Mathematical Surprises

ISBN-13: 9783031135651 / Angielski / Miękka / 2022

Mordechai Ben-Ari

Opis

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's purely 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.

Spis treści

- 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.

O autorze

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.

Blurb

This 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's purely 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.