Both the big-faced cat and the blue mouse think they run fast.
The big-faced cat said, "I have long legs and big steps." One step is two steps ahead of you. I must run faster than you! " "
Not to be outdone, Blue Mouse said, "Although my legs are short, I walk fast. You just took one step, and I took three steps. I must run faster than you! " "
After arguing for a long time, neither of them was convinced, so they had to compete on the spot.
Just drew three semicircles on a construction site (a big semicircle, two small semicircles; As we all know, the diameter of a large semicircle is twice that of a small semicircle.
The big-faced cat pointed to the semicircle and said, "You can run from A to B along this big semicircle and from A to B along these two small semicircles. Choose two roads. "
Blue mouse chose a road connected by two small semicircles. They both stood in the first place, and at the command, they ran quickly along their respective roads.
The big-faced cat has long legs, and the blue-skinned mouse has small and brisk steps. Strangely, both of them reached the second place at the same time. Although both of them were unconvinced, neither of them could say anything. Which of the two roads is longer?
In fact, they are the same length. If two small semicircles become three small semicircles, four small semicircles ... and the sum of the perimeters of a hundred small semicircles, a semicircle and these small semicircles will be equal?
The answer is yes. It is easy to see this conclusion from the formula for calculating the circumference. If you don't believe me, do it.