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A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
This is a list of surfaces in mathematics. They are divided into minimal surfaces , ruled surfaces , non-orientable surfaces , quadrics , pseudospherical surfaces , algebraic surfaces , and other types of surfaces.
Endrass surface, a certain surface of degree 8 with 168 nodes; Sarti surface, a certain surface of degree 12 with 600 nodes; Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces
An open surface with x-, y-, and z-contours shown.. In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball.
If a surface has constant Gaussian curvature, it is called a surface of constant curvature. [52] The unit sphere in E 3 has constant Gaussian curvature +1. The Euclidean plane and the cylinder both have constant Gaussian curvature 0. A unit pseudosphere has constant Gaussian curvature -1 (apart from its equator, that is singular).
In mathematics, a minimal surface is a surface that locally minimizes its area. ... Textbooks. R. Courant. Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces.
Around 300 BC, geometry was revolutionized by Euclid, whose Elements, widely considered the most successful and influential textbook of all time, [16] introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof.
Although the book includes some computer-generated images, [2] most of it is centered on hand drawing techniques. [1] After an introductory chapter on topological surfaces, the cusps in the outlines of surfaces formed when viewing them from certain angles, and the self-intersections of immersed surfaces, the next two chapters are centered on drawing techniques: chapter two concerns ink, paper ...