Benjamin Johnson

Undergraduate Composite Materials Engineering Student
Winona State University
Winona, MN

I create wooden models of mathematical functions using CNC (computer numeric control) machining technology. I combine the skills and techniques used in modern manufacturing and tool making to study and understand mathematics. I create mathematical art for its asthetic beauty and to gain a greater understanding of math in the real world.

Level Curves on a Smooth Surface
Laminated Wood

This artwork shows a smooth surface and the level curves visually created by the multiple laminations of wood. The 3-dimensional piece, cut with a CNC machine, illustrates the inverse relationship between the closeness of a function's level curves and the maximum rate at which the function is increasing. The piece illustrates a number of multivariable calculus concepts, including the need, when finding a function's maxima and minima, to check critical points along a region's boundary.