Mathematics, not my cup of tea.

January 29, 2007

After watching last night's 60 minutes episode, I thought I'd brush up on some collegiate mathematics.
I wiki-ed Pi and along came all these other formulas.
Just going through them one by one, is giving me a massive headache and I'm about to give up.
Nothing makes sense and I'm starting to feel anger set in.

The area of the unit disc:

$2\int_{-1}^1 \sqrt{1-x^2}\,dx = \pi$

Half the circumference of the unit circle:

$\int_{-1}^1\frac{dx}{\sqrt{1-x^2}} = \pi$

François Viète, 1593 (proof):

$\frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots = \frac2\pi$

Wallis product, 1655 (proof):

$\prod_{n=1}^{\infty} \left ( \frac{n+1}{n} \right )^{(-1)^{n-1}} = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots = \frac{\pi}{2}$