Pi as a circle's circumference integrated using two points and a right triangle

[ewmon]

I got to thinking about this from two recent threads on the nature of pi.

 

We're all familiar with scribing a semi-circle using two points (A and C) and a right triangle, shown below.

 

 

How then would the distance along the circumference of the semi-circle be computed using integration? Can it be done without using trigonometry, or is trig inherently part of the process?

 

Pi would then be the ratio of the semi-circle's circumference to ½ of AC.

 

I apologize for not thinking this out myself, but I haven't focused in this mathematical direction in quite some time.

[ADreamIveDreamt]

 

Use my Design as it is easier to Understand.

A=PI3

Edited August 26, 2013 by ADreamIveDreamt