Rational Curve
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In mathematics, algebraic curves are the simplest objects of Euclidean geometry that can not be defined by linear properties. Specifically, in Euclidean geometry, a plane algebraic curve is the set (mathematics)|set of the points of the Euclidean plane whose coordinates are zero of a function|zeros of some polynomial in two variables.For example, the unit circle is an algebraic curve, being the set of zeros of the polynomial x2 + y2 − 1 Various technical considerations have led to consider that the complex number|complex zeros of a polynomial belong to the curve. Also, the notion of algebraic curve has been generalized to allow the coefficients of the defining polynomial and the coordinates of the points of the curve to belong to any field (mathematics)|field, leading to the following definition. In algebraic geometry, a plane affine algebraic curve defined over a field k is the set of points of K2 whose coordinates are zeros of some polynomial#Number of variables|bivariate polynomial ...
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