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oapen-20.500.12657-583892022-09-16T03:16:51Z Mathematical Surprises Ben-Ari, Mordechai 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 bic Book Industry Communication::P Mathematics & science::PB Mathematics bic Book Industry Communication::U Computing & information technology::UY Computer science 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. 2022-09-15T20:14:13Z 2022-09-15T20:14:13Z 2022 book ONIX_20220915_9783031135668_35 9783031135668 https://library.oapen.org/handle/20.500.12657/58389 eng application/pdf n/a 978-3-031-13566-8.pdf https://link.springer.com/978-3-031-13566-8 Springer Nature Springer International Publishing 10.1007/978-3-031-13566-8 10.1007/978-3-031-13566-8 6c6992af-b843-4f46-859c-f6e9998e40d5 1a72f9ce-e695-4dd5-89a4-af670d7983ee 9783031135668 Springer International Publishing 226 Cham [...] Weizmann Institute of Science מכון ויצמן open access
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OAPEN
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DSpace
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language |
English
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description |
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.
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title |
978-3-031-13566-8.pdf
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spellingShingle |
978-3-031-13566-8.pdf
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title_short |
978-3-031-13566-8.pdf
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title_full |
978-3-031-13566-8.pdf
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title_fullStr |
978-3-031-13566-8.pdf
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title_full_unstemmed |
978-3-031-13566-8.pdf
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978-3-031-13566-8.pdf
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publisher |
Springer Nature
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2022
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url |
https://link.springer.com/978-3-031-13566-8
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1771297415004946432
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