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    Mathematical Surprises

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    Author(s)
    Ben-Ari, Mordechai
    Language
    English
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    Abstract
    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.
    URI
    https://library.oapen.org/handle/20.500.12657/58389
    Keywords
    open access high school mathematics book; origami book; elementary mathematics book; mathematics circle book; Moti Ben-Ari mathematical surprises; what is mathematics book; mathematics independent study; mathematics problems book
    DOI
    10.1007/978-3-031-13566-8
    ISBN
    9783031135668, 9783031135668
    Publisher
    Springer Nature
    Publisher website
    https://www.springernature.com/gp/products/books
    Publication date and place
    Cham, 2022
    Grantor
    • Weizmann Institute of Science - [...]
    Imprint
    Springer International Publishing
    Classification
    Mathematics
    Computer science
    Pages
    226
    Rights
    http://creativecommons.org/licenses/by/4.0/
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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