This curve, with the form
of the Greek capital delta, has been given also as names:
This quartic curve 1) is the hypocycloid
for which the rolled circle is three times as large as the rolling circle.
Given a tangent l to the curve. It cuts the curve in points P and Q. Then PQ has a length
of 4, and the tangents to the curve in P and in Q make a right angle.
The length of the deltoid is 16, and the area it encloses: 2π.
Some other properties of the curve:
Three pedals of the curve are:
The curve has been investigated as first by Leonhard Euler (1745), while studying
an optical problem.
1) In Cartesian coordinates:
(x2 + y2)2 -8x(x2 - 3y2) + 18(x2 + y2) = 27