## Experiencing Geometry: Euclidean and Non-Euclidean with History |

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### Contents

Historical Strands | 1 |

What Is Straight? | 9 |

Straightness on Spheres | 25 |

Copyright | |

24 other sections not shown

## Experiencing Geometry: Euclidean and Non-Euclidean with History |

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Historical Strands | 1 |

What Is Straight? | 9 |

Straightness on Spheres | 25 |

Copyright | |

24 other sections not shown

2-manifold 3-dimensional 3-sphere absolute geometry algebra annular hyperbolic plane annular strips Apollonius bisector bolic plane called Chapter circle cone angle cone point construction coordinate curvature curve cylinder define definition differential geometry dihedral angles discussion distance dodecahedron draw edges equations equivalent by dissection Euclid's Euclidean 3-space example explore extrinsic Figure finite flat torus geodesics geometric 2-manifold glued hemisphere holonomy hyperbolic 3-space hyperbolic geometry hyperbolic plane interior angles intersect intrinsic inversion isometry Khayyam Klein bottle Law of Cosines linkage locally isometric look manifold mathematicians mathematics Note notion parallel postulates parallel transport parallelogram patterns perpendicular planar polygon polyhedra Problem proof properties prove quadrilateral radius rectangle reflection Reuleaux triangle right angles rotation Show side similar triangles small triangles solid angles space spheres and hyperbolic spherical geometry square root stereographic projection straight line Strand surface symmetry tangent Theorem tion Universe upper-half-plane model vector vertex vertices