Topics in geometry
This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered. The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.
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4-centers absolute plane altitudes assume axes of reflections axis CA/CB Ceva's Theorem circle JC circumcenter circumcircle collinear points complete quadrangle conic section conic section JC contains cross-ratios determined directed distances discussion accompanying Figure division ratios elementary perspectivity equal length equidistant Euclidean ellipse Euclidean plane Euclidean space extended plane following result four points h-line h-points harmonic set hyperbolic plane ideal line identity map Illustrate this result implies interchanges internal angle bisector intersects isometries last two sentences let ABC let JC line BC midpoint nine-point circle nontrivial glide reflections ordinary line ordinary points orthocenter pairs Pappus parabola parallel lines perpendicular bisector point F point on line points of JC positive end possible approach previous paragraph projections between planes projective geometry Proof properties Prove real numbers right angle rotations symmetry group three points translation triangle ABC unique line unique point vertex vertices wallpaper group