marshall wrote:
Tollorin wrote:
swbluto wrote:
Callista wrote:
I love math. When I say an equation or a proof is "beautiful", I mean it.
This, especially:
e^(i*pi) + 1 = 0
If you don't get it, try assuming that the exponential is polar coordinates for a complex number...
Beautiful, right?

I'm not a mathematician and probably never will be. It's just a hobby. But I love the pure logic of it.
Oddly enough, I sucked at arithmetic to the point that I didn't know the multiplication table until high school.
That is pretty cool. Have you seen this?
e^(i*pi) = -1
and so
e^(i*pi) = i^2
Kind of weird! Do you know what it *means*? It's so elegant and yet so odd how mixing two irrational numbers with a self-defined imaginary number would result in this weird equality that must geometrically mean something.
I wish I knew enough to understand that...
I think of complex numbers as two dimensional vectors with a neat multiplication property that works out such that the angles relative to the positive real axis add together while the lengths are multiplied.
Complex numbers are fascinating. It's really a shame they barely cover them in school. From an addition stand point, complex numbers can be viewed as an extension to real numbers by adding the imaginary axis. However, from a multiplication standpoint, they can be viewed as an extension to the
positive numbers by adding argument. You see, multiplication behaves the same way over the positive numbers as addition does over the real numbers (if you need an explanation on how, I'll give it to you), and multiplication over complex number is really just a way to extend multiplication to negative numbers in a way that makes sense, is closed, and is also easy to add across. Complex numbers are remarkable.