The Reuleaux Triangle is a curve of constant width formed by the intersection of three circles, with each vertex lying on one of their centers.
Drag point A to move the triangle, point B to rotate it around circle A, and the slider to adjust the triangle's width.

Try moving points D, E, and F. Watch what happens to their distance from the opposite vertex. Does it change? What does this number represent?
Why is the base triangle always equilateral? Is there any way to change that?
What would happen if a cardboard version of this shape were placed under a board? Would it roll like a circle, or more like a triangle? Could this shape be used as a wheel?