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Are there two non-isomorphic ellipses with the same area and circumference? Difficult question...

Mathematics
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|dw:1349851817988:dw| the area of ellipse is easily calculated. the problem is the circumference of ellipse.
all math questions are difficult questions...
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two equations, two unknowns, I don't think you will find more than one solutions for positive value of a and b.
Yes, very awkward. The area is easy, u can imagine half-axes like 2,3 or 1,6 to give same area. But then the circumference varies as 4aE where e varies as to the eccentricity sqrt(1- (a^2/b^2)). Which using the above figures 8*sqrt(5/9) or 4 *sqrt(35/36) so u would need to find some a,b combination that would make these 2 expressions be equal.

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