Foundations of Geometry

The mathematical discipline that addresses inquiries pertaining to size, shape, relative positioning of figures, and spatial properties is referred to as geometry. Fundamental concepts within geometry encompass notions of Point, plane, angle, line, curve, surface, topology, and manifold. Its applications span diverse domains including architecture, physics, art, and other mathematical branches. Sub-disciplines within this sphere include algebraic geometry, differential geometry, and Euclidean geometry. Differential geometry employs calculus and linear algebra techniques to investigate geometric quandaries. Euclidean geometry finds utility in computer graphics, computational geometry, incidence, geodesy, and navigation. This book is a compilation of chapters that discuss the most vital concepts in the field of geometry. The topics covered herein deal with the core aspects of this area. It will also serve as a reference guide for students and academicians.