Treks into Intuitive Geometry : The World of Polygons and Polyhedra / by Jin Akiyama, Kiyoko Matsunaga.

Format:

Book

Author/Creator:

Akiyama, J.

Contributor:

Matsunaga, Kiyoko.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Mathematics.

Arts.

Architecture--Mathematics.

Architecture.

Polytopes.

Discrete mathematics.

Mathematics in Art and Architecture.

Discrete Mathematics.

Local Subjects:

Mathematics in Art and Architecture.

Polytopes.

Discrete Mathematics.

Mathematics.

Physical Description:

1 online resource (642 pages)

Edition:

2nd ed. 2024.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2024.

Summary:

This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theories―their trials, errors, and triumphs―in reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the book’s rich content even further.

Contents:

1 Art From Tiling Patterns

2 The Tile-Maker Theorem and Its Applications to Art and Designs

3 Treks into Intuitive Geometry

4 Patchwork

5 Reversible Pairs of Figures

6 Reversibility and Foldability of Conway Tiles

7 Platonic Solids

8 Cross-Sections of Polyhedra

9 Symmetry of Platonic Solids

10 Double Duty Solids

11 Nets of Small Solids with Minimum Perimeter Lengths

12 Tessellation Polyhedra

13 Universal Measuring Boxes

14 Wrapping a Box

15 Bees, Pomegranates and Parallelohedra

16 Reversible Polyhedra

17 Elements of Polygons and Polyhedra

18 The Pentadron.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-9986-08-7

OCLC:

1435753670