In a golden triangle (an isosceles triangle where the ratio of the side to the base equals the golden ratio [math]\varphi[/math], and whose angles measure 36°-72°-72°), removing a golden gnomon (an isosceles triangle whose side lengths are in the golden ratio relative to the longest side of the original triangle) results in another golden triangle.[br][br]These steps can be repeated over and over, decomposing the original triangle into an infinite sequence of similar golden triangles, by fixing a direction and determining the intersection of the base angle bisector with the opposite side at each step.[br][br]By drawing circular arcs with an angular width equal to the vertex angle of the gnomon, 108°, you obtain a golden logarithmic spiral.

This applet demonstrates the Fibonacci Squares and the Fibonacci Spiral without going through all construction steps. It is a variation of the constructing applet. [url]http://www.geogebratube.org/material/show/id/6095[/url][br]Click the Play button.

To do a hands-on construction, open [url]http://www.geogebratube.org/material/show/id/6095[/url] and follow the steps.