Treks into Intuitive Geometry

1. Front Matter

   Pages i-xv

   PDF

2. Art From Tiling Patterns

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 1-34

3. The Tile-Maker Theorem and Its Applications to Art and Designs

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 35-65

4. Patchwork

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 67-80

5. Reversible Pairs of Figures

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 81-141

6. Platonic Solids

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 143-158

7. Cross-Sections of Polyhedra

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 159-174

8. Symmetry of Platonic Solids

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 175-191

9. Double Duty Solids

   • Jin Akiyama, Kiyoko Matsunaga

   Pages 193-212

10. Nets of Small Solids with Minimum Perimeter Lengths

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 213-233

11. Tessellation Polyhedra

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 235-255

12. Universal Measuring Boxes

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 257-283

13. Wrapping a Box

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 285-308

14. Bees, Pomegranates and Parallelohedra

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 309-333

15. Reversible Polyhedra

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 335-372

16. Elements of Polygons and Polyhedra

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 373-398

17. The Pentadron

    • Jin Akiyama, Kiyoko Matsunaga

    Pages 399-416

18. Back Matter

    Pages 417-425

    PDF

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.

• Art
• Dehn's invariant
• Element number
• Equidecomposable
• Hilbert's Third Problem
• Intuitive Geometry
• Johnson Solid
• Lattice
• Measuring Box
• Parallelohedron
• Pentadron
• Polygon
• Polyhedron
• Reversibile
• Sphere Packing
• Tile-maker
• Tiling
• Voronoi domain
• Wrapping

“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’ suchas 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)

• Tokyo University of Science, Tokyo, Japan

  Jin Akiyama

• Yokohama, Japan

  Kiyoko Matsunaga

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.

Policies and ethics