cut a circle in half not through middle

We can also cut a circle with radius R in half by removing a circular area with a radius = R/√2 from within the circle...

To prove this, we have

pi*R^2 - pi*r^2 = (1/2)*pi*R^2   ......where r is the radius we're looking for........so.......

(1/2)pi*R^2 = pi*r^2   divide both sides by pi

(1/2)R^2 = r^2   take the positive root of both sides

r = (1/√2)R = R/√2

Note that......as long as the circular area removed lies totally witin the circle, it doesn't have to be concentric with the larger circle!!!

I don't understand what you are trying to say.

If you don't use a straight line, there will be an infinite number of ways to divide a circle into two parts, where each part has the same area as the other.

The yin-yang picture is one.

are you trying to say there are $${\mathtt{\infty}} = \infty$$ possibilities to make a circle into $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ ? oh, i knew that. :)

-Robert

I really like Gino's and Chris's logic.  Thanks guys  

Geno had logic out the ying-yang....me???....I was just throwing something against the wall and hoping that some part of it would stick !!!!