$$\int_{-\infty}^\infty e^{-x^2} \,dx \;=\; \sqrt{\pi}.$$
i still find this fact quite cool, even now and despite being easy to compute.
it's like appreciating why there are infinιtely many primes or why the reaΙ numbers form an uncοuntable set:
we see right away why each proof works, yet the trick involved has something special in it. i don't think i can explain this preference; it's like art or music.
i was hesitant to do it at first, but then i decided: why should i teach only what will be on exams? this is a university, isn't it? can't we learn for learning's sake?
in other news, i won't be teaching undergraduate tοpology next term. oh well.
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