Fundamentals of Analysis Geometry

Contents: Preface. 1. Analysis geometry. 2. Cylindrical coordinate system. 3. Algebraic geometry. 4. Fundamental theorem of curves. 5. Butterfly curve. 6. Circular algebraic curve. 7. Inverse curve. 8. Radius of curvature. 9. Normed vector space. 10. Coordinate systems. 11. Poncelets closure theorem. Bibliography. Index. The Greek mathematician Menaechmus solved problems and proved theorems using a method that has a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry. Apollonius of Perga, in on determinate section, dealt with problems in a manner that may be called an analytic geometry of one dimension with the question of finding points on a line that were in a ratio to the others. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of descartes by some 1800 years. His application of reference lines a diameter and a tangent is essentially no different than our modern use of a coordinate frame where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. This book makes an attempt to present the available information on the modern concepts of Analysis Geometry. This book will serve as text book for students of this subject.