§@·~7
1-1.Construct the line segments joining points of the curve with the corresponding center of curvature for each of the following: the nephroid
1-2. the astroid
1-3. the deltoid
1-4. the cardioid.
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)
3.The deltoid: (2 cos t + cos 2t, 2 sin t - sin 2t)
4.The cardioid: (2 cos t - cos 2t, 2 sin t - sin 2t)
5.The cycloid: (t + sin t, cos t)
6.The ellipse: (5 cos t, 3 sin t)
7.The "egg": (5*cos(t)-cos(2t), 3*sin(t)-sin(2t)
8.The lemniscate of Bernoulli: (cos t / (2-cos2t), sin t cos t / (2-cos2t))
9.The curve (5 cos(t) + sin(2 t), 3 cos(3 t) - sin(4 t))
10.The spiral:
