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Mathematics in coin rolling
Two laps. (Using the method of theme synthesis to understand)

Did you learn some physics in grade three? We use physical thinking to solve problems (whole plus isolation) and use geographical terms "revolution" and "rotation":

First, study the "revolution" of sports currency. If the center of the moving coin is isolated, then the locus of this point is a great circle, the radius r of this great circle is twice that of the coin (if you still don't understand it, you can operate it yourself), and two coins can be regarded as a whole (particle), then the distance of the moving coin can be regarded as the movement of the center of the circle, and the length of the distance is L, and L can be represented by R.

Then study the "rotation" of a moving coin (the coin can't be regarded as a particle at this time). The movement distance of any point outside the coin is equal to the circumference l of the coin. After calculation, L=2l.

Therefore, if the angular velocity of the coin "revolution" and "rotation" are the same, it is 2 turns. (For example, it must be 1 circle after "revolution" for half a circle. )

If there is a problem, try to understand it comprehensively, which will be faster and deeper, provided that other subjects are better. ...