Geometric Visualization of a Cube Root

Notes:

The orange path forms right angles when it intersects with the axes.
x cubed = a; or the cube root of a = x
- Proof: By the laws of right triangles: (a)(x) = b squared, and (1)(b) = x squared, so (a)(x) = (x)^4 or a = x^3.
If given x, one can determine a using compass and unmarked straight-edge construction, However, if given a, one cannot, in general, determine x, using compass and unmarked straight-edge construction.
If you mouse click and release anywhere on this Applet, then hit "return" a new frame will appear that can be expanded and moved around.
The code for this Applet is based upon David Joyce's Geometry Applet