Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
Deltoid curve line segment can slide with each end on the deltoid and remain tangent to the deltoid. The point of tangency travels around the deltoid twice while each end travels around it once. 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. The area of the deltoid is formula_9 where again "a" is the radius of the rolling circle; thus the area of the deltoid is twice