Delta Curve

A curve which can be turned continuously inside an Equilateral Triangle. There are an infinite number of delta curves, but the simplest are the Circle and lens-shaped $\Delta$-biangle. All the $\Delta$ curves of height $h$ have the same Perimeter $2\pi h/3$. Also, at each position of a $\Delta$ curve turning in an Equilateral Triangle, the perpendiculars to the sides at the points of contact are Concurrent at the instantaneous center of rotation.

See also Reuleaux Triangle

References

Honsberger, R. Mathematical Gems I. Washington, DC: Math. Assoc. Amer., pp. 56-59, 1973.