This comprehensive, best-selling text focuses on the study of many different geometries--rather than a single geometry--and emphasizes practical applications. Designed to be a flexible teaching tool for a wide range of students (including math, education, or computer science majors), Smart's text features self-contained chapters organized so that instructors can cover as much or as little of each topic as they choose, from bare minimum one-section coverage to full-chapter coverage. Modern Geometries has earned a reputation for its logical progression of ideas, its well-constructed exercises, and its comprehensive coverage. In this edition, Smart covers the major new applied areas of computer graphics, and emphasizes matrices for transformations.
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Sets of Axioms and Finite Geometries
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application bisector boundary point center of inversion Chapter circle of inversion circle with center circular region collinear complete quadrangle computer graphics concept congruent conic constant width contains convex body convex hull convex set corresponding points definition determined distance distinct points elliptic geometry endpoint equations equilateral triangle Euclidean geometry exactly example fifth postulate Find the image finite geometry four points given line given point glide reflection harmonic set homogeneous coordinates hyperbolic geometry ideal point interior point invariant inverse points isogonal conjugates length matrix measure midpoint motions nine-point circle non-Euclidean geometry omega triangle perpendicular perspective plane dual point in common point of intersection problem projective geometry proof of Theorem properties radius ratio real numbers Reuleaux triangle rotation Saccheri quadrilateral segment set of axioms set of points shown in Figure shows similar simple closed curve straight line straightedge supporting line symmedian tangent three points three-space translation vector vertex vertices