Every triangle has an infinite sequence of sceptres. I call an interlocking pair of equilateral triangles a sceptre. This theorem says there is an infinite sequence of sceptres intimately associated with each triangle. I only show two sceptres here for obvious reasons. As with the infinite hexagon sequence theorem, move a red dot to change the given triangle to an arbitrary one, and slide the green dot along one side of the triangle to change the parameterization. See the paper for details, such as why the word "sceptre" works. See if you can spot the regular hexagons (from the infinite sequence) in this diagram and determine the relationship between them and the sceptres.

Don't give up. This applet takes several minutes to load. It's worth the wait.


Sorry, this page requires a Java-compatible web browser.


This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.