From Archytas' simple triangle to Archytas' solution (II)
This interactive diagram shows a simple way to obtain Archytas' solution from Archytas' triangle: given , , to find two mean proportionals of , starting with Archytas' triangle with AM = and ΑΔ = (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 AMK are aligned.
When moving K around the semicircle (or I along the diameter), you will see that IK is perpendicular to ΑΔ, a new circumference of diameter AI is buid and M is found intersecting the semicircle with a circle of centre A and radius .
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.