Algebraic equations and graphics of Bour’s minimal surfaces family

Abstract

We consider the family of the irreducible algebraic equations of the Bour’s minimal surfaces for integers m = 2, 3, 4 in the three dimensional Euclidean space, and obtain its degrees in cartesian coordinates, classes in inhomogeneous coordinates. We also reveal its integral free representations. Moreover, we visualise the equations of the surface family.

Subject Classification:

• Primary 53A10
• Secondary 53C42

Keywords:

• Bour’s minimal surfaces
• Algebraic equation
• Degree
• Class
• Integral free representation