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Axiomatic geometry

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Author(s): Lee, John M
Series: The Sally series; Pure ans applied undergraduate texts 21
Publisher: American Mathematical Society
Year: 2013

Language: English
Pages: 469
City: Providence, R.I
Tags: Axioms.;Geometry.;Axiomatik;Geometrie

Content: Euclid Incidence geometry Axioms for plane geometry Angles Triangles Models of neutral geometry Perpendicular and parallel lines Polygons Quadrilaterals The Euclidean parallel postulate Area Similarity Right triangles Circles Circumference and circular area Compass and straightedge constructions The parallel postulate revisited Introduction to hyperbolic geometry Parallel lines in hyperbolic geometry Epilogue: Where do we go from here? Hilbert's axioms Birkhoff's postulates The SMSG postulates The postulates used in this book The language of mathematics Proofs Sets and functions Properties of the real numbers Rigid motions: Another approach References Index