Mathematical Surprises by Mordechai Ben-Ari (English) Paperback Book

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This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss'spurely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass.Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems.Supplementary material to the book can be found at

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Back Cover

The book describes "surprising" results in mathematics that are extremely interesting but not widely known, and for the most part appear only in the research literature. There is an emphasis on geometric constructions: e.g., the "collapsing compass", the Mohr-Mascheroni and Poncelet-Steiner theorems on restricted constructions, Ramanujan's approximations to pi, and Gauss's construction of the heptadecagon. The mathematics of origami is treated in depth: the Huzita-Hatori axioms, the solution of cubic equations by Lill's method and Beloch's fold, and constructions that cannot be done with straightedge and compass. The material is explained in full detail with numerous high-quality TikZ illustrations. Only elementary mathematics is used: Euclidean geometry, analytic geometry, trigonometry, (non-abstract) algebra. This is an open access book.

Author Biography

Mordechai (Moti) Ben-Ari is professor emeritus at the Department of Science Teaching of the Weizmann Institute of Science. He has written numerous textbooks including Mathematical Logic for Computer Science and Elements of Robotics (with Francesco Mondada), both published by Springer. He has received the ACM SIGCSE Award for Outstanding Contributions to Computer Science Education and the ACM Karl V. Karlstrom Outstanding Educator Award.

Table of Contents

- 1. The Collapsing Compass. - 2. Trisection of an Angle. - 3. Squaring the Circle. - 4. The Five-Color Theorem. - 5. How to Guard a Museum. - 6. Induction. - 7. Solving Quadratic Equations. - 8. Ramsey Theory. - 9. Langford's Problem. - 10. The Axioms of Origami. - 11. Lill's Method and the Beloch Fold. - 12. Geometric Constructions Using Origami. - 13. A Compass Is Sufficient. - 14. A Straightedge and One Circle is Sufficient. - 15. Are Triangles with Equal Areas and Perimeters Congruent?. - 16. Construction of a Regular Heptadecagon.

Feature

This book is open access, which means that you have free and unlimited access Describes little known and surprising results in classical elementary Mathematics Perfectly suitable for an extra-curriculum high-school Mathematics circle Contains detailed explanations and high-quality illustrations

Details ISBN3031135652 Author Mordechai Ben-Ari Publisher Springer International Publishing AG Language English Year 2022 ISBN-10 3031135652 ISBN-13 9783031135651 Format Paperback DOI 10.1007/978-3-031-13566-8 Edition 1st Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Pages 226 Publication Date 2022-09-08 UK Release Date 2022-09-08 Edition Description 1st ed. 2022 Audience Professional & Vocational Illustrations 23 Illustrations, color; 147 Illustrations, black and white; XVI, 226 p. 170 illus., 23 illus. in color. We've got this

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