Geometry Revisited, Volume 19MAA, 1967 - 193 pages 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. |
Table des matières
Preface | 1 |
Chapter 2 | 27 |
Coaxal circles | 35 |
6 | 42 |
Chapter 3 | 51 |
Transformations | 80 |
An Introduction to Inversive Geometry | 103 |
An Introduction to Projective Geometry | 132 |
56 | 152 |
Hints and Answers to Exercises | 154 |
References | 181 |
| 189 | |
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Expressions et termes fréquents
AABC ABCD AC and BD altitudes bisectors bisects central dilatation cevians circle of inversion circle with center circles orthogonal circumcenter circumcircle coaxal collinear points common point concentric circles concurrent congruent construct cosh cross ratio cyclic quadrangle diagonals diameter ellipse equal angles equation equilateral triangle Euclidean plane Euler line excircle EXERCISES Figure given circle half-turn Hence hexagon hyperbola inscribed intersecting circles inversive distance Inversive Geometry inversive plane isometries isosceles line OA line segment locus Mathematics meet mid-circle midpoint nine-point circle non-intersecting circles notation opposite sides orthic triangle orthocenter pairs parallel lines parallelogram pedal triangle perpendicular pints point of contact points of intersection pole projective geometry proof radical axis radii radius reciprocal respect rotation secant Section Similarly Simson line spiral similarity Steiner's porism tangent tangent circles theorem transformation translation triangle ABC vertex vertices vessel ОА