125_Math and Art:Find the Connection

Where the angles of the shapes meet, they collectively equal 360°... Do you see perpendicular lines?90° 90° Perpendicular lines form two 90° angles where the two line segments or lines

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?

Monet Painting in His Garden at Argenteuil, 1873 by Pierre-Auguste Renoir

Do you see other shapes?

rectangle rectangle 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 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?

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

Irises, by Vincent Van Gogh (1889)

8 yellow to 11 blue Yellow Blue 8:11

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!

Image of Mona Lisa

http://www.ibiblio.org/wm/paint/auth/vinci/jocon de/joconde.jpg

Symmetry

http://www.haelmedia.com/OnlineActivities_txh/mc_txh4_001.html

Proportion

http://www.amathsdictionaryforkids.com/dictionary.html

http://www.gotcs.com/news/Colormixing.pdfhttp://www.drawinghowtodraw.com/drawing-lessons/drawing-faces-lessons/dme-good-human-proportions.html

Fractals

http://www.intmath.com/complex-numbers/fractals.php

Artwork

http://www.arts-wallpapers.com/wallpaper/renoir/07/renoir800.jpg

Artwork (continued)

09-22-07-23-christies-london-auction-of-old-masters-and-19th-century-art-realises-32-8-million.html

http://www.artknowledgenews.com/2009-07-http://hoocher.com/Gilbert_Stuart/

Gilbert_Stuart.htm

http://www.post-gazette.com/pg/

08233/905474-42.stm

%C3%BCrer_-_Melencolia_I_(detail).jpg

Artwork (continued)

expensive-oil-paintings-plus-2-more/

http://colorpaintingart.com/van-goghs-most-Quote

http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm

Mixing Colors

http://painting.about.com/library/blpaint/

blcolormixingpalette1.htm