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We've just started this today in first year applied maths at university. Today we were given the problem of deriving the formula for the area of an ellipse. I've got as far as saying there's some relationship between the semi-major axis and the semi-minor axis on the one hand, and the area of the ellipse on the other, but now I'm stuck.

I do not want a direct answer to the problem. I'm looking for a good online tutorial for these sorts of problems that might get me thinking in the right way. I've tried doing a search myself, but keep getting stuff on performing conversions. Can anyone point me to a good source for my purposes?

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Dimensional analysis? – Aryabhata Feb 25 '11 at 16:37
up vote 3 down vote accepted

There is an MIT OCW course and textbook called Street-Fighting Mathematics by Mahajan which discusses dimensional analysis among other things that you might find useful. For this problem the key observation is to think about what happens to an ellipse when you stretch or shrink along either axis. (Hint: you get another ellipse. What is the relationship between their areas? Between their semimajor / semiminor axes?)

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Aaah, I see, they do have a certain relationship. And there is a special kind of ellipse where they are the same :D Thanks a bunch, that was exactly what I was looking for! – Katherine Rix Feb 26 '11 at 14:25

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