Surface of revolution information

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally...

In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose...

(except at its boundary). The surface created by this revolution and which bounds the solid is the surface of revolution. Assuming that the curve does...

toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example...

classes of surfaces, giving, in particular, formulas for areas of graphs z = f(x,y) and surfaces of revolution. One of the subtleties of surface area, as...

As an example, the (half) pseudosphere (with radius 1) is the surface of revolution of the tractrix parametrized by t ↦ ( t − tanh ⁡ t , sech t ) , 0...

: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar...

cylinders are the only surfaces with two-parameter families of rigid motions and the surfaces of revolution and helicoids are the only surfaces with a one-parameter...

example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Minimal surfaces can be defined...

geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have...

catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies...

curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a...

Industrial Revolution, sometimes divided into the First Industrial Revolution and Second Industrial Revolution, was a period of global transition of the human...

dihedral symmetry, Dihn as subgroup symmetries. In 3-dimensions, a surface or solid of revolution has circular symmetry around an axis, also called cylindrical...

form the Meissner tetrahedron, which does. Alternatively, the surface of revolution of the Reuleaux triangle also has constant width. The Reuleaux triangle...

elliptic paraboloid is a circular paraboloid or paraboloid of revolution. It is a surface of revolution obtained by revolving a parabola around its axis. A circular...

generalized definition of surfaces) shows that a solution exists. A symmetry argument proves that the solution must be a surface of revolution, and it can be...

with the axis of the cylinder, the free surface will assume a parabolic surface of revolution known as a paraboloid. The free surface at each point is...

Fresnel, is called wave surface by mathematicians. The surface of the reflector of a telescope is a paraboloid of revolution. Other occurrences: Soap...

{\displaystyle {\frac {3}{8}}\pi a^{2}} Length of curve 6 a {\displaystyle 6a} Volume of the surface of revolution of the enclose area about the x-axis. 32 105...

Cultural Revolution, formally known as the Great Proletarian Cultural Revolution, was a sociopolitical movement in the People's Republic of China (PRC)...

a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes...

surfaces of revolution with the same constant width, the one with minimum volume is the shape swept out by a Reuleaux triangle rotating about one of its...

Microsoft Surface is a series of touchscreen-based personal computers, tablets, and interactive whiteboards designed and developed by Microsoft, most of them...