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Mathematical Surprises
English
103 b
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The book describes "surprising" results in mathematics that are extremely interesting but not widely known, and for the most part appear only in the research literature. There is an emphasis on geometric constructions: e.g., the "collapsing compass", the Mohr-Mascheroni and Poncelet-Steiner theorems on restricted constructions, Ramanujan's approximations to pi, and Gauss's construction of the heptadecagon. The mathematics of origami is treated in depth: the Huzita-Hatori axioms, the solution of cubic equations by Lill's method and Beloch's fold, and constructions that cannot be done with straightedge and compass. The material is explained in full detail with numerous high-quality illustrations. Only elementary mathematics is used: Euclidean geometry, analytic geometry, trigonometry, (non-abstract) algebra.This is an open access book.
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