A golden triangle is an isosceles triangle in which the ratio of one of the equal sides to the base is the golden ratio, that is, . The angle at the vertex of the golden triangle is .
In this applet we start with an isosceles triangle whose equal sides have length and the base is equal to . The angles at the base are .

Click the checkbox to show the first golden triangle.

Next, we generate a sequence of smaller embedded golden triangles. This sequence is constructed by rotating the previous triangle on or and rescaling it with factor .

Click the Construction ON/OFF button or drag the slider.

Using the construction below, we can evaluate the series
, the series and also the series
This applet is based on the note Proof Without Words: An Infinite Series Using Golden Triangles by Steven Edwards, The College Mathematics Journal Vol. 45, No. 2 (March 2014), p. 120.