Selected Topics in Geometry with Classical vs. Computer Proving
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Pech (mathematics, U. of South Bohemia) gives readers the basic theories of automatic theorem proving as well as computational methods as he explains topics of elementary geometry. He describes automatic theorem proving, derivation and discovery, then moves the a generalization of the formula of Heron (the area of a polygon and of a cyclic polygon), the Simson-Wallace theorem (including Gergonne's generalization, the generalization of Guzman and generalization to three dimensions), transversals in a polygon (the theorems of Ceva, Menelaus, Euler and Routh), the Peter-Douglas Neumann theorem (i...
Pech (mathematics, U. of South Bohemia) gives readers the basic theories of automatic theorem proving as well as computational methods as he explains topics of elementary geometry. He describes automatic theorem proving, derivation and discovery, then moves the a generalization of the formula of Heron (the area of a polygon and of a cyclic polygon), the Simson-Wallace theorem (including Gergonne's generalization, the generalization of Guzman and generalization to three dimensions), transversals in a polygon (the theorems of Ceva, Menelaus, Euler and Routh), the Peter-Douglas Neumann theorem (including Napoleon's theorem), geometric inequalities, and regular polygons. He closes with a collection of miscellaneous topics, including non-elementary constructions, the theorem of Viviani and the line of Gauss.
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