The WM Function

As if the world needed another trigonometric function, I give it the WM function, named after the letters apparent in its graph. It is the sine of the sine of x, times 2π, if x is measured in radians, as in the graph below.

WM function

Trigonometric Stained-Glass Windows

trigart

To make the virtual “painting” above, I plotted simple and moderately-complex trigonometric functions on a single coordinate plane, as shown below, using Geometer’s Sketchpad. I then erased all the text, etc., copied-and-pasted a screenshot into MS-Paint, and used that program to make the finished image above.

trigartexpl

A Rhombic Enneacontahedron, Augmented with Sixty Rhombic Dodecahedra, Along with Its Dual

REC augmented with 60 RDs

The dual to this cluster-polyhedron appears below. Both virtual models were created using Stella 4d: Polyhedron Navigator, software available here.

REC augmented with 60 RDs -- its amazing dual