Star, Six Pentagons and Golden Ratio
The following has been posted by Tran Quang Hung at the CutTheKnotMath facebook page.
Reflect a regular pentagon $ABCDE\,$ in each of its sides. Join the vertices of the so obtained pentagons skipping two at a time.
The resulting star cuts the sides of the pentagon $ABCDE\,$ in the Golden Ratio.
The diagram hides additional secrets that can be gleaned from the applet below:
In particular, there are additional occurences of the Golden Ratio. To discover them, you'll need to two or three boxes checked up.