Suvarna Garge (Editor)

Bullet nose curve

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit
Bullet-nose curve

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

a 2 y 2 − b 2 x 2 = x 2 y 2

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

f ( z ) = ∑ n = 0 ∞ ( 2 n n ) z 2 n + 1 = z + 2 z 3 + 6 z 5 + 20 z 7 + ⋯

then

y = f ( x 2 a ) ± 2 b  

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

References

Bullet-nose curve Wikipedia
(Text) CC BY-SA