Cissoid of Diocles

The cisoids (more precisely: cisoids Diocles ) is a special curve of 3rd order, which was described by the Greek mathematician Diocles ( about 200 BC ) to aid with this the problem of doubling cube (also known as Delos problem) to solve. ( With ruler and compass alone, this design task is not to create. ) The name comes from the Greek word Kissós (Ivy).

Equations of cisoids

• Cartesian coordinates:

• Parameter equation:

• Polar Coordinates:

Properties of cisoids

• The points of cisoids are characterized by the following geometric property: Given a circle of radius a, a point S on the circle and that tangent that touches the circle at the point opposite the south. Denoting now for an arbitrary point P of the cisoids the intersection of the line SP with the circle as K and the intersection of SP with the aforementioned tangent circle as A, the route lengths and equal in size.

• The straight line of the equation is the asymptote of the curve.

• The area which is bounded by the cisoid and its asymptote, has the surface area.