|
Trident Curve
In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula: :xy+ax^3+bx^2+cx=d Trident curves are cubic plane curves with an ordinary double point in the real projective plane at ''x'' = 0, ''y'' = 1, ''z'' = 0; if we substitute ''x'' = and ''y'' = into the equation of the trident curve, we get :ax^3+bx^2z+cxz^2+xz = dz^3, which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial n ... zero. References * External links * Algebraic curves {{algebraic-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's ''Elements'': "The urvedline is ��the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which ��will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: ''A curve is the image of an interval to a topological space by a continuous function''. In some contexts, the function that defines the curve is called a ''parametrization'', and the curve is a parametric curve. In this article, these curves are sometimes called ''topological curves'' to distinguish them from more constrained curves su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a '' chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula (often referred to as a '' well-formed formula'') is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton Trident
Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton (band), Spanish electronic music group * ''Newton'' (Blake), a print by William Blake * ''Newton'' (Paolozzi), a 1995 bronze sculpture by Eduardo Paolozzi * Cecil Newton (''Coronation Street''), a character in the British soap opera ''Coronation Street'' * Curtis Newton, "real" name of pulp magazine character Captain Future * George Newton, a character in the film series '' Beethoven'' * Newton Gearloose, a Disney character, nephew of Gyro Gearloose * Newton, a character in '' The Mighty Hercules'' animated series People * Newton (surname), including a list of people with the surname * Newton (given name), including a list of people with the given name Places Australia * Newton, South Australia Canada * Newton, Edmonton, Alberta * N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Projective Plane
In mathematics, the real projective plane is an example of a compact non- orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in passing through the origin. The plane is also often described topologically, in terms of a construction based on the Möbius strip: if one could glue the (single) edge of the Möbius strip to itself in the correct direction, one would obtain the projective plane. (This cannot be done in three-dimensional space without the surface intersecting itself.) Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane. Topologically, it has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. Since the Möbius strip, in turn, can be constructed from a square by g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton Trident Y=inf
Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton (band), Spanish electronic music group * ''Newton'' (Blake), a print by William Blake * ''Newton'' (Paolozzi), a 1995 bronze sculpture by Eduardo Paolozzi * Cecil Newton (''Coronation Street''), a character in the British soap opera ''Coronation Street'' * Curtis Newton, "real" name of pulp magazine character Captain Future * George Newton, a character in the film series '' Beethoven'' * Newton Gearloose, a Disney character, nephew of Gyro Gearloose * Newton, a character in '' The Mighty Hercules'' animated series People * Newton (surname), including a list of people with the surname * Newton (given name), including a list of people with the given name Places Australia * Newton, South Australia Canada * Newton, Edmonton, Alberta * N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation can be restricted to the affine algebraic plane curve of equation . These two operations are each inverse to the other; therefore, the phrase algebraic plane curve is often used without specifying explicitly whether it is the affine or the projective case that is considered. More generally, an algebraic curve is an algebraic variety of dimension one. Equivalently, an algebraic curve is an algebraic variety that is birationally equivalent to an algebraic plane curve. If the curve is contained in an affine space or a projective space, one can take a projection for s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Genus
In algebraic geometry, the geometric genus is a basic birational invariant of algebraic varieties and complex manifolds. Definition The geometric genus can be defined for non-singular complex projective varieties and more generally for complex manifolds as the Hodge number (equal to by Serre duality), that is, the dimension of the canonical linear system plus one. In other words for a variety of complex dimension it is the number of linearly independent holomorphic - forms to be found on .Danilov & Shokurov (1998), p. 53/ref> This definition, as the dimension of : then carries over to any base field, when is taken to be the sheaf of Kähler differentials and the power is the (top) exterior power, the canonical line bundle. The geometric genus is the first invariant of a sequence of invariants called the plurigenera. Case of curves In the case of complex varieties, (the complex loci of) non-singular curves are Riemann surfaces. The algebraic definition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
