The Expected Solution

One solution giives Phi = 1.618...

[y_=_x_+_1] [y_=_x_*_x] [Phi_=_1.618...] [Phi_=_-0.618?]


Phi = 1.618...

This was the answer we expected to find, since we already know this is the approximate value of phi from the Fibonacci Series earlier.

Naturally enough, if you consider the rectangle formed by the yellow lines, the x axis, and the y axis, you'll see it's a Golden Rectangle with sides of phi (horizontally) and both phi * phi and phi + 1 (vertically).

But it's not the only one. Where the green line crosses the y axis it reveals the next smaller rectangle, with sides of 1 and phi.

Then, the red line shows yet the next smaller rectangle. What are the lengths of its sides?

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