Math as Art
As
the study of natural and abstract patterns and patterning,
math is an inherently creative and artistic endeavor.
Recent advances in computing 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 mathematics can now be enjoyed by
all.
Unfortunately,
many students have been mistaught that math is a dry, rote,
onedimensional activity devoid of originality or
inventiveness and lacking any real connection to the arts.
Fortunately for me, I was not one of them.
On the contrary, 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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Designed
in 2018 using Google Search's
graphing
calculator:

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

Wrinkled
Paper
z = xy+tan(x)cos(8xsin(2y))

Fancy
Lapels
z = arcsec(sin(1/x)cos(1/y))

Corrugated
VRoof
z = abs(sin(2x)y)

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

Arizona
Desert
z = (xy)/(sin(x)+1/cos(y))

Celery
Row
z = (sin(x)cos(y))/(xy)

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

Plastic
Chair
z = abs(x)+2x^4abs(x^2*y^3)

Lettuce
Garden
z = 1/(sin(x)cos(y))
=
Designed
in 2018 using
Wolfram
Alpha:

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

Mesa
Group with Hills and Valleys
z = sin(2x)cos(2y)exp((x^2+y^2)/6)


Slanting
Waves
z = xsin(y)

Tartan
Forest
z = tan(.01sin(x)cos(y))^2

Techtonic
Rift
z = x^3+tan(y)+cot(x)+y^3


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

Spikes
z = tan(sin(x)cos(y))^2

Wavy
Incline
z = cos(xy)+y

Gaping
Maw
z = (x^2+1.5y^2)*e^(x^2y^2)

X
Marks the Spot
z = (arccos(abs(x)+abs(y))/arcsin(abs(x)abs(y))
=
Designed
in 2018 using Apple's
Grapher
app:

Splotches
sin(sin(x)+cos(y)) = cos(sin(xy)+cos(x))

Slinky
Toy
x = sin(t^2)
y = cos(t)
t = {0..10}

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

Basket
Math
x = cos(11t)
y = sin(13t)
t = {0..2π}
–
DoubleBack
r = t^2t
𝜃
= tsin(t)
t = {0..40}

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

Controlled
Chaos
x^3 = 1+7tan(xy^2)
–
Ripples
sin(xy) = cos(y)+sin(x)
–
Convergence
y = kx/3
k = {1..18}

Spiral
x = (u/5)cos(u)
y = (u/5)sin(u)
u = {0..20}
–
Fender
Butterfly
r = sec(x)
y = tan(x)+cot(x)+K
k = {5..5}
=
Designed
in the late 1990's using the pioneering Mac app
Graphing
Calculator:










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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 Maths 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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Other

GeoGebra: Math in
Art
A gallery of beautiful but simple GeoGebra math art
projects. Sliders enable interactivity, learning by
exploration. A playground for budding math artists.
Orbiform
None other than Leonhard Euler proved the constant width of
this intriguing solid. Acts like a sphere, looks like a ...
what? Artsy artillery shell? Details
here
and
here.
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Looking
for more?
Check out my
MathasArt
blog featuring additional original 2D and 3D graphs like
those shown above.
There's
no better way to refute the notion of the lifeless
sterility of mathematics than to visit the
Wolfram Demonstrations
Project.
I urge you to take a moment to enjoy the delightful
mathematical objects you'll find there. [Requires
software download to interact with the artwork].
I think you'll agree ...
Math is art, indeed!
Copyright
© 2006Present: Christopher R. Borland. All Rights
Reserved.