Josef Kurschak constructed a beautiful tile that constructs a dodecagon that makes several interesting observations possible. (See this sketch for that construction: [url]http://www.geogebratube.org/material/show/id/49694[/url])
In that sketch he inscribes four equilateral triangles in a tile. Well one of the things mathematicians love to ask is "What If?" What if it wasn't an equilateral triangle?
This sketch lets you see isosceles or right triangles (in the constrained option) or totally free exploration.
