Cartesian parametrization:  n > 0. Cylindrical equation: .

The cylindrical tangent waves are the coiling of a tangentoid around a cylinder (in other words, if we make a cylindrical tangent wave roll on a plane, we get a tangentoid).

For integral values of n, the number of branches is equal to n.

For n = 1, we get the horopter curve.

For n = 2, we get the section of a rectangular hyperbolic paraboloid by a cylinder of revolution with axis a generatrix.

For n = 4, we get the section of a Zindler conoid by a cylinder of revolution with the same axis.
 
 

When we apply the central projection onto the sphere with center O and radius a, the cylindrical tangent wave  becomes the clelia .

Figure made by Alain Esculier

See also the cylindrical sine waves.
 

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© Robert FERRÉOL 2018