Square - ness of Rectangles - revisited

If you drag the ORANGE dot you can produce different rectangles. Devise a measure of 'Squareness' that allows you to arrange any collection of rectangles in order of 'Squareness'. How many such measures can you devise? Which of these measures do you prefer? Under what circumstances? Under what circumstances does the average of two different measures of squareness lie between the two individual measures of squareness? What questions could / would you ask your students based on this applet?