SHM and UCM: multiple projection
This activity belongs to the GeoGebra book The Domain of the Time.
We can project the point describing the UCM onto any diameter of the circle. The point obtained will always follow a SHM. If we project onto the horizontal and vertical diameters, we obtain the familiar diagram used to explain the cosine and sine functions in the unit circle.
However, a curious effect occurs when we project onto ALL the diameters. The points obtained, each traveling along its diameter in SHM, will form a new circle with half the radius, rotating inside the larger circle. And in turn, this new circle...
Author of the activity and GeoGebra construction: Rafael Losada.