7

Is there a "visual proof" for sophomore's dream?

$$\int_0^1 x^{-x}\,dx = \sum_{n=1}^\infty n^{-n}.$$

In the wikipedia article there are two algebraic proofs, but the integral and the summation has a geometric interpretation. Because of that, I was thinking about it, that maybe there is a nice geometric proof for this statement.

user153012
  • 12,890
  • 5
  • 42
  • 115
  • what is the geometric interpretation, exactly? – MichaelChirico May 25 '15 at 22:27
  • 1
    I have yet to find a satisfactory visual representation of exponentiation with a real exponent. And that's just one of the ingredients here so the outlook is grim. It doesn't matter though! After a while algebraic statements portray as vivid a scenery as do other arguments. – GPerez May 25 '15 at 22:52

0 Answers0