A bijection doesn't have to preserve measure.
-
-
-
The inner circle is slipping.
-
Found the engineer.
-
Haha, I wish. Physicist.
-
Better, isn’t it?
-
Using Sheldon to tell that physics is better than engineering. Ironic!
-
I was imagining a room of physicists and engineers, where the physicist looks at an engineer, says that engineering is better, and then turn his/her head to another physicist and blinking so that the engineer doesn't get hurt (even though the engineer is understanding sarcasm)

- 1 more reply
New conversation -
-
-
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
-
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
-
Well of course we know the two circumferences aren't equal, we want to know why they both cover the same length with equal number of rotation. As said, it's a fallacy.
-
I already said that. It is just a projection on the horizontal axis (x axis). Not the actual distance covered by outer circle C & the inner circle B. It's applicable to any geometrical shape though, the only criteria is the X value of any two points in that figure should be same
-
Oh ok ok ... I just got it. The x-y plane solves the trick. Thsnk you
-
You're welcome!

-
Again, in another way; Point B is not rolling alongside it's circumference but along the circumference of the bigger circle. So it is simply tracing A. As if it's sliding Thats why they didn't use a dot at the centre, but a much smaller circle to facilitate the illusion.
- 2 more replies
New conversation -
-
-
The inner wheel is turning a lot slower than the outer one is!
-
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?
-
The falicy is actually that the illustration is compressing the top line as the small wheel rolls across it. Otherwise it would be accumulating a bit of “slack” as it attempted to roll up the same length of line as the large wheel, given a smaller circumference.
-
Key is both circles have the same center with same angular speed(not linear), So both lines are 2•pi (full rotation) imagine both circles to be part of the same solid: like the inner and outer part of a car tyre, you will see this same effect if you draw a radius on it.
-
If you put both circles in the same “ground level” so they don’t share the center, the length of both lines would be different.
-
Lol I can’t tell if you are disagreeing with me or just expanding upon the explaination.
-
Just wanted to say there is no compression or any special effect on the .gif as this is something you can see in real life (think about the car tyre)
-
Please provide a proof a line of a fixed length fits around two different sized circles. There is no way around this. The gif must compress line b in order for it to wrap around the inner circle with one rotation.
- 7 more replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.