Math and Art:
Find the
Connection
©2012 M.B. Pardington
What
“math”
can you
find
in visual
arts?
Do you see angles?
Do you see angles?
Do you see triangles?
Do you see triangles?
Monet Painting in His Garden at Argenteuil, 1873 by Pierre-Auguste Renoir
Do you see other shapes?
rectangle
rectangle
Do you
see
other
shapes?
The Bedroom (1889),
by Van Gogh
rectangle
oval
rectangle
Do you see the golden
rectangle?
Do you see the golden
rectangle?
Do you see tessellations?
Tessellations are regular patterns of shapes fitting snugly together
without gaps or overlaps. Where the angles of the shapes meet, they
collectively equal 360°.
Do you see tessellations?
Metamorphosis II by M. C. Escher
Do you see numbers?
Look for Arabic Numbers:
1 2 3 4 5 6 7 8 9 0
Look for Roman Numerals:
I II III IV V VI VII
VIII IX X XI XII XIII
XIV XV XVI XVII XVIII
XIX XX
L C D M
Do you
see
numbers?
Melencolia I,
by Albrecht Durer
Do you see symmetry?
An object has symmetry if it
can be divided in half to form
its reflection.
Do you see symmetry?
Sun by Tony Hunt
Do you see parallel lines?
Parallel lines are lines that
are always the same distance
from each other. They never
“cross” or intersect.
Do you see parallel lines?
Depiction by John Trumbull of Washington resigning his
commission as Commander-in-Chief
Do you see perpendicular lines?
90°
90°
Perpendicular lines form two
90° angles where the two line
segments or lines meet.
Do you see perpendicular lines?
Composition With Yellow, Red, Black, Blue, and Grey, by Piet Mondrian
Do you see fractions or proportions?
1
¾
½
¼
0
Do you see fractions or
proportions?
1
½
What is the prominent color? What
is the ratio of colors that make up
this color?
To get this orange, mix 3
parts red to 1 part yellow, or
Red + Yellow 3:1
What is a prominent color in this
painting? What’s the ratio for
making this color?
GREEN
8 yellow to 11 blue
Yellow Blue 8:11
Irises, by Vincent Van Gogh (1889)
Do you see fractals?
“With computers, we can generate beautiful art from complex
numbers. These designs, some of which you can see on this page, are
called fractals.
Fractals are produced using an iteration process. This is where we
start with a number and then feed it into a formula. We get a result
and feed this result back into the formula, getting another result. And
so on and so on...
Fractals start with a complex number. Each complex number produced
gives a value for each pixel on the screen. The higher the number of
iterations, the better the quality of the image.”
http://www.intmath.com/complex-numbers/fractals.php
Do you see fractals?
“Without
mathematics
there is no art.”
PACIOLI
Now find some
math in some
art!
Bibliography:
Image of Mona Lisa
http://www.ibiblio.org/wm/paint/auth/vinci/jocon
de/joconde.jpg
Types of Angles
http://www.mathsisfun.com/angles.html
Types of Triangles
C:\Documents and Settings\mp04bps\Local
Settings\Temporary Internet
Files\Content.Outlook\52U8PE94\Triangles_750.gif
Bibliography:
Image of Shapes
www.mrsacolwell.wikispaces.com
Images for Golden Rectangle
www.bondispace.wikispaces.com
www.jwilson.coe.uga.edu
http://britton.disted.camosun.bc.ca/goldslide/goldanim7.gif
Examples of Tessellations
http://gwydir.demon.co.uk/jo/tess/triex.htm
M. C. Escher Website
http://www.mcescher.com/
Fractions
http://pdi-studio5.wp.rpi.edu/files/2011/12/orange_recipe.jpg
Bibliography
Symmetry
http://www.haelmedia.com/OnlineActivities_tx
h/mc_txh4_001.html
Proportion
http://www.amathsdictionaryforkids.com/dictio
nary.html
http://www.gotcs.com/news/Colormixing.pdf
http://www.drawinghowtodraw.com/drawinglessons/drawing-faces-lessons/dme-goodhuman-proportions.html
Bibliography
Fractals
http://www.intmath.com/complexnumbers/fractals.php
Artwork
http://www.artswallpapers.com/wallpaper/renoir/07/renoir800
.jpg
http://annhortonquilts.com/img/Van-Gogh.jpg
Bibliography
Artwork (continued)
http://www.artknowledgenews.com/2009-0709-22-07-23-christies-london-auction-of-oldmasters-and-19th-century-art-realises-32-8million.html
http://hoocher.com/Gilbert_Stuart/Gilbert_Stu
art.htm
http://www.postgazette.com/pg/08233/905474-42.stm
Bibliography
Artwork (continued)
http://www.britannica.com/bps/mediaview/97443/1/0/0
http://upload.wikimedia.org/wikipedia/commons/
thumb/7/7e/Albrecht_D%C3%BCrer__Melencolia_I_(detail).jpg/220pxAlbrecht_D%C3%BCrer_-_Melencolia_I_(detail).jpg
Bibliography
Artwork (continued)
http://colorpaintingart.com/van-goghs-mostexpensive-oil-paintings-plus-2-more/
Quote
http://britton.disted.camosun.bc.ca/goldslide/jbgo
ldslide.htm
Mixing Colors
http://painting.about.com/library/blpaint/blcolor
mixingpalette1.htm