/sci/ - Science & Math

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

In picrel, The point B is a fixed point on the line and point A a fixed point on the circumference of the circle. They are positioned so that if the circle rolled on the line (without skidding), the points would come to contact with each other.

Now imagine that the line in picrelated was horizontal tangent on top of the circle, and the circle rolled on it so that 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 would now trace a curve. The riddle is this: are the two curves the same, or are they two different 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.