The inner wheel is turning a lot slower than the outer one is!
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Regardless of speed, how is a wheel with a much smaller circumference able to cover the same amount of distance as a wheel with a larger circumference, both only making 1 complete rotation?
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It's only considering the relative displacement of a circle in the horizontal axis. Not the "actual distance" traveled by 'B' or 'C'. Which is known as Cycloid. Equation of cycloid => x = r(t - sin t) , y = (1 - cos t) length => 8 r where r = radius and t = angle of rotation.pic.twitter.com/YDU3m54Itc
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Typo. y = r (1 - cos t) So here the radius is dependent on the position of (x,y) coordinates. Hence it affects the original distance traveled as well. So length of inner cycloid = 8 r (r = inner circle radius) length of outer cycloid = 8 R (R = outer circle radius) 8 R =/= 8 r
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A bijection doesn't have to preserve measure.
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The inner circle is slipping.
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Here is my answer coded in a
#WolfLang notebook demostration at#WSS17@WolframSummer@WolframResearch https://www.wolframcloud.com/objects/summerschool/pages/2017/MarianoCanoSantos_TE … -
I love the effort you put into solving this. I was going to do the same as a JavaScript demo but yours is so well done!pic.twitter.com/JWBB38kuCW
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