+128473 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!!!
+23246 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
+128473 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!!!
