4
$\begingroup$

I think this is a bug

Area @ Ellipsoid[{0, 0, 0}, {1, 2, 3}]

returns Infinity in Mathematica 11.

Is there a way I can compute the surface area of an ellipsoid in Mathematica?

$\endgroup$
2
  • 4
    $\begingroup$ 1. This is not a question, and as such not fit for a QA site (unless you rephrase appropriately). 2. Please do not use the bugs tag when posting new question. This is in the tag description. 3. Reporting bugs is good, but they must be reported to Wolfram directly. This is not a Wolfram site. $\endgroup$
    – Szabolcs
    Aug 28 '17 at 16:39
  • $\begingroup$ @Szabolcs Sorry, actually I wanted a way to compute the surface area, a workaround. I'll edit. $\endgroup$
    – becko
    Aug 28 '17 at 18:30
19
$\begingroup$

In the documentation of Area:

The area of a region of dimension three or higher is $\infty$:

For the surface area you can do:

Area @ RegionBoundary @ Ellipsoid[{0, 0, 0}, {1, 2, 3}]

π (2 + 8 Sqrt[2] EllipticE[ArcCos[1/3], 27/32] + Sqrt[2] EllipticF[ArcCos[1/3], 27/32])

$\endgroup$
4
  • $\begingroup$ Also, the "Properties & Relations" section of the documentation for Area states "To get the surface area of a 3D region, use RegionBoundary" $\endgroup$
    – Bob Hanlon
    Aug 28 '17 at 17:50
  • 1
    $\begingroup$ However, Area@Sphere[{0, 0, 0}, 1] gives the correct surface area. Seems inconsistent, @BobHanlon. $\endgroup$
    – becko
    Aug 28 '17 at 18:31
  • 10
    $\begingroup$ @becko That's because RegionDimension[Sphere[{0, 0, 0}, 1]] is 2, not 3. Ball is the equivalent of Ellipsoid. $\endgroup$
    – Carl Woll
    Aug 28 '17 at 18:46
  • $\begingroup$ @CarlWoll Oh, I see. $\endgroup$
    – becko
    Aug 28 '17 at 20:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.