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Math as Art

Math as Art

As the study of real and abstract patterns, mathematics is an inherently creative and artistic endeavor.

Recent advances in computer technology have finally made possible the widespread discovery and appreciation of the sublime beauty of mathematics. Once the province of a select few, the art of math can now be freely enjoyed by all.

Unfortunately, many of us have been mistaught that math is a dry, rote, one-dimensional activity devoid of originality or inventiveness and lacking any real connection to the arts. Fortunately for me, I was not one of them. I've always been intrigued by the astonishing musicality of mathematics and entranced by its subtle aesthetics and alluring forms, and I strive to share this perspective with my students.

I hope you'll enjoy the following graphs of mathematical relations I created involving nothing more sophisticated than high school precalculus.

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Created in the 1990's using the pioneering Mac app Graphing Calculator:

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tan[rx(cos[rysin(rx)])] < xcosy

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Created in 2018 using Apple's free Grapher app:

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cos(2x)-sin(xy)-tan(2y) = .5

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x = cos(11t)
y = sin(13t)



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x^3 = 1+7tan(xy^2)



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x = (u/5)cosu
y = (u/5)sinu



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y = tanx+cotx+{-5..5}
r = secx

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cos(x^2)+sin(xy)+tan(y^2) = 1

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Created in 2018 using Google Search's graphing calculator features:

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Egg Carton
z = sin(x/2)+cos(y/2)

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Wrinkled Paper
z = x-y+tanx-cos(8x-sin(2y))

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Corrugated V-Roof
z = abs(sin(2x)-y)

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Bed o' Nails
z = sin(4y)+cos(4x)

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Arizona Desert
z = (x-y)/(sinx+1/cosy)

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Celery Row
z = (sinxcosy)/(x-y)


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Three Fingers
z = log(sin(1.1x)-y)

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Lettuce Garden
z = 1/(sinx-cosy)

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Created in 2018 using comutational knowledge engine Wolfram Alpha:

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Dimpled Vase
z = x^6-x^2+y^6+y^2 = z^2

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Spikes
z = tan(sinxcosy)^2

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Techtonic Rift
z = x^3+tany+cotx+y^3

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Tartan Forest
z = tan(.01sinxcosy)^2

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Squarish Tube
x^2-y^3+z^4 = 1

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Mesa with Rift
z = abs(xy+tan(sinx-cosy)^2)-1/x

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Odd Hills
z = sin(x^2)+cos(sqrt(3)y^2)

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Single Mesa
z = tan(1.5sinxcosy)^2

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Articles

Mathematics and Art
Comprehensive article exploring the close relationship between math and art throughout the centuries.

Seven Times Mathematics Became Art and Blew Our Minds
Science Alert article highlights seven modern instances in which math and art imitate each other in beautiful ways.

Using Ancient Mathematics to Enrich Your Design Skills
Nowhere is the magical intersection of art and mathematics more clear than in areas comprising the broad field of design.

Making Mathematical Art
"Stunning symmetrical images created with just a few equations and a computer." From the venerable Scientific American.

Why the History of Math is Also the History of Art
Article in The Guardian exploring how artists have utilized the inherent beauty of mathematical ideas in their work for thousands of years (at least).

Fifty Famous Curves
The title says it all. 50 fascinating general mathematical curves: Sinusoidal Spirals, Nephroids and Lissajous Curves, Fermat's Spiral, Epitrochoid/Epicycloid, more.

List of Curves
Wikipedia's accessible yet comprehensive index of articles discussing mathematical curves, their forms, properties.

Wolfram Alpha Examples: Popular Curves
Yes, you can use mathematical relations to draw convincing portraits of luminaries like
Lady Gaga and Albert Einstein (among others). Also this.

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Looking for more?

There's no better place to refute the notion of the lifeless sterility of mathematics than the Wolfram Demonstrations Project. Take a moment or two to enjoy the delightful mathematical pictures you'll find there. [Requires software download to interact with the artwork].

Math is art, indeed!


Copyright © 2006-Present Christopher R. Borland. All Rights Reserved.