Math In colorsMath In colors

MeaningMeaning

a phenomenon of light or visual perception that enables one to differentiate otherwise identical objectsa specific combination of hue, saturation, and lightness or brightness

History~ AristotleHistory~ Aristotle

The first known studies of color were done in ancient Greece by Aristotle, who theorized that color existed in the form of rays sent down from the heavens by God.

His theory was not doubted until the Renaissance when more sophisticated color systems were developed by Aguilonius and Sigfrid Forsius.

History~ ForsiusHistory~ Forsius

1611: The oldest known color system is credited to astronomer, priest and Neoplatonist Aron Sigfrid Forsius

History~ AguiloniusHistory~ Aguilonius

1613: Franciscus Aguilonius’ color diagram is possibly the oldest system to use the trio of red, yellow and blue wherein colors are defined within a linear divisionBased on his observations of the changing color of the sky from dawn to dusk

History~ NewtonHistory~ Newton1660: Using a prism, Newton acknowledged that white light could be broken down into the colors of the rainbow, and as such had a clear, set order. Newton’s work in optics led to his creation of the color wheel.

History~ GoetheHistory~ Goethe1810: While Newton's studies in color were scientifically based, Goethe's interest was more in the psychological effects of color. He wished to investigate whether rules could be found to govern the artistic use of color.

History~ GoetheHistory~ GoetheTo Goethe it was most important to understand human reaction to color, and his research marks the beginning of modern color psychology.Published the book

Theory of Colors

History~ RungeHistory~ RungeAt the around the same time, Phillip Otto Runge developed a three dimensional color model in the form of a sphere.To arrange colors based on hue (red, cyan, orange, etc..), whiteness, and blackness.

History~ MaxwellHistory~ Maxwell1872: Sir James Clerk Maxwell developed a chart in the form of an equilateral triangle from his studies of the electromagnetic theory of light.Similar to Goethe’s, but chose green as a primary color instead of yellow

History~ MunsellHistory~ Munsell

1915, Albert H. Munsell made his own 3D color spaceUsed Runge’s work as basis but pointed out two things

History~ MunsellHistory~ Munsell

2.) Some colors(red) are more vivid than others(green), and therefore, they should be further away from the axis.

1.) Pure hues vary in their degree of lightness, and therefore all (red, yellow, green, blue, violet) should not be on the same horizontal plane.

History~ CIEHistory~ CIE

In 1931, the CIE made the color space chromaticity diagram. It mapped out the space of observable colors and assigned a set of three numbers to each

The Math! :OThe Math! :O

The human eye is able to decipher patterns of light according to the primary colors of the additive system: red, green and blue (RGB).However, it is the subtractive system’s primaries: cyan, magenta and yellow (CMY) that best lend themselves to understanding the COLORCUBE and the concept of Color Math.

The Math! :O ~Color Cube The Math! :O ~Color Cube

The Math! :O ~Basic PrinciplesThe Math! :O ~Basic Principles

Principle of Symmetry:The order in which colors are added to one another does not alter the outcome.

The Math! :O ~Basic PrinciplesThe Math! :O ~Basic Principles

Principle of Cumulative Volume:For example, mixing one measurable unit of color with another yields twice the volume of the resulting color.

The Math! :O ~Basic PrinciplesThe Math! :O ~Basic Principles

Principle of Cumulative Volume:Also applies to those operations involving varying colors as well.

The Math! :O ~Subtractive ColorsThe Math! :O ~Subtractive Colors

1 part Cyan + 1 part Magenta = 2 parts Blue

1 part Cyan + 1 part Magenta + 1 part Yellow = 3 parts Black

1 part Cyan + 2 parts Red = 3 parts Black

1 part Red + 1 part Blue + 1 part Green = 3 parts Black

The Math! :O ~Subtractive ColorsThe Math! :O ~Subtractive Colors

Same principles apply to the additive colors;

e.g. 1 part Red + 1 part Green = 2 parts Yellow

1 part Red + 1 part Green +1 part Blue = 3 parts White

The Math! :O ~Four Color TheoremThe Math! :O ~Four Color Theorem

States that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color.

The Math! :O ~Four Color TheoremThe Math! :O ~Four Color Theorem

The only proof, by a computer program, is not accepted by all mathematicians because it will be infeasible to check by human hand, and they have to assume that the program works perfectly.

The Math! :O ~Trichromatic ColorsThe Math! :O ~Trichromatic Colors

This theory began in the 18th century, when Thomas Young proposed that color vision was a result of three different photoreceptorsHermann von Helmholtz later expanded on Young's ideas using color-matching experiments which showed that people with normal vision needed three wavelengths to create the normal range of colors.

The Math! :O ~Trichromatic ColorsThe Math! :O ~Trichromatic Colors

Applications!~ Color ScreensApplications!~ Color Screens

Color television sets and computer monitors use these same three primary colors to produce all the other colors. Closely, one can see tiny dots/bars of red, blue and green. These colors were chosen to match the three types of cones in the human retina. The color dots are so tiny we can see them individually; they blend into the colors we see.

Applications!~ Wallpaper GroupApplications!~ Wallpaper Group

MC Escher’s first mathematical studyThis is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the patternSome patterns, without color are of a group; but with color they are of another distinct group

Applications!~ Wallpaper GroupApplications!~ Wallpaper Group

If with colors, this is of group p1 (translations only, no rotations, reflections or glide reflections)

If without colors, this is of group cmm (just like the most common arrangement of bricks in a brick building)

SourcesSources

http://www.inform.umd.edu/MCTP/Courses/ColorLesson/index.htmlhttp://www.colorcube.com/articles/math/math.htmhttp://www.cs.brown.edu/courses/cs092/VA10/HTML/ColorModels.htmlhttp://www.coloryourcarpet.com/History/ColorHistory.htmlhttp://en.wikipedia.org/wiki/CIE_1931_color_spacehttp://www.merriam-webster.com/dictionary/colorhttp://en.wikipedia.org/wiki/Colorshttp://en.wikipedia.org/wiki/Trichromatic_color_visionhttp://en.wikipedia.org/wiki/Wallpaper_grouphttp://en.wikipedia.org/wiki/Mc_escher

http://photo.net/philg/photo/edscott/cube_rgb.jpghttp://mathforum.org/~sarah/shapiro/4color.mapping.gifhttp://en.wikipedia.org/wiki/File:Four_Colour_Map_Example.svghttp://numb3rs.wolfram.com/409/images/Four-ColorTheorem.gifhttp://www.colorsystem.com/projekte/Grafik/03for/xfor03.jpghttp://www.colorsystem.com/projekte/Grafik/03for/xfor02.jpghttp://www.colorsystem.com/projekte/Grafik/03for/xfor01.jpghttp://prosjekt.ffi.no/unik-4660/lectures04/chapters/jpgfiles/RGB_cube_color_s.jpghttp://www.cv.iit.nrc.ca/~cs410/downloads/sfucourse/chap3.3/rgb_cmyk.gif