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In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical ...
Plane curves of degree 2 are known as conics or conic sections and include Circle. Unit circle; Ellipse; Parabola; Hyperbola. ... Two Dimensional Curves;
Lines in a Cartesian plane, or more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form: = + where: m is the slope or gradient of the line. b is the y-intercept of the line.
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation + =. In general, every implicit curve is defined by an equation of the form (,) =
Then is a plane , the circles can be represented in this plane by parabolas of the form = + +. In an analogous way, the classical 4 {\displaystyle 4} -dimensional Laguerre plane is related to the geometry of complex quadratic polynomials.
Plane equation in normal form. In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.
For example, the circle given by the equation + = has degree 2. The non-singular plane algebraic curves of degree 2 are called conic sections , and their projective completion are all isomorphic to the projective completion of the circle x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} (that is the projective curve of equation x 2 + y 2 − z 2 = 0 ...