A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem.
It was also investigated by Steiner in 1856 and is sometimes called Steiner's hypocycloid
(Lockwood 1967; Coxeter and Greitzer 1967, p. 44; MacTutor). The equation of
the deltoid is obtained by setting in the equation of the hypocycloid,
where is the radius
of the large fixed circle and is the radius of the small rolling
circle, yielding the parametric equations
The length of the tangent to the tricuspoid, measured between the two points , in which it cuts the curve again, is constant and equal to
. If you draw tangents
at and , they are at right angles.