What (not-often-seen and not-well-known) theorem is dynamically being illustrated in the applet below? (Feel free to move the [b]BIG POINTS[/b] around at any time during the animation!)
[b]Theorem:[/b][br][br]Suppose [color=#ff7700][b]equilateral triangles[/b][/color] are constructed off all 6 sides of a hexagon (convex or concave -- doesn't matter.) Then the midpoints of the segments that connect the centroids of [b][color=#ff7700]equilateral triangles built on pairs of opposite sides[/color][/b] of the hexagon (there are 3 such points) [color=#ff00ff][b]will yet ALWAYS form vertices of another equilateral triangle! [/b][/color] [br][br]([b]Source:[/b] This [url=https://twitter.com/pickover/status/762357785120088064]tweet[/url] from [url=https://twitter.com/pickover]Cliff Pickover[/url])