We have already looked at the deltoid as a type of three-pointed ornamental star. As usual, to find the evolute, we take the envelope of the normals drawn at points of the curve.

Click on the diagram below to open the applet, and then click on the ‘Animate’ button to generate the evolute of the deltoid. Clicking the little red x at bottom right will clear the drawing from the applet window. Now drag the red point Q once slowly around the circle. Can you describe the evolute construction? Is this a curve we have seen before?