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Hi Folks --
What's the formula for the area of an ellipse?
More interesting question: How do you know?
-- Do you remember the formula from high-school geometry?
-- Did you look it up just now?
-- Or do you have some other way of knowing?
I recently wrote up my notes on one way of figuring it out:
I like this way because
a) It illustrates a particular type of scaling argument that is
super-easy but often under-emphasized.
b) It serves as a good excuse for a riff on "figuring things out"
in general, and its relationship to memorization.
This also makes contact with our recent discussions of "new math"
and its relation to "old math":
This issue is commonly referred to as the “Math Wars” but I don’t
like to use that term. The warlike aspects are a discredit to
everyone involved. The sensible approach is to use smart, efficient
algorithms *and* to understand the principles involved.