Originally Posted by

**manjohn12** **Theorem.** Suppose $\displaystyle f $ is entire and $\displaystyle \Gamma $ is the boundary of a rectangle $\displaystyle R $. Then $\displaystyle \int_{\Gamma} f(z) \ dz = 0 $.

Are we assuming that the rectangle bounds the curve? Or the curve bounds the rectangle?

So the general idea of the proof is that we bisect a rectangle infinitely many times? Because then we have $\displaystyle \int_{\Gamma} f = \sum_{i=1}^{4} \int_{\Gamma_{i}} f $. Then why is it that from some $\displaystyle \Gamma_k, \ 1 \leq k \leq 4 $ we have $\displaystyle \int_{\Gamma^{(1)}} f(z) \ dz \gg I/4 $?