Golden Ratio - Flowers
Ben Sparks made the excellent Numberphile video (above) with a similar applet to the one below. I made a new version that lets the user change more parameters than Ben's applet does.
quarter of square
GeoGebra Within OneNote: How to EMBED GeoGebra Applets and Constructions
Parallel Lines w/Transversal
Properties of Tangents (CO)