## Modern Geometries: Non-Euclidean, Projective, and Discrete |

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### Contents

Introduction | 1 |

PLANE GEOMETRY | 51 |

PROJECTIVE GEOMETRY | 138 |

Copyright | |

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13 other sections not shown ## Common terms and phrasesabsolute geometry algebraic angle Apqr axiom system axis Bachmann's bundles called Chapter clines complex numbers complex plane congruent coordinates cross ratio curve cut set cycle deﬁned Deﬁnition Let dimensional dimensions distance edges elements elliptic geometry equation Erlanger Programm Euclid Euclidean geometry Euclidean plane Euclidean transformation example Exercise ﬁgure ﬁnd ﬁnite ﬁxed point ﬂats formula frieze groups fundamental theorem glide reﬂection graph Hilbert's axioms Hint homothetic transformation horocycle hyperbolic geometry hyperbolic plane hyperbolic straight line ideal point identiﬁed inﬁnite intersect invariant inversion involutions lattice line segment mathematics matroid metric absolute geometry Mobius geometry Mobius transformation motions multiplication non-Euclidean geometry perpendicular polar form postulate projective geometry projective plane proof properties Prove quatemions real numbers reﬂection reﬂection planes satisﬁes Show single elliptic geometry space Steiner circles stereographic projection subgeometries subset symmetry groups three-dimensional transformation group translational geometry translational symmetry triangle unit circle unit disk vector vertex x-axis ## Bibliographic information |