Mathematical Surprises

A book that presents fascinating mathematical results that do not appear in textbooks, such as the mathematical formalization of origami, construction with straightedge and compass, the five- and six-color theorems, Ramsey theory, and little-known theorems proved by induction. The highlight of the book is a detailed presentation of Gauss's purely algebraic proof that a regular heptadecagon can be constructed with straightedge and compass.

Format: Paperback / softback
Length: 226 pages
Publication date: 08 September 2022
Publisher: Springer International Publishing AG

This captivating open-access book offers a delightful treasure trove of mathematical wonders. Within its pages, readers will encounter a multitude of captivating results that transcend the confines of traditional textbooks, yet remain accessible to those with a solid foundation in secondary-school mathematics. This book presents a curated selection of these intriguing topics, encompassing the mathematical formalization of origami, the art of construction with straightedge and compass (and other instruments), the profound five- and six-color theorems, a tantalizing glimpse into Ramsey theory, and numerous lesser-known theorems proven through induction. Among the most astonishing theorems, we find the Mohr-Mascheroni theorem, which asserts that a compass alone possesses the capability to execute all classical constructions with straightedge and compass. Furthermore, Steiner's theorem emerges, stating that a straightedge alone suffices, provided a single circle is given. The pinnacle of this book lies in a meticulous presentation of Gauss's purely algebraic proof that a regular heptadecagon, a regular polygon with seventeen sides, can be constructed with the aid of only a straightedge and compass. While the mathematics employed herein may be considered elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and all enthusiasts of mathematics will undoubtedly relish the opportunity to embark on the challenging journey of comprehending these remarkable theorems. For additional supplementary material, please visit https://github.com/motib/suprises.

Weight: 379g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031135651
Edition number: 1st ed. 2022