Treks into Intuitive Geometry

The World of Polygons and Polyhedra

Authors: Akiyama, Jin, Matsunaga, Kiyoko

  • Is a unique book combining the rich mathematical content of polygons and polyhedra, in a writing style that appeals to all readers
  • Shows how the world of polygons and polyhedra connects to the world of aesthetics, with an interplay between mathematics and art
  • Introduces a history of old mathematical problems and explains such problems in a fresh, enticing manner
  • Presents non-trivial mathematical results in a way that is both unique and accessible, combining the richness of dialogues, mathematical proofs, and beauty of shapes
  • Shows how the world of polygons and polyhedra can be viewed as useful and enjoyable without sacrificing the beauty of the deeper mathematics
  • Introduces a wide range of interplay between mathematics and art and presents a more visually entertaining form of mathematics that attracts readers
see more benefits

Buy this book

eBook $54.99
price for Brazil (gross)
  • ISBN 978-4-431-55843-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for Brazil
  • ISBN 978-4-431-55841-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people 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.

About the authors

Jin Akiyama is a mathematician at heart. Currently, he is a fellow of the European Academy of Science, the founding editor of the journal Graphs and Combinatorics, and the director of the Research Institute of Math Education at Tokyo University of Science. He is particularly interested in graph theory and discrete and solid geometry and has published many papers in these fields. Aside from his research, he is best known for popularizing mathematics, first in Japan and then in other parts of the globe: his lecture series was broadcast on NHK (Japan’s only public broadcaster) television and radio from 1991 to 2013. He was a founding member of the Organizing Committee of the UNESCO-sponsored traveling exhibition “Experiencing Mathematics”, which debuted in Denmark in 2004. In 2013, he built a hands-on mathematics museum called Akiyama's Math Experience Plaza in Tokyo. He has authored and co-authored more than 100 books, including Factors and Factorizations of Graphs< (jointly with Mikio Kano, Lect. Notes Math., Springer, 2011) and A Day’s Adventure in Math Wonderland (jointly with Mari-Jo Ruiz, World Scientific, 2008), which has been translated into nine languages.Kiyoko Matsunaga is a science writer for mathematics. She has contributed not only through Japanese-language books, but also in NHK TV programs on mathematics, including Math, I Like It for elementary students, Math Time Travel for junior and senior high school students, and The Joy of Math and Math Wonderland for the broader public.

Reviews

“The subjects within Treks into Intuitive Geometry directly relate to what German mathematician David Hilbert distinguished as topics that could interest a ‘man on the street.’ … The book contains colorful diagrams and reprints of famous artwork. … Summing Up: Recommended. General readers through lower-division undergraduates.” (M. D. Sanford, Choice, Vol. 54 (2), October, 2016)

“Treks into Intuitive Geometry is a delightful read covering various topics in geometry, from tilings of the plane to three-dimensional solids. … This book is also filled with wonderful full-color illustrations. … With these concrete topics and easy-going style, this book can be enjoyed by mathematicians and recreational puzzlers alike.” (Tricia Muldoon Brown, MAA Reviews, maa.org, April, 2016)

“The authors' efforts to provide figures and experiments, as well as the many references with ‘everyday life’ such as art, architecture and optimization, will be appreciated by teachers or self-taugth readers. In various way, this book is poetic, and contains several references to the Japanese culture and history. It is uncommon in its construction, well illustrated and entertaining. In summary, a good outreach book for a broad audience.” (Matthieu Jacquemet, zbMATH 1339.52001, 2016)


Table of contents (16 chapters)

  • Art From Tiling Patterns

    Akiyama, Jin (et al.)

    Pages 1-34

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

    Akiyama, Jin (et al.)

    Pages 35-65

  • Patchwork

    Akiyama, Jin (et al.)

    Pages 67-80

  • Reversible Pairs of Figures

    Akiyama, Jin (et al.)

    Pages 81-141

  • Platonic Solids

    Akiyama, Jin (et al.)

    Pages 143-158

Buy this book

eBook $54.99
price for Brazil (gross)
  • ISBN 978-4-431-55843-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for Brazil
  • ISBN 978-4-431-55841-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Treks into Intuitive Geometry
Book Subtitle
The World of Polygons and Polyhedra
Authors
Copyright
2015
Publisher
Springer Japan
Copyright Holder
Springer Japan
eBook ISBN
978-4-431-55843-9
DOI
10.1007/978-4-431-55843-9
Hardcover ISBN
978-4-431-55841-5
Edition Number
1
Number of Pages
XV, 425
Topics