This movie displays the values of w and the area of the N-shape, as w changes.
Can you spot when the area is a mimimum? You might want to PAUSE the movie at various points, since the numbers change so rapidly (or use the arrow keys or the JAVA-N worksheet to show it frame-by-frame).

The range of values taken by the area is larger than for the M-shape but still fairly small, and we have again measured the area to several (4) decimal places. The minimum area (of 0.875) is easier to spot this time: it occurs when w = 0.25, so the question, "Roughly what fraction (of 1) is this?", is more obvious than for the M-shape.

It might be worth drawing examples of the N-shape on squared paper, using a multiple of 4 units, rather than a length of 1, for the sides of the bounding square. This again results in friendlier numbers.

On the next two pages we go through the same procedure with the T-shape. If you prefer, you might want to skip to the P-shape pages, which introduce a more analytic approach.