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:

trident curve with a = b = c = d = 1

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

trident curve at y = ∞ with a = b = c = d = 1

which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.

References

  • Lawrence, J. Dennis (1972). A Catalog of Special Plane Curves. Dover Publications. p. 110. ISBN 0-486-60288-5.


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