Tuesday, June 2, 2009
As we all know, the area of circle is PiR2.But what about the formula for area of an Ellipse?
Consider the picture shown on the right, where A and B are
semi-major axis of the large and small diameter of the ellipse respectively.
A standard equation for such an ellipse centered at origin:(x2/A2) + (y2/B2) = 1.
The area of ellipse is PiAB , so similar to that of circle!
Facts behind it
The above diagram can be seen as a unit circle that has been stretched by a factor A in the x-direction, and a factor B in the y-direction. Hence the area of the ellipse is just AB times the area of the unit circle.
However, the perimeter of an ellipse is not at all generalize with that of a circle. :)
The area of ellipse is PiAB , so similar to that of circle!
Facts behind it
The above diagram can be seen as a unit circle that has been stretched by a factor A in the x-direction, and a factor B in the y-direction. Hence the area of the ellipse is just AB times the area of the unit circle.
However, the perimeter of an ellipse is not at all generalize with that of a circle. :)
Su, Francis E., et al. "Area of an Ellipse." Mudd Math Fun Facts. .
Xiao Yuting
Wan Tian Chong
