Dan Bach

Statement

Dan Bach has been using Mathematica for over 25 years in the classroom, in teacher workshops and conference talks, and now outside of academics as a 3D math artist and interactive book author. Multivariable Calculus, especially, can provide us with plenty of nice-looking graphs, patterns, and intricate pictures. Dan's students have been inspired to create graphics, movies, and sounds; either as class assignments or purely for pleasure.

Artworks

The starting red curve has a center of curvature at each of its points. The colored parallel curves go toward that center in increasing amounts. Some groups of curves are rotated, some are reduced in number, but all originate from the same ball-shaped bundle at the top, appropriately used as the dansmath.com logo.

A central curve (not shown) has tangent, normal, and binormal directions at each point, making a local {T, N, B} frame. Using a trigonometric combination of the N and B vectors, we describe a toroidal mesh of curves with hues of green, yellow, and orange. Spheres of varying colors and sizes are placed along an equatorial helix and some try to escape their bonds.