+0

# cut a circle in half not through middle

+3
319
6

cut a circle in half not through middle

Guest Oct 26, 2014

#4
+85677
+13

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!!!

CPhill  Oct 26, 2014
Sort:

#1
+5

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

Guest Oct 26, 2014
#2
+17721
+8

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.

geno3141  Oct 26, 2014
#3
+3

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

Guest Oct 26, 2014
#4
+85677
+13

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!!!

CPhill  Oct 26, 2014
#5
+92206
+5

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

Melody  Oct 27, 2014
#6
+85677
+5

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 !!!!

CPhill  Oct 27, 2014

### 17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details