one-third area of circle with vertical cut line.

John E. Franklin · 2011-10-21 12:31:22

I wrote a BASIC program to avoid using calculus to
get an estimate on the following statement I got:

To cut a circle's area into 2/3's and 1/3 parts, simply
cut along a vertical line that is 63.25% (approx)
along the diameter in the x direction.

Here is an equation that might help someone to
check my answer with any method, calculus, etc...

(y+0.265)^2 + x^2 = 1
The above equation drops the circle down so you can
do a definite integral on the positive portion and ignore
the negative margin areas below.
The 0.265 is a measure on the radius of 26.5% that
I dropped the circle in my BASIC program.
The actual value ofcourse is not 0.265, but something
a little different but close by this value.

If someone wants to check my 63.25% on the diameter
answer, which is 1.265/2, where 2 is the diameter, then
that would be fun to see, but if you are too busy, don't
worry about it.

Have a beautiful day!! Bye now.

TheDude · 2011-10-21 15:11:48

Picture a unit circle centered on the origin being sliced with the horizontal line y = c. The area contained between the top portion of the circle and the line is

The full area of the circle is pi, so we want to leave pi/3 after the slice:

This turns out to be 0.262 above the origin, or 1.262/2 = 63.1%. So your program got pretty close.

John E. Franklin · 2011-10-22 00:56:26

Merci beaucoup, mon ami!!!! J'adore the answer, pi div 12 from center with a radius=1. Love it, love it, love it!! Thanks a lot!!!!

How come you didnt have to find the zeros on the x-axis and do the definite integral between the zeros?
My calculus is 25 years old and I haven't used it since much.
_________________________________________
Eat lots of tomatos

TheDude · 2011-10-22 02:28:36

Well, umm, you see, the answer is that you do have to, and my solution is wrong. I have what should be the correct expression now, but I'm not sure how to solve it. Here's what I have so far. Instead of integrating from -1 to 1, you have to integrate between where the circle intersects y = c.

Again we set this to pi/3:

I'm not sure where to go with it from here.

bobbym · 2011-10-22 05:01:00

Hi;

That equation can be solved numerically through iteration:

Math Is Fun Forum

#1 2011-10-21 12:31:22

one-third area of circle with vertical cut line.

#2 2011-10-21 15:11:48

Re: one-third area of circle with vertical cut line.

#3 2011-10-22 00:56:26

Re: one-third area of circle with vertical cut line.

#4 2011-10-22 02:28:36

Re: one-third area of circle with vertical cut line.

#5 2011-10-22 05:01:00

Re: one-third area of circle with vertical cut line.

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