In a golden triangle, i.e. an isosceles triangle whose ratio side/base is [math]\phi[/math], and having angles of 36°, 72°, 72°, subtracting a golden gnomon - that is an isosceles triangle having sides equal to the golden ratio of the longest triangle side - you obtain a golden triangle.[br][br]Therefore it is possible to decompose the given triangle into an infinite sequence of triangles having the same property, fixing a direction and determining the intersection of the base angle bisector with the opposite side of each triangle.[br][br]Drawing circumference arcs having 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.