Inversive GeometryCourier Corporation, 15.01.2014 - 288 Seiten This introduction to algebraic geometry makes particular reference to the operation of inversion and is suitable for advanced undergraduates and graduate students of mathematics. One of the major contributions to the relatively small literature on inversive geometry, the text illustrates the field's applications to comparatively elementary and practical questions and offers a solid foundation for more advanced courses. The two-part treatment begins with the applications of numbers to Euclid's planar geometry, covering inversions; quadratics; the inversive group of the plane; finite inversive groups; parabolic, hyperbolic, and elliptic geometries; the celestial sphere; flow; and differential geometry. The second part addresses the line and the circle; regular polygons; motions; the triangle; invariants under homologies; rational curves; conics; the cardioid and the deltoid; Cremona transformations; and the n-line. |
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acobian algebraic antigraphy antilogy apse arcs axis base-circle base-line base-point becomes bilinear bitangent canonical form cardioid centre centroid circumcentre circumcircle clinant co-ordinates coefficients coincide common normal configuration conjugate consider constant corresponds cos2 cross-ratios curvature curves of flow cusp cylinder defined definite denote direction distance double point doublets edges elliptic envelope Euclidean geometry Euclidean group Euclidean space Exercise Fermat points fig figure find finite first five fixed points focal pairing foci focus four points function geometry given gives Hence Hessian points homography homology hyperbolic images infinity intersect invariant inversive group involution limacon map-equation meet mid-point motion negative nine-point circle orthocentre orthogonal osculant circle parabola parallel parameters perpendicular plane point 00 polar polygon positive quadratic radius rational reflexion rhombus rotation self-conjugate equation sends sin2 singular points sink sphere tangents theorem three lines three points touch triangle vanishes vector vertices whence write x-plane