I’m planning to drive this blog in a slightly different direction. That is, I want to narrow down what I write about here to a few categories that interest me most, instead of shooting off in all directions with no depth in any of them. Of course, I still reserve the right to write about any topic at any time, but…
Anyhoo, the average reader should get what I’m saying.
In that vein, here’s a little bit more math geekery; Euler’s formula. This is not new in any way, or even something that isn’t blogged on often (it is, and by people who are far more knowledgeable, talented, and better at writing about math) and in true blog tradition, I’m swiping it wholesale from someone else. Go there to see a better explanation for all this.
[tex]e^{i\phi} = cos(\phi) + i sin(\phi)[/tex]
Let [tex]\phi = \pi[/tex], and you end up with
[tex]e^{i\pi} = – 1[/tex]
which leads to a striking equation that links together the most commonly used constants in mathematics:
[tex]e^{i\pi} + 1 = 0[/tex]
Interestingly, if you let [tex]\phi = \frac{\pi}{2}[/tex], then you get
[tex]e^{i\frac{\pi}{2}} = i[/tex]
Raising both sides to the power [tex]i[/tex], you get
[tex]e^{-\frac{\pi}{2}} = i^i[/tex]
Which can be calculated as [tex]i^i = 0.2078795763\cdots[/tex]