Trident curve
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In mathematics, Trident curve is the name for a family of curves that have the formula:
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- xy + ax3 + bx2 + cx = d
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Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x=0, y=∞, z=0; if we substitute x=x/z and y=1/z into the equation of the trident curve, we get
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- ax3 + bx2z + cxz2 + xz = dz3,
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which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus one.
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