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Re: [Phys-l] elliptical thinking



A have now read John's piece (clicking on his first link). Would a math teacher call this a proof or an observation? Yes, the upper limit for S is 4*a*b, while the lower is 2*a*b. By why is 2 or 4 must be replaced by pi? How do we know that what is true for a circle must also be true for an ellipse?
Ludwik

On Jul 21, 2008, at 2:46 PM, John Denker wrote:

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:
http://www.av8n.com/physics/scaling.htm#sec-ellipse

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 also makes contact with our recent discussions of "new math"
and its relation to "old math":
http://www.av8n.com/physics/thinking.htm#sec-algo

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

Ludwik Kowalski, a retired physics teacher
5 Horizon Road, Apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/