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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 Analytic geometry, Cartesian methods to study conic sections. See also * Plücker's conoid * Ruled surface * Right conoid 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 Edge from MathWorld. Surfaces Geometric shapes {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruled Surface
In geometry, a Differential geometry of surfaces, surface in 3-dimensional Euclidean space is ruled (also called a scroll) if through every Point (geometry), point of , there is a straight line that lies on . Examples include the plane (mathematics), plane, the lateral surface of a cylinder (geometry), cylinder or cone (geometry), cone, a conical surface with ellipse, elliptical directrix (rational normal scroll), 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 thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Equation
In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point (mathematics), point, as Function (mathematics), functions of one or several variable (mathematics), variables called parameters. In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a Surface (mathematics), surface, called a parametric surface. In all cases, the equations are collectively called a parametric representation, or parametric system, or parameterization (also spelled parametrization, 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 is the parameter: A point is on the unit circle if and only if there is a value of ... [...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 * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wallis
John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 Wallis 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. He 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, Lady Blencowe (4 June 1656 – 5 April 1718), married Sir John Blencowe (30 November 1642 – 6 May 1726) in 1675, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Geometry
In 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 definitions and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Sections
A conic section, conic or a quadratic curve is a curve obtained from a Conical surface, cone's surface intersecting a plane (mathematics), 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 it was sometimes considered a fourth type. The Greek mathematics, 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 (mathematics), set of those points whose distances to some particular point, called a ''Focus (geometry), focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''Eccentricity (mathematics), eccentricity''. The type of conic is determined by the value of the ec ... [...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 (s ... [...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 Analytic geometry, Cartesian methods to study conic sections. See also * Plücker's conoid * Ruled surface * Right conoid 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 Edge from MathWorld. Surfaces Geometric shapes {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker's Conoid
In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder. Plücker's conoid is the surface defined by the function of two variables: : z=\frac. This function has an essential singularity at the origin. By using cylindrical coordinates in space, we can write the above function into parametric equations : x=v\cos u,\quad y=v\sin u,\quad z=\sin 2u. Thus Plücker's conoid is a right conoid, which can be obtained by rotating a horizontal line about the with the oscillatory motion (with period 2''π'') along the segment of the axis (Figure 4). A generalization of Plücker's conoid is given by the parametric equations : x=v \cos u,\quad y=v \sin u,\quad z= \sin nu. where denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruled Surface
In geometry, a Differential geometry of surfaces, surface in 3-dimensional Euclidean space is ruled (also called a scroll) if through every Point (geometry), point of , there is a straight line that lies on . Examples include the plane (mathematics), plane, the lateral surface of a cylinder (geometry), cylinder or cone (geometry), cone, a conical surface with ellipse, elliptical directrix (rational normal scroll), 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 thr ... [...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 * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
