The Golden Ratio: Phi = 1.618 or .618

Golden Ratio: "We can also form a Golden Ellipse. This ellipse has its two axes in the Golden Ratio.


Let's turn back to one of the Golden Triangles for a moment. If we take the isoceles triangle that has the two base angles of 72 degrees and we bisect one of the base angles, we should see that we get another Golden triangle that is similar to the first (Figure 1). If we continue in this fashion we should get a set of Whirling Triangles (Figure 2).


Figure 1 Figure 2
Out of these Whirling Triangles, we are able to draw a logarithmic spiral that will converge at the intersection of the the two blue lines in Figure 3.


Figure 3
We can do a similar thing with the Golden Rectangle. We can make a set of Whirling Rectangles that produces a similar logarithmic spiral. Again this spiral converges at the intersection of the two blue lines, and these ratio of the lengths of these two lines is in the Golden Ratio. "