Random number generation: Difference between revisions
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[[File:Bullet nose curve.svg|thumb|right|226px|Bullet-nose curve with ''a'' = 1 and ''b'' = 1]] | |||
In [[mathematics]], a '''bullet-nose curve''' is a [[algebraic curve|unicursal quartic curve]] with three [[inflection point]]s, given by the equation | |||
:<math>a^2y^2-b^2x^2=x^2y^2 \,</math> | |||
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 [[geometric genus|genus]] zero. | |||
If | |||
:<math>f(z) = \sum_{n=0}^{\infty} {2n \choose n} z^{2n+1} = z+2z^3+6z^5+20z^7+\cdots</math> | |||
then | |||
:<math>y = f\left(\frac{x}{2a}\right)\pm 2b\ </math> | |||
are the two branches of the bullet curve at the origin. | |||
==References== | |||
* {{cite book | author=J. Dennis Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | pages=128–130 }} | |||
[[Category:Curves]] | |||
[[Category:Algebraic curves]] | |||
Revision as of 15:40, 31 December 2013
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.
If
then
are the two branches of the bullet curve at the origin.
References
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