[color=#0000ff]Creation of the following applet was inspired by a [url=https://twitter.com/pickover/status/725694306162372608]tweet[/url] from [url=https://twitter.com/pickover]Cliff Pickover[/url]: [/color][br][color=#980000][b]Problem: [/b][/color][color=#000000] [br][br]Given that [/color][b][color=#7f6000][i]ABCD[/i] is a square, [/color][/b][color=#000000]the measure of angle [/color][i]EAF[/i][color=#000000] = 45 degrees, [/color][color=#ff00ff][i]BE[/i] = [i]a[/i][/color][color=#000000], and [/color][color=#1e84cc][i]DF[/i] = [i]b[/i][/color][color=#000000], [br]prove that x = [/color][color=#ff00ff]a [/color][color=#000000]+ [/color][color=#1e84cc]b[/color][color=#000000]. [br][br]In this applet, feel free to move [/color][b]point [i]E[/i][/b][color=#000000] around anywhere you'd like! You can also move the white vertices at the bottom, although all this will do is change the side length of the square. [br][br]Can you formally prove what this applet informally illustrates? [/color]