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The bicorn is also known as a cocked hat curve, due to its resemblance to a bicorne. It is a curve with equation
## References

- $y^2(a^2-x^2)=(x^2+2ay-a^2)^2\; ,$

The bicorn is a plane algebraic curve of degree four and genus zero. It has two cusp singularities in the real plane, and a double point in the complex projective plane at x=0, z=0 . If we move x=0 and z=0 to the origin substituting and perform an imaginary rotation on x bu substituting ix/z for x and 1/z for y in the bicorn curve, we obtain

- $(x^2-2az+a^2z^2)^2\; =\; x^2+a^2z^2.,$

- J. Dennis Lawrence (1972).
*A catalog of special plane curves*. Dover Publications.

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Last updated on Monday August 25, 2008 at 07:20:02 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday August 25, 2008 at 07:20:02 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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