Ok, we've been discussing the square dissection problem for a few days now. The original problem was here and Solution Method I was here.
Now don't start laughing at these crude, low-tech videos! The 1st video is 2-3 minutes long. It provides a quick overview of the squares problem and a demonstration of why the product of the areas is the same for either pair of non-adjacent rectangles. It ends abruptly with part of the derivation I gave in the previous post.
The remaining presentation is split into 3 segments in order to control the file size (Blogger has a problem with larger files). In these segments, I derive a formula for the maximum product using the Arithmetic-Geometric Mean Inequality (AM-GM) and apply it to the square dissection problem. The first of these clips reviews this important and useful inequality, presenting a standard algebraic derivation. The 2nd of these 3 clips presents a geometric derivation and the final clip shows how we can derive a formula, m4/16, for the maximum possible product of the areas in the general case of a square of side length m.
As I say on the video, there's no SmartBoard technology, no Mimio, no whiteboard with vivid color dry erase markers! Just an old chalkboard my kids use in the basement, some inexpensive chalk and sheets of paper towel to erase. I wore my favorite 'Pop-Pop' sweatshirt - sorry, no formal wear.
Let me know if you find this helpful (once you stop chuckling!). At least you'll be able to match a name to a face and it isn't Archimedes! If I get few if any comments, I'll know that my 15 minutes of fame have expired.