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Re: [Phys-l] elliptical thinking

On Jul 21, 2008, at 3:53 PM, LaMontagne, Bob wrote:

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.


That would be a convincing argument if an ellipse were defined as a shadow (due to a parallel beam of light) of a tilted circle. That is good enough for me. But a mathematician would probably begin be convincing students that the shape of the boundary of a tilted tilted circle satisfies the ellipse definition--the sum of distances from two focal points being constant everywhere on the boundary.

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/