Richard Guy wrote:

>See also Martin Gardner's article on the Asymmetric Propellor,

>somewhere in this year's Coll. Math. J. R.

The Asymmetric Propeller

Martin Gardner

A theorem, seventy years old at least and of unknown origin,

says that if three congruent equilateral triangles are have

corners meeting, the midpoints of the lines joining the other

two vertices of the triangles are vertices of an equilateral

triangle. The late Leon Bankoff discovered that the triangles

don't have be congruent and don't have to meet at a point.

Martin Gardner describes the results, and conjectures that the

triangles don't have to be triangular--squares seem to work

as well.

The College Mathematics Journal, January 1999.

Antreas