/sci/ - Science & Math

Here's a brain melting geometric riddle that I came up with.

In picrel, the line or the circle rolls (without skidding) so that the points A and B will come to contact with each other. Now imagine that the line in picrelated was horizontal, and the circle rolled on it and the point A traced a curve (a cycloid to be specific). Then imagine an alternate situation where the circle stayed stationary where it is, and it was the line that rolled along the circle, so that the point B (a fixed point on the line) would now trace a curve. The riddle is this: are the two curves the same curve, or are they two different types of curves?

I came up with this by playing around with Desmos and it took me a really long time to wrap my head around this.