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Student Support Forum: 'Surface area of ellipsoid equation' topicStudent Support Forum > General > "Surface area of ellipsoid equation"

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Chris Vinyard
03/25/00 06:21am

I am trying to estimate the surface area of the articular surface of the mandibular condyle (i.e., the jaw joint). I have measurements of condylar width, length and height (i.e. the three axes of an ellipsoid)for the articular surface of the condyle for several individuals. What I would like to do is use these measurements to estimate the surface area of the articular surface. It is my impression that the surface area of an ellipsoid would give the best estimate of the surface area given my dimensional data and the shape of the condyle. Unfortunately for me, the equation for estimating the surface area of an ellipsoid goes beyond my mathematical knowledge. I have written a notebook, that uses the equation provided in the Mathematica 4.0 book, to estimate the surface area of an ellipsoid and attached it below. I wanted to ask someone that is more familar with elliptical integrals whether the formula and output appears to be correct. I would appreciate any advice on how to go about estimating this surface area. Thanks in advance for the assistance.

Notebook:

In[31]:=
a = 3.0


Out[31]=
3.

In[32]:=
b = 2.


Out[32]=
2.

In[33]:=
c = 1.0

Out[33]=
1.

In[34]:=
NIntegrate[
Sin[\[Theta]]\[Sqrt](b^2*c^2*Sin[\[Theta]]^2*Cos[\[Phi]]^2 +
a^2*c^2*Sin[\[Theta]]^2*Sin[\[Phi]]^2 +
a^2*b^2*Cos[\[Theta]]^2), {\[Phi], 0, 2\[Pi]},
   {\[Theta], 0, \[Pi]}]


Out[34]=
48.8822

END;

Once again thanks.

Chris Vinyard

cvinyard@acpub.duke.edu


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