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? Do you see other shapes ? The Bedroom (1889), by Van Gogh rectangl e rectangl e rectangl e ov al rectangl e Do you see the golden rectangle? Do you see the golden rectangle? Do you see fractions or proportions?1 ¾ ½ ¼ Do you see fractions or proportions? ½ What is the prominent color? What is the ratio of colors that make up this color? To get this orange, mix parts red to part yellow, or Red + Yellow 3:1 What is a prominent color in this painting? What’s the ratio for making this color? GREEN 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\52U8PE 94\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_txh/mc_txh4_001.html Proportion http://www.amathsdictionaryforkids.com/dictionary.html http://www.gotcs.com/news/Colormixing.pdf http://www.drawinghowtodraw.com/drawing-lessons/drawing-faces-lessons/dme-good-human-proportions.html Bibliography Fractals http://www.intmath.com/complex-numbers/fractals.php Artwork http://www.arts-wallpapers.com/wallpaper/renoir/07/renoir800.jpg http://annhortonquilts.com/img/Van-Gogh.jpg Bibliography Artwork (continued) http://www.artknowledgenews.com/2009-07-09-22-07-23-christies-london-auction-of-old-masters-and-19th-century-art-realises-32-8-million.html http://hoocher.com/Gilbert_Stuart/Gilbert_Stuart.htm http://www.post-gazette.com/pg/08233/905474-42.stm Bibliography Artwork (continued) http://www.britannica.com/bps/media-view/97443/1/0/0 http://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Albrecht_D%C3%BCrer_-_Melencolia_I_(detail).jpg/220px-Albrecht_D%C3%BCrer_-_Melencolia_I_(detail).jpg Bibliography Artwork (continued) http://colorpaintingart.com/van-goghs-most-expensive-oil-paintings-plus-2-more/ Quote http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm Mixing Colors http://painting.about.com/library/blpaint/blcolormixingpalette1.htm ... 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... 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. .. Renoir Do you see other shapes? Do you see other shapes ? The Bedroom (1889), by Van Gogh rectangl e rectangl e rectangl e ov al rectangl e Do you see the golden rectangle? Do you see the golden rectangle?