shapes of constant width 2D (Reuleaux polygons)
Press button in upper-left corner to cycle through various shapes.
Animation may be controlled with start/stop button. When stopped, you slider may be dragged.
Checkbox in lower-left corner toggles visibility of path that centerpoint traces out as function of .
In the case of the regular Reuleaux polygon, the path looks sinusoidal, but it is not quite truly sinusoidal.
In the case of the regular polygon, the path looks like the graph of a sinusoidal function inside an absolute value function, but it is not quite truly that shape.
Also check out shape of constant width 3D (Meissner body).