I've got some wonderful answers this morning on Mathematica Stack Exchange. See Diagonals of a regular octagon and Determine the height of a box packed with spheres. I'm just smiling with the amount I am learning with these responses, so I'd like to ask one more question.
The diagram below shows the circular face of a clock with radius 20 cm and a circular disk with radius 10 cm externally tangent to the clock face at 12 o’clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?
How can I use Mathematica to animate the smaller circle with the arrow rotating about the large circle to show students the answer?
My adaption from the Plotting the Epicycloid
R = 20; r = 10;
fy[\[Theta]_, a_: 1] := (R + r) Cos[\[Theta]] +
a r Cos[(R + r) \[Theta]/r];
fx[\[Theta]_, a_: 1] := (R + r) Sin[\[Theta]] +
a r Sin[(R + r) \[Theta]/r];
plot[max_] :=
ParametricPlot[{fx[\[Theta]], fy[\[Theta]]}, {\[Theta], 0, max},
PlotStyle -> {Red, Thick},
Epilog -> {
Thick,
Blue, Circle[{0, 0}, R],
Black, Circle[{fx[max, 0], fy[max, 0]}, r],
Red, PointSize[Large], Point[{fx[max], fy[max]}],
Green, PointSize[Large], Point[{fx[max, -1], fy[max, -1]}],
Black, Line[{{fx[max, 0], fy[max, 0]}, {fx[max], fy[max]}}]
},
PlotRange -> 40]
Manipulate[
plot[max], {max, 0.000001, 2 Pi}]
Looks like the answer is 4 pm. Sorry about the image, as the number in the entry box should show $2\pi/3$, but it is blocked because of size after I typed it in.
Also, that is what the solution is as posted at The Art of Problem Solving.