This is crazy interesting!
I did not watch this video but did read about this math. Visualize the larger circle unwrapped into a flat line, and the smaller circle sliding along the length of the line so its bottom point is fixed to the line. You’ll see the small circle never rotates. Now slide the small circle with a point fixed onto the large circle in the same way, and you’ll see the small circle makes one complete rotation. That rotation happens in addition to the rotations you get from dividing the larger circumference by the smaller circumference, so the answer is 4 in this case
That’s what you’d think, but there’s an extra rotation involved in the act of the small circle moving around the larger circle rather than along a straight line, so it’s (6π/2π) + 1
The center travels 2π per rotation but need to travel 8π because the path of the center of the small circle is a circle 4r the radius of the large circle plus the radius of the small circle. It would be three if the center of the small circle traveled along the edge of the larger circle but it’s edge to edge.
if the path had been straight yeah, but the path itself rotates 360 degrees, which gives us an extra rotation
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
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.
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.
Godamn thats a phenominal example of reletivity.
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.
