Fundamentals of Coordinate Geometry

Contents: Preface. 1. Coordinate system. 2. Polar coordinate system. 3. 6-Sphere coordinates. 4. Line coordinates. 5. Derivations of the quadratic formula. 6. Treatment of infinity. 7. The Hypersphere of rotations. 8. Rotation matrix. 9. Uniform Random rotation matrices. 10. Surface area of a sphere. 11. Dot product and generalization. Bibliography. Index. In three dimensions common alternative coordinate systems include cylindrical coordinates and spherical coordinates. The reduction of geometry to algebra requires the notion of a transformation group. The transformation group supplies two essential ingredients. First it is used to define the notion of equivalence in the geometry in question. For example in Euclidean geometry, two triangles are congruent if there is distance preserving transformation carrying one to the other and they are similar if there is a similarity transformation carrying one to the other. Secondly in each kind of geometry there are normal form theorems which can be used to simplify coordinate proofs. In analytic geometry the plane is given a coordinate system, by which every point has a pair of real number coordinates. The present book provides an authoritative review of many aspects of this subject. This book will be useful to teachers and students.