For the first time, people started talking about the wheel paradox even before Aristotle, but he was the first to study it closely. Then Galileo Galilei struggled to solve this problem.
The essence of the paradox is as follows:
We have two wheels of different sizes, one in the other. Both wheels roll synchronously and travel a certain distance. The question is: Will both wheels go the same way?
If you look closely at the gif above, you will notice that both wheels completely rotate around their entire circumference in order to cover the same distance (see the red line). And it is also obvious that one circle is smaller than the other. This means that either the wheels have the same circumference (which is fundamentally wrong), or different circles "unfold" to the same length (which cannot be the case).
And if we imagine that all this is true? It is then technically possible that a wheel with a circumference of 2.54 centimeters is able to travel the same path in one revolution as a wheel with a circumference of 1.6 kilometers.
But that just doesn't happen. The length of a circle with a smaller radius cannot be equal to the length of a circle with a larger radius. So what's the deal?
Let's trace the route that each point of the circle goes from the beginning of the red line to its end. Move your finger along the line indicating the radius of the circle, while following the path that the small circle travels from the beginning of the path to the end.
Promotional video:
Then trace the path that the great circle travels from the beginning of the path to the end. Obviously, a point on a larger circle travels a longer path, and therefore a longer path, to get to the same point.
In other words, you can go to Moscow from Nizhny Novgorod through Vladimir, or you can go through Arkhangelsk or Astrakhan. The distance from Nizhniy to Moscow remains unchanged, but the paths that will have to be done along these routes are far from the same.
This is precisely the explanation of the paradox, over which the most outstanding minds of mankind have puzzled.
