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Re: [Phys-l] elliptical thinking

Area of a circle is pi*r^2.

Tilt circle away from you by angle theta and projected area is pi*r^2 cos(theta), but r cos(theta) is same as the a for the observed projected ellipse - therefore pi*a*r = pi*a*b.

Bob at PC


From: on behalf of John Denker
Sent: Mon 7/21/2008 2:46 PM
To: Forum for Physics Educators
Subject: [Phys-l] elliptical thinking

Hi Folks --

Quick question:

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.
Forum for Physics Educators