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.