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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 . 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. A quartic curve can have a maximum of: * Four connected components * Twenty-eight bi-tangents * Three ordinary double points. One may also consider quartic curves over other fields (or even rings), for instance the complex numbers. In this way, one gets Riemann surfaces, which are one-dimensional objects over C, but are two-dimensional over R. An example is the Klein quartic. Additionally, one can look at curves in the projective plane, given by homogeneous polynomials. ==Examples== Various combinations of coefficients in the above equation give rise to various important families of curves as listed below. *Bicorn curve *Bullet-nose curve *Cartesian oval * Cassini oval *Deltoid curve * Hippopede * Kampyle of Eudoxus *Klein quartic *Lemniscate * *Lemniscate of Bernoulli * *Lemniscate of Gerono *Limaçon *Lüroth quartic *Spiric section *Squircle * *Lamé's special quartic *Toric section *Trott curve 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quartic plane curve」の詳細全文を読む スポンサード リンク
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