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Wallis's Conical Edge
In geometry, Wallis's conical edge is a ruled surface given by the parametric equations : x=v\cos u,\quad y=v\sin u,\quad z=c\sqrt where , and are constants. Wallis's conical edge is also a kind of right conoid. It is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections. See also * Ruled surface * Right conoid In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the ''axis'' of the right conoid. Using a Cartesian coordinate system in three-dimensiona ... References * A. Gray, E. Abbena, S. Salamon, ''Modern differential geometry of curves and surfaces with Mathematica'', 3rd ed. Boca Raton, Florida:CRC Press, 2006() External linksWallis's Conical Edgefrom MathWorld. Surfaces Geometric shapes {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallis's Conical Edge
In geometry, Wallis's conical edge is a ruled surface given by the parametric equations : x=v\cos u,\quad y=v\sin u,\quad z=c\sqrt where , and are constants. Wallis's conical edge is also a kind of right conoid. It is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections. See also * Ruled surface * Right conoid In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the ''axis'' of the right conoid. Using a Cartesian coordinate system in three-dimensiona ... References * A. Gray, E. Abbena, S. Salamon, ''Modern differential geometry of curves and surfaces with Mathematica'', 3rd ed. Boca Raton, Florida:CRC Press, 2006() External linksWallis's Conical Edgefrom MathWorld. Surfaces Geometric shapes {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallis Conical Edge
Wallis (derived from ''Wallace'') may refer to: People * Wallis (given name) **Wallis, Duchess of Windsor * Wallis (surname) Places * Wallis (Ambleston), a hamlet within the parish of Ambleston in Pembrokeshire, West Wales, United Kingdom * Wallis, Mississippi, an unincorporated community, United States * Wallis, Texas, a city, United States * Wallis and Futuna, a French overseas department ** Wallis Island, one of the islands of Wallis and Futuna * Valais, a Swiss canton with the German name "Wallis" * Walliswil bei Niederbipp, a municipality in the Oberaargau administrative district, canton of Bern, Switzerland * Walliswil bei Wangen, a municipality in the Oberaargau administrative district, canton of Bern, Switzerland Brands and enterprises * Wallis (retailer), a British clothing retailer * Wallis Theatres, an Australian cinema franchise See also * Wallace (other) Wallace may refer to: People * Clan Wallace in Scotland * Wallace (given name) * Wallace (su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruled Surface
In geometry, a surface is ruled (also called a scroll) if through every point of there is a straight line that lies on . Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is ''doubly ruled'' if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points . The properties of being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry. In algebraic geometry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. For example, the equations :\begin x &= \cos t \\ y &= \sin t \end form a parametric representation of the unit circle, where ''t'' is the parameter: A point (''x'', ''y'') is on the unit circle if and only if there is a value of ''t'' such that these two equations generate that point. Sometimes the parametric equations for the individual scalar output variables are combined into a single parametric equation in vectors: :(x, y)=(\cos t, \sin t). Parametric representations are generally nonunique (see the "Examples in two dimensions" section belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Conoid
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the ''axis'' of the right conoid. Using a Cartesian coordinate system in three-dimensional space, if we take the to be the axis of a right conoid, then the right conoid can be represented by the parametric equations: :x=v\cos u :y=v\sin u :z=h(u) where is some function for representing the ''height'' of the moving line. Examples A typical example of right conoids is given by the parametric equations : x=v\cos u, y=v\sin u, z=2\sin u The image on the right shows how the coplanar lines generate the right conoid. Other right conoids include: *Helicoid: x=v\cos u, y=v\sin u, z=cu. *Whitney umbrella: x=vu, y=v, z=u^2. *Wallis's conical edge: x=v\cos u, y=v \sin u, z=c\sqrt. *Plücker's conoid: x=v\cos u, y=v\sin u, z=c\sin nu. *hyperbolic paraboloid: x=v, y=u, z=uv (with x-axis and y-axis as its axes). See also * Cono ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wallis
John Wallis (; la, Wallisius; ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the symbol ∞ to represent the concept of infinity. He similarly used 1/∞ for an infinitesimal. John Wallis was a contemporary of Newton and one of the greatest intellectuals of the early renaissance of mathematics. Biography Educational background * Cambridge, M.A., Oxford, D.D. * Grammar School at Tenterden, Kent, 1625–31. * School of Martin Holbeach at Felsted, Essex, 1631–2. * Cambridge University, Emmanuel College, 1632–40; B.A., 1637; M.A., 1640. * D.D. at Oxford in 1654 Family On 14 March 1645 he married Susanna Glynde ( – 16 March 1687). They had three children: # Anne Blencoe (4 June 1656 – 5 April 1718), married Sir John Blencowe (30 November 1642 – 6 May 1726) in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, Aerospace engineering, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including Algebraic geometry, algebraic, Differential geometry, differential, Discrete geometry, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Sections
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a ''focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''eccentricity''. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of deg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruled Surface
In geometry, a surface is ruled (also called a scroll) if through every point of there is a straight line that lies on . Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is ''doubly ruled'' if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points . The properties of being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry. In algebraic geometry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Conoid
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the ''axis'' of the right conoid. Using a Cartesian coordinate system in three-dimensional space, if we take the to be the axis of a right conoid, then the right conoid can be represented by the parametric equations: :x=v\cos u :y=v\sin u :z=h(u) where is some function for representing the ''height'' of the moving line. Examples A typical example of right conoids is given by the parametric equations : x=v\cos u, y=v\sin u, z=2\sin u The image on the right shows how the coplanar lines generate the right conoid. Other right conoids include: *Helicoid: x=v\cos u, y=v\sin u, z=cu. *Whitney umbrella: x=vu, y=v, z=u^2. *Wallis's conical edge: x=v\cos u, y=v \sin u, z=c\sqrt. *Plücker's conoid: x=v\cos u, y=v\sin u, z=c\sin nu. *hyperbolic paraboloid: x=v, y=u, z=uv (with x-axis and y-axis as its axes). See also * Cono ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surfaces
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat *Surface (differential geometry), a differentiable two-dimensional manifold *Surface (topology), a two-dimensional manifold * Algebraic surface, an algebraic variety of dimension two *Coordinate surfaces *Fractal surface, generated using a stochastic algorithm *Polyhedral surface * Surface area *Surface integral Arts and entertainment * Surface (band), an American R&B and pop trio ** ''Surface'' (Surface album), 1986 *Surfaces (band), American musical duo * ''Surface'' (Circle album), 1998 * "Surface" (Aero Chord song), 2014 * ''Surface'' (2005 TV series), an American science fiction show, 2005–2006 * ''Surface'' (2022 TV series), an American psychological thriller miniseries that began streaming in 2022 *'' The Surface'', an American film, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
