cissoid

Then the cissoid is the locus of points R.

In this case the roulette is the cissoid of Diocles.

In fact, the family of cissoids is named for this example and some authors refer to it simply as the cissoid.

The conchoid is, therefore, the cissoid of a circle with center O and the given curve.

Then one would readily admit that such a cissoid can be used to correctly solve the Delian problem.

So the cissoid of two non-parallel lines is a hyperbola containing the pole.

The reason is that the cissoid of Diocles cannot be constructed perfectly, at least not with compass and straightedge.

This cissoid could then be translated, rotated, and expanded or contracted in size (without changing its proportional shape) at will to fit into any position.

Note however that this solution does not fall within the rules of compass and straightedge construction since it relies on the existence of the cissoid.

The pedal curve of a parabola with respect to its vertex is a cissoid of Diocles.

The geometrical properties of pedal curves in general produce several alternate methods of constructing the cissoid.

When C and C are parallel lines then the cissoid is a third line parallel to the given lines.

A similar derivation show that, conversely, any hyperbola is the cissoid of two non-parallel lines relative to any point on it.

The cissoid of Diocles, studied by Diocles and use a method to double the cube.

Also, if two congruent parabolas are set vertex-to-vertex and one is rolled along the other; the vertex of the rolling parabola will trace the cissoid.

In geometry, a cissoid is a curve generated from two given curves C, C and a point O (the pole).

To construct the cissoid of Diocles, one would construct a finite number of its individual points, then connect all these points to form a curve.

On the other hand, if one accepts that cissoids of Diocles do exist, then there must exist at least one example of such a cissoid.

The cissoid of Diocles also be defined as the inverse curve of a parabola with the center of inversion at the vertex.

However, because a point may be represented in multiple ways in polar coordinates, there may be other branches of the cissoid which have a different equation.

The cissoid of the circle and the line , where k is a parameter, is called a Conchoid of de Sluze.

His name is associated with the geometric curve called the Cissoid of Diocles, which was used by Diocles to solve the problem of doubling the cube.

In geometry, the cissoid of Diocles is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio.

If they are connected by line segments, then the construction will be well-defined, but it will not be an exact cissoid of Diocles, but only an approximation.

Then the path traced by the vertex of the top parabola as it rolls is a roulette shown in red, which happens to be a cissoid of Diocles.