| 7-1 |
Construct the line segments
joining points of
the curve with the corresponding
center of
curvature for each of the
following: the
nephroid, the astroid, the
deltoid and the
cardioid. |
|
| 7-2 |
Construct an animation displaying
the various positions of the osculating circle of the following
curves:
The
astroid: (3 cos t + cos 3t, 3 sin t - sin 3t)
|
|
| 7-3 |
The deltoid: (2 cos t + cos
2t, 2 sin t - sin 2t) |
|
| 7-4 |
The cardioid: (2 cos t + cos
2t, 2 sin t - sin 2t) |
|
| 7-5 |
The cycloid: (t + sin t, cos
t) |
|
| 7-6 |
The ellipse: (5 cos t, 3 sin
t) |
|
| 7-7 |
The "egg": (5*cos(t)-cos(2t),
3*sin(t)-sin(2t) |
|
| 7-8 |
The lemniscate of Bernoulli:
(cos t /
(2-cos2t), sin t cos t / (2-cos2t)) |
|
| 7-9 |
The curve (5 cos(t)2 + sin(2
t), 3 cos(3 t) -sin(4t)) |
|
| 7-10 |
The spiral: |
|