Bullet-nose curve

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Bullet-nose curve with a = 1 and b = 1

In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation

The bullet curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 and z=0, and is therefore a unicursal (rational) curve of genus zero.



are the two branches of the bullet curve at the origin.


  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 128–130. ISBN 0-486-60288-5.