Mordechai Ben-Ari: Mathematical Surprises

Cover: 9783031135651 | Mathematical Surprises | Mordechai Ben-Ari | Taschenbuch | xvi | 2022

Rückseite: 9783031135651 | Mathematical Surprises | Mordechai Ben-Ari | Taschenbuch | xvi | 2022

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Sprache: Englisch

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Beschreibung

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 [...]

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

- 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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xvi 226 S. 147 s/w Illustr. 23 farbige Illustr. 226 p. 170 illus. 23 illus. in color.
ISBN-13:	9783031135651
ISBN-10:	3031135652
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Ben-Ari, Mordechai
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 14 mm
Von/Mit:	Mordechai Ben-Ari
Erscheinungsdatum:	08.09.2022
Gewicht:	0,376 kg