#
The Expected Solution

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

**[Derive_Phi_Graphically]**

## 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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