Help me remember this math puzzle about a rolling wheel

[pancakes3]

@glowacks

It took me a very long time to figure out why this was true, because I kept doing it in three dimensions, with one wheel perpendicular to the other. I kept coming to the conclusion that it didn’t matter what the angle between them was, it was effectively the same as if they were just sitting on top of each other. But when you align them anti-parallel, you introduce a second rotation that in some sense was always there, but hidden by the fact that if you have them at any other angle, the rotations are not in the same plane.

A very poorly worded problem.

hahaha. me too. it wasn’t until after reading moes lotion’s proof and corroborated with indistinguishable’s that i finally laid that dime down flat (in my head).

[astro]

The whole trick is that the words “rotation” and “revolution” do not mean the same thing in the context of this question. Using two quarters with the eagles head to head and rolling one around the other, the edge of the moving (rolling) quarter makes one complete revolution around the static quarters until it comes back to the head to head position, but it rotates twice around it’s own axis while making this trip.

[Bryan_Ekers]

Matrin Gardner discusses this in Mathematical Circus. He said it came down to how rotation was defined.

[Indistinguishable]

@astro

The whole trick is that the words “rotation” and “revolution” do not mean the same thing in the context of this question. Using two quarters with the eagles head to head and rolling one around the other, the edge of the moving (rolling) quarter makes one complete revolution around the static quarters until it comes back to the head to head position, but it rotates twice around it’s own axis while making this trip.

Sure, but the wording given in, say, post #2 just mentions “revolution upon its own axis” and “rolling … around a fixed wheel”. The word “rotation” never comes up, and the uses of “revolution” and “rolling” make clear what is meant. The puzzle isn’t one of trick wording.