Bullet-nose curve explained

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

a ^{2y} ^{2-b} ^{2x} ^{2=x} ^{2y} ^{2}

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

If

f(z) = \sum ^{inf ty} _{n =0} { 2 n \choose n} z ^{2n+1} = z +2 z ^{3+6z} ^{5+20z} ^{7+ …} theny = f\left( (x)/(2 a) \right)\pm 2 b are the two branches of the bullet curve at the origin.

References

• Book: J. Dennis Lawrence . A catalog of special plane curves . Dover Publications . 1972 . 0-486-60288-5 . 128–130 . registration .