Colon (math)

Colon in the origin of the Cartesian leaf

If the graph of a curve runs through a point twice, this point is called a colon , if the curve is run several times , it is called a triple point , etc.

At this singular point , the eigenvalues ​​of the Hessian matrix of the curve, in contrast to the isolated point and the return point (peak), are less than zero.

In the context of algebraic varieties , multiple zeros of such are also referred to as colon .

Examples

Examples of curves with a colon and a loop are:

• Extended cycloid ,
• Trisffektix ,
• Cartesian sheet ,
• Strophoids ,
• Conchoid and
• Pascal snail .