Deltoid curve

In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three or one-and-a-half times its radius. It is named after the Greek letter delta which it resembles. In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three or one-and-a-half times its radius. It is named after the Greek letter delta 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. A deltoid can be represented (up to rotation and translation) by the following parametric equations where a is the radius of the rolling circle, b is the radius of the circle within which the aforementioned circle is rolling. (In the illustration above b = 3a.)