD - Diskrete Mathematik PB - Mathematik

Höhe

235 mm

Breite

15.5 cm

Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH

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