Geometry RevisitedRandom House, 1967 - 193 pages The chief purpose of this book is to revisit those regions of elementary geometry that were enjoyed by our ancestors, making use of the idea of transformations: an idea that facilitates geometric understanding and links the subject with other branches of mathematics. In particular, Chapter 5 introduces the reader to inversive geometry, which has an important application to analysis, and Chapter 6 introduces conics with special emphasis on the notions of focus and eccentricity, notions obviously relevant to the study of orbits of comets, planets, and satellites. The early chapters take the reader by easy stages from very simple ideas to the core of the subject. The problems throughout the book contain extensions of the text as well as challenges to the reader. |
Table des matières
Preface | 1 |
Chapter 2 | 27 |
Coaxal circles | 35 |
Droits d'auteur | |
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Expressions et termes fréquents
AABC ABCD altitudes angles applied bisectors called cevians circle circle with center circumcircle collinear common point concurrent congruent conic Consider construct Conversely corresponding cosh diagonals diameter dilatation directed distance divide Draw equal equation equilateral triangle EXERCISES expressions extended external fact Figure follows four geometry given half-turn Hence hexagon inscribed interesting intersection inverse joining length lies locus mathematics means meet midpoint natural obtain opposite sides orthocenter orthogonal pairs parallel parallelogram pass pencil perpendicular plane points points of intersection polar pole positive problem projective proof proved quadrangle radical axis radii radius ratio reciprocal reflection regarded respect result rotation Section shows sides similar Similarly sphere square tangent theorem third touching transformation translation triangle triangle ABC vertex vertices