Futility Closet

Loopy

Posted in Oddities,Science & Math by Greg Ross on January 1st, 2007

You can measure a circle’s circumference by “unrolling” it along a line, like this:

circumference fallacy

But note that the smaller circle unrolls at the same time … and it gives the same length. Clearly we could do the same thing with circles of any size. Therefore all circles have the same circumference.