Differential Geometry Algebraic Geometry Discrete Geometry
Elementary Geometry Topology Computational Geometry
Affine Geometry Projective Geometry Non-Euclidean Geometry
A logical conceptual form (or structure) serving as a medium in which other forms and some structures are realized. For example, in elementary geometry the plane or space serves as the medium in which one constructs various figures.
The fundamental concepts of analytic geometry are the simplest geometric elements (points, straight lines, planes, second-order curves and surfaces). The principal means of study in analytic geometry are the method of coordinates and the methods of elementary algebra. The genesis of the method of coordinates is closely linked with the intense development of astronomy, mechanics and technology in the 17th century. In his Géometrie, R. Descartes (1637) gave a clear and exhaustive account of this method and of the foundations of analytic geometry. P. Fermat, a contemporary of Descartes, was also familiar with the principles of this method. Subsequent development of analytic geometry is due to the studies of G. Leibniz, I. Newton and, particularly, L. Euler. The tools of analytic geometry were utilized by J.L. Lagrange in his construction of analytic mechanics and by G. Monge in differential geometry. In our own days, analytic geometry has no significance as an independent branch of science, but its methods are extensively employed in various fields of mathematics, mechanics, physics and other sciences.
Geometric regions such as points, curves, surfaces, volumes, and their higher-dimensional analogs occur in a variety of contexts, including mathematics, engineering, science, computer games, and geography.
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M. Postnikov - Lectures in Geometry [Volumes 1-5]
I. M. Singer, J. A. Thorpe - Lecture Notes on Elementary Topology and Geometry
Daniel Coray - Notes on Geometry and Arithmetic
Jeremy Gray - Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century
Carl B. Boyer - History of analytic geometry
David M. Clark, Samrat Pathania - A Full Axiomatic Development of High School Geometry
Răzvan Gelca, Ionuţ Onişor, Carlos Yuzo Shine - Geometric Transformations
Athanase Papadopoulos - Surveys in Geometry I
Alan F. Beardon - The Geometry of Discrete Groups