For anyone still struggling with the intuition:
How many times does a circle rotate if you roll it around a tiny dot? 1
How many times does it rotate if you roll it around another circle the same size? Gotta be more than the dot, right?
I would’ve never gotten that! I started getting lost trying to think about the differences in circumferences and radii before they mentioned the right or wrong answers
My only intuition was this: if you take two identical coins and rotate them together (like a pair of gears), it takes one rotation each to reach the starting point. If you now rotate your head along with one of the coins, it will appear standing still, while the other one will be rotating twice as fast.
I still would have guessed the answer was 6, though. It took me awhile to figure out how extrapolate this model to a 3:1 ratio. As it turns out, it still works, and you get 4, but evidence of that was far from obvious to me.
I probably would have gotten four because I would have visually saw the answer without knowing the equation.
I bet you would have discovered gravity first if only the apple fell on your head instead of pesky Newton
I don’t think that’s a brag.
Assuming they did what I did, they saw it and went ‘no fucking idea’ and visualised the wheel rotating and counting the rotations seen.
The smart people stuff is the trying to do the radius shit.
Watched the video and was still confused. Had to stare at the cardioid animation on the Wikipedia page for like 10 minutes before I could wrap my head around it.
One thing that helped me intuit the “sidereal” result (4) was to consider what happens as the radius of circle B approaches 0. At least in my mind, it seems pretty clear that A has to undergo at least one rotation.
That said, I am unsure that I would have caught this as a test-taker. Derek’s videos always have some “trick”, putting me on guard, but in a testing scenario I would have seen the answer for 3 with no answer for 4, marked it down, and moved on quickly.
VG video. Confused by the word ‘revolve’? How many times does the Earth ‘revolve’ around the Sun in a year?
But, worse yet, there were THREE correct answers … none listed!
