Historical reconstruction of Archytas' proof
Initial disposition of Archytas' construction, including the sphere. You can achieve the final disposition following the instructions below. The final disposition is achieved when A, M, K are aligned. The diagram will show also the trace of point K.
How to manipulate left and right panels:
- On the left panel there is the three-dimensional canvas, with the initial disposition of Archytas' construction with the sphere and the Archytas' triangle ΑΜΔ.
- On the right panel, there is a plane canvas with the same Archytas' triangle ΑΜΔ.
- At the top there are some bars for each panel.
- With the right button of the mouse, you can rotate the three-dimensional canvas to change the point of view: while clicking on the canvas, move the mouse to change the point of view.
- You can select the point Δ with the left button of the mouse on the three-dimensional panel and move it along the semicircle of diameter ΑΔ, to find the correct disposition of elements to achieve Archytas' solution. NB: To move the point Δ, it must be selected the arrow in the top menu.
- After clicking in one panel, you can Zoom In (Ctrl+) or Zoom out (Ctrl-) in the panel.
- The three-dimensional canvas can have a uniform rotation from its center by clicking the play button surrounded by a circular arrow on the second bar of the left panel.