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]]
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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 09:46, 1 March 2014

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