## A Day's Adventure in Math WonderlandMath Wonderland is a museum of interactive mathematical models in Hokkaido, Japan, founded by one of the authors, Jin Akiyama, in 2003. The models in Wonderland, many of which have been exhibited all over Japan and in cities around the world, are meant to help children and young adults discover and experience the wonders of mathematics. This book is centered around the experiences of three fictional middle-school students during a visit to Wonderland. They spend a day in Wonderland, handling the interactive models and participating in the activities offered there. At the end of the day, they leave with a genuine appreciation of mathematics gained from witnessing its beauty, applicability and inevitability. The book is an important contribution to the genre because it presents mathematics and models that have never before appeared in books in the same category: reversible solids, plane tiling with developments of tetrahedrons, and double-packable solids, which are derived from the authors'' own research papers published in mathematics journals. It is designed to entertain, inform and even teach some mathematics. Although it is targeted at young adults, parents and teachers may learn something from the book as well. Chapter 1: Fat Triangles & Flattened Bagels (1,962 KB). Contents: Math is Fun?; Fat Triangles and Flattened Bagels; Cool Curves; A Roomful of Right Triangles; Math in Music; Pachinko Math; GCF-LCM Machine; Baumkuchen, Spaghetti and Watermelon; Automat(h); A Slice of a Cone; Paper Twists; Fold and Cut; Jigsaws from Tetrahedrons; Single and Double Duty Solids; Reversible Solids. Readership: Secondary-school students, math teachers and parents. |

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### Contents

Fat Triangles Flattened Bagels | 7 |

Cool Curves | 27 |

A Roomful of Right Triangles | 43 |

Math in Music | 59 |

Pachinko Math | 73 |

GcfLcm Machine | 81 |

Baumkuchen Spaghetti Watermelon | 89 |

Automath | 101 |

A Slice of a Cone | 119 |

Paper Twists | 141 |

Fold Cut | 157 |

Jigsaws From Tetrahedrons | 171 |

Single Double Duty Solids | 185 |

Reversible Solids | 203 |

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### Common terms and phrases

balls Baumkuchen bisect black squares blade catenaries Chie chords circle circular clothoid loops compartments congruent constant width continues cube double-duty solids ellipse epitrochoid Escher's explain fat triangle figure fill space focus fold Fuji-Q Highlands Hiro hole Ichiro and Jai Ichiro answers Ichiro asks Ichiro observes Ichiro says Ichiro suggests intentionally left blank inverted Cycloid Jai is thinking Jai says Keiko kidney stones Kino asks Kino observes Kino remarks Kino says Kino takes Kino wonders Kyoko length M.C. Escher Masao says mental note Miho Miki Mobius bands move musical paper parabola paraboloid path to pin piece poster Pythagoras Pythagorean Theorem quadrilateral radius Reuleaux triangle rhombic dodecahedron right triangles Satsu says second slide shape shows side single-duty solid skates space-fillers surface cut tetrahedron tetrapak tile the plane Toshi says trapezoid truncated octahedron turned inside vending machines Wonderland