/sci/ - Science & Math

[Anonymous No.2911060]

Hi /sci/.

I was watching a khanacademy video over polynomial approximations for my Calculus II class last night. Sal showed how the functions e^x, sinx, and cosx all have very similar polynomial approximations despite the fact that the expressions come from completely different fields of mathematics. He said that to this day, it is inexplicable why it is so. The fact we discovered sin/cos from the ratios of triangles, e^x from interest over time, and somehow the two mesh together perfectly.
For instance:

e^i(pi) = -1.

The pi comes from the ratio of a circumference of a circle to its diameter, the e comes from continuous compound interest, and i, which is the imaginary number. All of the fundemental numbers of mathematics coming together in one unified, orderly expression.

http://www.khanacademy.org/video/polynomial-approximation-of-functions--part-7?playlist=Calculus
Link.

Thoughts?

[Anonymous No.2911180]

eww, sounds metaphysical.