Mathematics as Art Introduction

Mathematics is sometimes referred to as the language of science, and I certainly believe that it is.  However, I also believe that certain areas of mathematics intersect with the world of art.  This is certainly not a new idea; the National Art Gallery in Washington DC houses a famous painting by Salvador Dali entitled “Sacrament of the Last Supper.”  Dali constructed this painting based on geometric shapes and straight lines.

I find the idea of using mathematics to produce art particularly evident in the classic algebraic curves.  When these curves are graphed, there is a clear beauty to my eye, an intrinsic gracefulness that can only be described as artistic.  Through experiment, I have found that when geometric constructions of these curves are done in concert with a dynamic-geometry software application, such as 
Geometer’s Sketchpad®, they form a platform for computerized, abstract art and design. I’m not claiming that it is great art—maybe it’s not art at all—but it’s fun and fascinating to watch as it is animated on the computer screen.  And you don’t need to know anything about math to enjoy it!

I have organized these animations by the type of algebraic curve (shape) it depicts, under the curve’s historic name with a static graph and a bit of background information, and then into one or more sets of paired computer animations for each curve.  First is an animation that generates the curve on the computer screen or demonstrates a mathematical property of the curve, and this animation will use a geometric construction of the curve to do so.  Notes on the animation screen provide information about the construction, for those who are interested.  Second is my attempt at creating art based on the first animation, usually with very minor modifications but with all the underlying mathematical information hidden.

The curves for which I have developed animations so far are:
The Astroid
The Cardioid
The Lemniscate of Bernoulli
The Deltiod
The Conic Section
Cissoid of Diolcles
Compass Only
The Right Strophoid

Periodically, I will be adding additional curves and developing new animations for all the curves.