Modern GeometriesThis comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems. |
Contents
Sets of Axioms and Finite Geometries | 1 |
Geometric Introduction to Topological | 8 |
Geometric Transformations | 37 |
Copyright | |
11 other sections not shown
Other editions - View all
Common terms and phrases
angle application bisector boundary point center of inversion Chapter circle of inversion circle with center circular region collinear computer graphics concept congruent constant width contains convex body convex hull convex polygonal convex set coordinates definition dilation dimensions distance distinct points elliptic geometry endpoints equations equilateral triangle Euclidean geometry Exercises Find the image finite geometry fractal given line given point glide reflection golden ratio group of transformations Helly's theorem hyperbolic geometry interior point invariant inverse points isogonal conjugates length mapping measure midpoint motions nine-point circle orthocenter pairs parallel perpendicular point of intersection postulate problem Problem-Solving Idea projective geometry proof of Theorem properties Prove quadrilateral R₁ radius ratio real numbers Reuleaux triangle rotation Section segment set of axioms set of points shown in Figure shows sides similarity simple closed curve straightedge supporting line symmedian tangent tessellations three-space topological translation vector vertex vertices