Why Does Pi Equal 180 Degrees and 2 Pi Equal 360 Degrees?

[Curious3141]

I think your method is fair, as it doesn't use the numerical expression for pi - rather it just uses relationships between [the ratio of a circle's circumference and diameter] and right triangles. (The former of which happens to be pi).

If OP wants a numerical expression for pi - one that generates it - perhaps an infinite series is what OP wants (although I feel from the responses that OP may be missing some of the prerequisite material, but perhaps it's just a language barrier).

How about something like this:

\pi = 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9})

I don't know the derivation though unfortunately.

Perhaps you meant this: \pi = 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - ...)

That ellipsis ('...') is all important.

Alternatively, you could've stated: \pi \approx 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9}), but the approximation is really quite mediocre with so few terms.

 

[middleCmusic]

Perhaps you meant this: \pi = 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - ...)

That ellipsis ('...') is all important.

Alternatively, you could've stated: \pi \approx 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9}), but the approximation is really quite mediocre with so few terms.

Oops! What an embarrassing mistake on my part. Fixed my post.

 

[micromass]

We have asked the OP repeatedly to clarify his ideas. He never clearly answered. And now he seems to be gone from this thread. Time to lock.