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Plateau Curves
Parametric Cartesian equation:
x
=
a
sin
(
m
+
n
)
t
sin
(
m
−
n
)
t
x = a\Large\frac{ \sin(m + n)t}{\sin(m - n)t}
x
=
a
s
i
n
(
m
−
n
)
t
s
i
n
(
m
+
n
)
t
,
y
=
2
a
sin
(
m
t
)
s
i
n
(
n
t
)
sin
(
m
−
n
)
t
y = 2a\Large\frac{ \sin(mt) sin(nt)}{\sin(m - n)t}
y
=
2
a
s
i
n
(
m
−
n
)
t
s
i
n
(
m
t
)
s
i
n
(
n
t
)
View the interactive version of this curve.
Description
This curve was studied by the Belgium physicist and mathematician Joseph
Plateau
.
If
m
=
2
n
m = 2n
m
=
2
n
the
Plateau
curves become a circle, centre
(1
,
0)
and radius
2
.
The particular curves drawn above are with the parameters
m
=
5
,
n
=
3
m = 5, n = 3
m
=
5
,
n
=
3
.
Associated Curves
Definitions of the Associated curves
Evolute
Involute 1
Involute 2
Inverse curve wrt origin
Inverse wrt another circle
Pedal curve wrt origin
Pedal wrt another point
Negative pedal curve wrt origin
Negative pedal wrt another point
Caustic wrt horizontal rays
Caustic curve wrt another point
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