Watch One Equation Weave an Infinite 3D Horn

BEHIND THE WORK

Can one equation twist an infinite horn into 3D space? In 1865, Italian mathematician Ulisse Dini discovered a remarkable differential geometry manifold: by taking the pseudosphere (the surface of constant negative curvature generated by rotating a tractrix) and applying a uniform helical screw motion, the surface twists into a spiraling trumpet tower of constant Gaussian curvature K = -1. Here, twelve continuous helical turns weave forty pseudospherical ribs into a soaring golden spire—traced as a single unbroken, continuous 3D line.

Related Video: The Hidden Geometry of Kinematic Curves (https://youtu.be/ukPGsj29-Hg)

Artismathic turns equations into visual art—one function at a time.

#MathArt #DifferentialGeometry #Geometry #3DArt #Mathematics #Blender3D #DiniSurface #Spire