boost97gst
10+ Year Contributor
- 3,034
- 137
- Apr 2, 2012
-
st jacob,
Illinois
What they have the same is their perimeter or circumference. That is what doesn't change as you distort it from circular to ellipitcal or any other shape.
If you have a circle of some perimeter, and any ellipse with the same perimeter, the area of the ellipse will always be smaller than the area of the circle with same perimeter.
You could spend a good couple hours proving this to yourself with formulas. Because, unfortunately, the formula for perimeter of an ellipse is not a simple one.
Perimeter of Ellipse
So basically, you can start out with numbers for the a and b dimensions of an ellipse, any ellipse you want. Calculate the perimeter of that ellipse. Then go find a formula for calculating the area of an ellipse (same web site has it) and calculate the area of your ellipse.
Now take your perimeter number and figure out how big a circle you would have with that perimeter. Get the area of that circle.
Now you have the area comparison.
Do this as many times as you want, with different ellipses.
Take coffee breaks as needed
Gotcha bud. Thank you
