Geometry Revisited, Volume 19
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
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AABC ABCD altitudes bisects called central dilatation Ceva's theorem cevians chords circle with center circles orthogonal circumcenter circumcircle circumradius coaxal collinear points common point concentric circles concurrent congruent conic construct cosh cyclic quadrangle diagonals diameter equal angles equation equilateral triangle Euler line excircle EXERCISES given circle half-turn Hence hyperbola incircle inscribed internal bisector intersecting circles inversive distance inversive plane isosceles line segment mathematics medians meet mid-circle midpoint Napoleon triangle nine-point circle non-intersecting circles opposite sides orthic triangle orthocenter parallel lines parallelogram pedal triangle pencil point of contact points of intersection pole problem projective geometry proof proved quadrilateral radical axis radii radius reciprocal respect rotation secant Section sides BC sides of AABC similar triangles Similarly Simson line sphere spiral similarity Steiner's porism Stewart's theorem tangent circles Theorem three circles three points touching transformation translation triangle ABC vertex vertices
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Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37
Visualização parcial - 1995