This is what makes mathematics so damn fascinating. The Basel problem is another example: for any small number you pick I can pick a large enough N that sum(1/n^2) from 1 to N will be closer to pi^2/6 that that small number. That boggles the mind, really. I mean, I just use multiplication, inversion and addition a lot on integer numbers in a rather predictable fashion and get to ... pi^2/6?? There's a huge "why" / "how come" here.
Perhaps one would think that "pi" is this geometry thing ... but then maybe not :) And again, there's \lim_{n\to\infty} 2^n \sqrt{2-\sqrt{2+... \sqrt 2}} = \pi as well which is perhaps even more baffling.
Peter Rozsa most excellent book, "Playing with Infinity" has a chapter "Mathematics is one". There's no such parts of maths as geometry and calculus separately. That book is perhaps the best maths book for people with ... less affinity towards maths, I guess.
Perhaps one would think that "pi" is this geometry thing ... but then maybe not :) And again, there's \lim_{n\to\infty} 2^n \sqrt{2-\sqrt{2+... \sqrt 2}} = \pi as well which is perhaps even more baffling.
Peter Rozsa most excellent book, "Playing with Infinity" has a chapter "Mathematics is one". There's no such parts of maths as geometry and calculus separately. That book is perhaps the best maths book for people with ... less affinity towards maths, I guess.