Tanton Square Challenge

The goal of this applet is to show geometrically, that Below you see a unit square with 4 inscribed squares, each equal to 1/5 the total area. The tan rectangle represents , the blue , and the red rectangle represents
Initially, for values of , the solution is trivial as After crossing this threshold, a blue square, equal to appears, and the problem is to show that the blue square contains enough area to fill in the gaps left by the receding red square (in the lower right square) Finally, when , the solution again becomes trivial because for the remainder of possible lengths of a The "Wrap" Blue area checkbox will rearrange the area of the blue square around the red square to visually illustrate that the area is always greater than 1/5 of the entire area