The deltoid is defined by these equations:

c(t) = RR * [ cos(t)+0.5*cos(-2t), sin(t)+0.5*sin(-2t) ]

Of course it is a special case of the Hypocycloids with frequency = -2 and stick = 1. It is shown separately because its rolling construction has beautiful additional properties:

The tangent intersects the deltoid in a segment of constant length and this "needle" is rotated through 180 degrees while one radius of the rolling circle draws the deltoid once. The midpoint of the needle is also center of a larger rolling circle which intersects the deltoid at the endpoints of the needle. And, this midpoint also lies on the rolling circle.

c(t) = RR * [ cos(t)+0.5*cos(-2t), sin(t)+0.5*sin(-2t) ]

Of course it is a special case of the Hypocycloids with frequency = -2 and stick = 1. It is shown separately because its rolling construction has beautiful additional properties:

The tangent intersects the deltoid in a segment of constant length and this "needle" is rotated through 180 degrees while one radius of the rolling circle draws the deltoid once. The midpoint of the needle is also center of a larger rolling circle which intersects the deltoid at the endpoints of the needle. And, this midpoint also lies on the rolling circle.

"Rolling" means that the point of the rolling circle that touches the
"street"-circle has velocity zero.

A motion with a point at rest is a rotation around this rest point. Applied to the drawing pen on the stick

this means: the curve tangent at the point just drawn is orthogonal to its connection to its rest point.

Compare Cycloid

A motion with a point at rest is a rotation around this rest point. Applied to the drawing pen on the stick

this means: the curve tangent at the point just drawn is orthogonal to its connection to its rest point.

Compare Cycloid