[color=#000000]In the applet below, simply slide the slider very slowly and enjoy the phenomena you witness. [br][br]After doing so, feel free to adjust the [b][color=#38761D]green [/color][/b]and [b][color=#BF9000]yellow[/color][/b] sliders to change the sizes of the [b][color=#38761D]green [/color][/b]and [b][color=#BF9000]yellow[/color][/b] squares, respectively. You can also change the locations of any of the white points. [br][br]Interact with this applet for a few minutes. Then answer the questions that follow. [/color][br][br]
Write the phenomena you've witnessed several times as a conditional ("if-then") statement.
The applet above dynamically illustrates the Finsler-Hadwiger Theorem. [br][url=https://en.wikipedia.org/wiki/Finsler%E2%80%93Hadwiger_theorem]Wikipedia describes it here[/url].
Can you use coordinate geometry to formally prove what this applet informally illustrates? [br](For starters, why not let the common vertex be (0,0) and go from there?)