Another 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 I is in the perpendicular from Κ to ΑΔ. 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.