The quintic with 15 cusps is a so-called world record surface: To our knowledge, it is not known if there may be a quintic with more than 15 cusps although it is known that a quintic cannot have more than 20 cusps.
A math vase of degree 3 without bottom. It has been created by rotating a graph of a polynomial of degree 3 about an axis.
A math vase of degree 3. It has been creating by rotating a graph of a polynomial of degree 3 about an axis.
Cubic surfaces are a math model classic from the 19th century. We provide one of our favourite examples (cubic surface KM 42) in the form of a pendant.
The sculpture we present here is a 3D-printed modern object consisting of the 27 lines only, and a thin part of the surface as a border.
This visualizes a 1-parameter family of cubic functions or a 3d graph of a function in one variable in a 3d-coordinate system.
The Barth Sextic is probably the most famous example of the sometimes so-called world record surfaces. This post shows a smoothed variant of it.