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Trident curve : ウィキペディア英語版
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'' = ''x''/''z'' and ''y'' = 1/''z'' 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 zero.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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