From Archytas' simple triangle to Archytas' solution (I)

This interactive diagram shows a simple way to obtain Archytas' solution from Archytas' triangle, i.e. given [math]a, b[/math], [math]a>b[/math], to find two mean proportionals of [math]a, b[/math], starting with Archytas' triangle with AM = [math]b[/math] and ΑΔ = [math]a[/math] (shown in the figure). Selecting K with the left button of the mouse, and moving it around the circumference, you can achieve Archytas' solution, when I and I' coincide. To clean the canvas and get the initial configuration displayed, click on the button with two circular arrows in the right upper corner of the canvas.