Jin Akiyama, Kiyoko Matsunaga

Treks into Intuitive Geometry (eBook, PDF)

The World of Polygons and Polyhedra

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Nature Singapore
• Seitenzahl: 612
• Erscheinungstermin: 21. Mai 2024
• Englisch
• ISBN-13: 9789819986088
• Artikelnr.: 70735550

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

"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 teachersor 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)