[Phys-l] old-school scaling

[John Denker <jsd@av8n.com>]

As I've often said:
 -- Scaling arguments are easy to make.  They are appropriate in any physics
  course, from the most introductory level on up.
 -- They are remarkably powerful.
 -- They have been part of modern science since Day One.  Galileo (1638) made
  good use of scaling arguments.
 -- They are still used in cutting-edge work.

People often ask for pedagogical examples.  Well, here's an oldie but a goodie:

Did you know that scaling arguments go back 2300 years, to Euclid (if not
earlier)?

Euclid gave two proofs of the Pythagorean theorem.  The second one not only
proves the theorem, but generalizes it, using a scaling argument.
  http://www.av8n.com/physics/scaling.htm#sec-py

See also Proof #7 at
  http://www.cut-the-knot.org/pythagoras/index.shtml
which is a collection of proofs of the Pythagorean theorem.

I really like this proof, because 
 -- it is easy and well-nigh unforgettable,
 -- it yields an extra-general result, and
 -- the method is transferable to a host of other problems.

(although I rate the "dot product" proof slightly higher, for the same reasons).