Length of an Arc of an Ellipse and the Area It Subtends

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This Demonstration computes the length of an arc of an ellipse and the area that the arc subtends. Let the semimajor and semiminor axes of the ellipse be and
. The total length (the circumference) is given by
, where
is the complete elliptic integral of the second kind. If
(the ellipse is a circle), the circumference is
. The total area is
.
Contributed by: Jaime Rangel-Mondragon (September 2013)
Open content licensed under CC BY-NC-SA
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"Length of an Arc of an Ellipse and the Area It Subtends"
http://demonstrations.wolfram.com/LengthOfAnArcOfAnEllipseAndTheAreaItSubtends/
Wolfram Demonstrations Project
Published: September 6 2013