18.2.2 Osculating circle of a curve
The
osculating_circle
command finds and draws the osculating circle of a curve.
To find the osculating circle from a parameterization,
osculating_circle
takes three arguments:
C
, a curve.
t
, the parameter of the curve.
t
0
, a value of the parameter.
osculating_circle(
C
,
t
,
t
0
)
draws and returns the osculating circle of the curve at the point specified by
t
0
.
To find the osculating circle from a curve object,
osculating_circle
takes two arguments:
C
, a curve.
p
, a point on the curve.
osculating_circle(
C
,
p
)
draws and returns the osculating circle of
C
at the point
p
.
Examples
osculating_circle
(
plot
(
x
^2),
point
(1,1))
equation
(
osculating_circle
(
plot
(
x
^2),
point
(1,1)))
⎛
⎝
x
+4
⎞
⎠
2
+
⎛
⎜
⎜
⎝
y
−
7
2
⎞
⎟
⎟
⎠
2
=
125
4
equation
(
osculating_circle
([
t
^2,
t
^3],
t
,1))
⎛
⎜
⎜
⎝
x
+
11
2
⎞
⎟
⎟
⎠
2
+
⎛
⎜
⎜
⎝
y
−
16
3
⎞
⎟
⎟
⎠
2
=
2197
36
