Cylindrical parametrization : . Infimite area. Volume of the domain limited by the plane z = 0 :  where K is the Catalan's constant.

The second tractroid is the surface of revolution generated by the rotation of the tractrix around its axis of symmetry (the first
tractroid, rather called pseudosphere, being obtained by rotation of the tractrix around its asymptote).
 
 

As seen above, the area of the total surface is infinite, but the volume of the domain bounded by the surface and its asymptote plane is finite.

See also the Gabriel's horn.
 

surface suivante

surface précédente

courbes 2D

courbes 3D

surfaces

fractals

polyèdres

© Robert FERRÉOL  2022