I'm really not a π day hater, but I do roll my eyes when I read articles exclaiming π "goes on forever!" as if that is a rare and notable property that makes it unique among numbers. I mean, 1/3 "goes on forever" too.
Indeed, this approach also provides the most natural elementary explanation of Euler's answer to the Basel problem -- that is, to why the sum of the reciprocal squares is [(pi)^2]/6.
-
-
This is the log-derivative of the product formula for the sine, right? Which is connected to both the Basel problem and the Wallis product. (Basel, Wallis, and Leibniz united under one formula, woot)
-
Yeah. And the key here is that Eisenstein unites all these threads by stressing periodicity, which he enforces via what is now called "averaging over the group" (in this case, the additive group of the integers.) Hard to exaggerate how far these ideas reach.
- 4 more replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.