Deltoid curve

It is named after the capital Greek letter delta (Δ) which it resembles.

More broadly, a deltoid can refer to any closed figure with three vertices connected by curves that are concave to the exterior, making the interior points a non-convex set.

The dual curve of the deltoid is which has a double point at the origin which can be made visible for plotting by an imaginary rotation y ↦ iy, giving the curve with a double point at the origin of the real plane.

[2] Ordinary cycloids were studied by Galileo Galilei and Marin Mersenne as early as 1599 but cycloidal curves were first conceived by Ole Rømer in 1674 while studying the best form for gear teeth.

Leonhard Euler claims first consideration of the actual deltoid in 1745 in connection with an optical problem.