Topics in GeometryThis 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. |
Contents
Division Ratios | 21 |
Menelaus Theorem | 42 |
Cevas Theorem | 56 |
Copyright | |
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Common terms and phrases
4-centers absolute plane altitudes angle bisector assume axes of reflections Axiom axis CA/CB Ceva's Theorem circle K circumcenter circumcircle collinear points complete quadrangle conic section cross-ratios directed distances discussion accompanying Figure distinct division ratios elementary perspectivity equidistant Euclidean ellipse Euclidean plane Euclidean space Exercise extended plane following result four points G contains h-line h-points harmonic set holds hyperbolic plane ideal line identity map Illustrate this result implies interchanges internal angle bisector intersects isometries last two sentences let ABC let G lies lines AA midpoint nine-point circle nontrivial glide reflections notation ordinary line ordinary points orthocenter pairs Pappus parallel lines perpendicular bisector point on line positive end possible approach previous paragraph projections between planes projective geometry Proof properties Prove real numbers reflections in G right angle rotations symmetry group t₁ three points translations in G triangle ABC unique point vertices wallpaper group