1.NounA plane curve defined by an equation whose highest degree is 3. Formally, the set of solutions to an equation of the form
"
a
30
x
3
+
a
21
x
2
y
+
a
12
x
y
2
+
a
03
y
3
+
a
20
x
2
+
a
11
x
y
+
a
02
y
2
+
a
10
x
+
a
01
y
+
a
00
=
0.
{\displaystyle a_{30}x^{3}+a_{21}x^{2}y+a_{12}xy^{2}+a_{03}y^{3}+a_{20}x^{2}+a_{11}xy+a_{02}y^{2}+a_{10}x+a_{01}y+a_{00}=0.}
"