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: phys-l-bounces@carnot.physics.buffalo.edu 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 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. http://www.av8n.com/physics/thinking.htm#sec-derive
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
Phys-l@carnot.physics.buffalo.edu https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l