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Triangle in an ellipse



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Yah, you got it.
Here's basically just a different wording:
The largest triangle inscribed in a circle is an equilateral triangle.
For a unit circle (area = pi) an inscribed equilateral triangle has area (3/4) sqrt(3) = 1.299038....

If we scale y by f and scale x by 1/f  areas are preserved.
For f=2, a unit circle becomes an ellipse whose axes are 1 and 4 (area = pi).

So the largest triangle inscribed in that ellipse has area (3/4) sqrt(3).


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