Treks into Intuitive Geometry

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.


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.