Re: [Phys-L] Fictitious Mathalon.

[John Denker <jsd@av8n.com>]

On 7/6/22 4:10 AM, David Bowman wrote:

> But regardless of Kepler's methods one can easily find the area of an
> ellipse without calculus by a simple application of one dimensional
> scale factors.

^^^ This! ^^^



Students might find this less than obvious, insofar as
it involves scaling one direction and not another, which
is different from the classic zoom-in / zoom-out scaling.

Even so, it is a totally legit scaling argument.

If anybody disagrees, ask them what is their most basic
fundamental definition of /area/. Or approximate the
area by counting squares on graph paper. Then replace
it with /rectangles/ on graph paper. We know area of
rectangles.

A diagram is here:
  https://www.av8n.com/physics/scaling.htm#sec-ellipse

My advice: Think about scaling laws until this example
becomes obvious.

==================

Scaling arguments are reeeeally important. They have
been fundamental to modern physics since Day One
(Galileo) and remain so today.

They are simpler, more powerful, and more age-appropriate
than a lot of stuff that is covered typical introductory
courses.