Square - ness of Rectangles
None of these rectangles is square !
They are arranged in columns from left to right in order of width.
They are also arranged in rows from bottom to top in order of height.
Can you devise a single measure of 'Square-ness' to answer the following -
a. Which rectangle is the "squarest"?
b. Arrange the rectangles in order of square-ness.
c. What is the difference in "square-ness" between the
most square and the least square of the rectangles?
d. Does your measure of "square-ness" have a smallest
value? a largest value? a "special" value when the
rectangle is a square?
e. Devise a different measure of "square-ness" and
discuss the circumstances in which each of your
measures would be the better measure.
[You can position a rectangle by dragging it.
You can rotate a rectangle by dragging the white dot at one of its vertices.]
What questions could / would you put to your students based on this applet?