Experiencing Geometry: In Euclidean, Spherical, and Hyperbolic Spaces
The book conveys a distinctive approach, stimulating readers to develop a broader, deeper understanding of mathematics through active participation?including discovery, discussion, and writing about fundamental ideas. It provides a series of interesting, challenging problems, then encourages readers to gather their reasonings and understandings of each problem.
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What is Straight?
Straightness on Spheres
What Is an Angle?
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2-D person 2-dimensional 2-manifold 2/3-ideal triangles 3-sphere absolute geometry annular hyperbolic plane Baudhayana's bisector bolic plane called Chapter circle cone angle cone point construction curvature curve definition differential geometry dihedral angles discussion distortion dodecahedron dual edges equations equivalent by dissection Euclid Euclidean 3-space example explore extrinsic Figure flat torus formula geometric 2-manifold glued half plane model hemisphere holonomy hyperbolic 3-space hyperbolic geometry hyperbolic plane ideal triangle interior angles intersect intrinsic inversion isometry Khayyam Klein bottle Law of Cosines locally isometric look lune mathematics notion parallel postulates parallel transport parallelogram path patterns perpendicular polygon polyhedra pradesa Problem projection proof properties prove quadrilateral radius rectangle reflection right angles rotation Show side similar triangles small triangles solid angles space spheres and hyperbolic square root straight line strip Sulbasutram surface tangent Theorem tion transversal turn manifold two-holed torus Universe upper half plane vector vertex vertices