Quartic plane curve

（重定向自Bean curve）

Ampersand curveBean curveBicuspid curveBow curveCruciform curve with parameters (b,a) being (1,1) in red; (2,2) in green; (3,3) in blue.Cruciform curve with parameters (b,a) being (1,1) in red; (2,1) in green; (3,1) in blue.Spiric sectionThree-leaved clover in cartesian coordinatesThree-leaved clover in polar coordinates

A quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation:

with at least one of A, B, C, D, E not equal to zero. This equation has 15 constants. However, it can be multiplied by any non-zero constant without changing the curve; thus by the choice of an appropriate constant of multiplication, any one of the coefficients can be set to 1, leaving only 14 constants. Therefore, the space of quartic curves can be identified with the real projective space $\mathbb{RP}^{14}$ . It also follows that there is exactly one quartic curve that passes through a set of 14 distinct points in general position, since a quartic has 14 degrees of freedom.

单词	Bean curve
释义	Bean curve 英语百科 Quartic plane curve （重定向自Bean curve） A quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: with at least one of A, B, C, D, E not equal to zero. This equation has 15 constants. However, it can be multiplied by any non-zero constant without changing the curve; thus by the choice of an appropriate constant of multiplication, any one of the coefficients can be set to 1, leaving only 14 constants. Therefore, the space of quartic curves can be identified with the real projective space $\mathbb{RP}^{14}$ . It also follows that there is exactly one quartic curve that passes through a set of 14 distinct points in general position, since a quartic has 14 degrees of freedom.
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