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{{Short description|Arrangement of colors within a triangle}}
{{Use American English|date=March 2021}}
{{Use mdy dates|date=March 2021}}
[[File:Lichtenberg color triangle Tobias Mayer 1775.jpg|thumb|right|200px|A 1775 color triangle by [[Tobias Mayer]].]]
[[File:CIExy1931 srgb gamut.png|right|thumb|200px|The [[sRGB]] color triangle, shown as a subset of ''x,y'' space, a [[chromaticity]] space based on [[CIE 1931]] colorimetry]]

A '''color triangle''' is an arrangement of [[color]]s within a [[triangle]], based on the [[Additive color|additive]] or [[Subtractive color|subtractive]] combination of three [[primary color]]s at its corners.

An additive [[color space]] defined by three primary colors has a [[chromaticity]] [[gamut]] that is a color triangle, when the amounts of the primaries are constrained to be nonnegative.<ref>{{cite book | title = Digital Pictures: Representation, Compression, and Standards | author = Arun N. Netravali |author2=G. Haskell | author-link = Arun Netravali | edition = second | publisher = Springer | year = 1995 | isbn = 0-306-42195-X | url = https://books.google.com/books?id=-TXYfZrCBuQC&q=gamut+color-triangle&pg=PA101 }}</ref><ref>{{cite book | title = Color Vision: Perspectives from Different Disciplines | author = Werner Backhaus, Reinhold Kliegl and John Simon Werner | publisher = Walter de Gruyter | year = 1998 | isbn = 3-11-015431-5 | url = https://books.google.com/books?id=DrduOSrOFegC&q=positive+color-triangle&pg=PA58 }}</ref>

Before the theory of additive color was proposed by [[Thomas Young (scientist)|Thomas Young]] and further developed by [[James Clerk Maxwell]] and [[Hermann von Helmholtz]], triangles were also used to organize colors, for example around a system of [[RYB color model|red, yellow, and blue primary colors]].<ref>{{cite book | title = The Creation of Color in Eighteenth-Century Europe | author = Sarah Lowengard | publisher = Columbia University Press | year = 2008 | url = http://www.gutenberg-e.org/lowengard/A_Chap03.html | isbn = 978-0-231-12454-6 }}</ref>

After the development of the [[CIE 1931 color space|CIE system]], color triangles were used as chromaticity diagrams, including briefly with the [[trilinear coordinates]] representing the chromaticity values.<ref>{{cite journal|title=A Maxwell Triangle Yielding Uniform Chromaticity Scales|journal=[[JOSA]]|first=Deane B.|last=Judd|volume=25|issue=1|date=January 1935|pages=24–35| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-25-1-24|doi=10.1364/JOSA.25.000024|url-access=subscription}}</ref> Since the sum of the three chromaticity values has a fixed value, it suffices to depict only two of the three values, using Cartesian co-ordinates. In the modern ''x,y'' diagram, the large triangle bounded by the imaginary primaries X, Y, and Z has corners (1,0), (0,1), and (0,0), respectively; color triangles with real primaries are often shown within this space.

==Maxwell's disc==

Maxwell was intrigued by [[James David Forbes]]'s use of color [[Spinning top|top]]s. By rapidly spinning the top, Forbes created the illusion of a single color that was a mixture of the primaries:<ref>{{cite book|title=The Natural Philosophy of James Clerk Maxwell|author=Peter Michael Harman|publisher=[[Cambridge University Press]]|isbn=0-521-00585-X|year=1998| url=https://books.google.com/books?id=qf6jtc4nZisC&q=forbes+maxwell+color+top&pg=PA41}}</ref>

{{blockquote|[The] experiments of Professor J. D. Forbes, which I witnessed in 1849… [established] that blue and yellow do not make green, but a pinkish tint, when neither prevails in the combination…[and the] result of mixing yellow and blue was, I believe, not previously known.|James Clerk Maxwell|Experiments on colour, as perceived by the eye, with remarks on colour-blindness (1855), [[Transactions of the Royal Society of Edinburgh]]}}

Maxwell took this a step further by using a circular scale around the rim with which to measure the ratios of the primaries, choosing [[vermilion]] (V), [[emerald (color)|emerald]] (EG), and [[ultramarine]] (U).<ref>{{cite book|title=The Scientific Papers of James Clerk Maxwell|author=James Clerk Maxwell|publisher=[[Dover Publications]]|isbn=0-486-49560-4|year=2003| url=https://books.google.com/books?id=duyKrTNps_AC&q=maxwell+vermilion+emerald+ultramarine&pg=PA127}}</ref>

Initially, he compared the color he observed on the spinning top with a paper of different color, in order to find a match. Later, he mounted a pair of papers, snow white (SW) and [[ivory black]] (Bk), in an inner circle, thereby creating shades of gray. By adjusting the ratio of primaries, he matched the observed gray of the inner wheel, for example:<ref name=maxwell>James Clerk Maxwell (1855), [http://www.jimworthey.com/archive/index.html Experiments on colour as perceived by the eye, with remarks on colour-blindness]</ref>

<math>0.37V+0.27U+0.36EG=0.28SW+0.72BK</math>

To determine the chromaticity of an arbitrary color, he replaced one of the primaries with a sample of the test color and adjusted the ratios until he found a match. For [[pale chrome]] (PC) he found <math>0.33PC+0.55U+0.12EG=0.37SW+0.63BK</math>. Next, he rearranged the equation to express the test color (PC, in this example) in terms of the primaries.

This would be the precursor to the [[CIE 1931 color space#Color matching functions|color matching functions]] of the [[CIE 1931 color space]], whose chromaticity diagram is shown above.

<gallery>
Image:Color top 1895.png|Drawing of Maxwell's color top
Image:YoungJamesClerkMaxwell.jpg|[[James Clerk Maxwell|Maxwell]] with his wheel
Image:Maxwell color Triangle Luckiesh 1921.png|Maxwell's color triangle
Image:Fick color triangle.png|<small>A color triangle attributed to Fick in 1892, based on imaginary primaries corresponding to the three primary sensations of the human eye. In such a triangle, all real colors fall within the curved outline defined by the "pure sensations".</small>
</gallery>

==See also==
* [[Color wheel]]

==References==
{{reflist}}

{{Color space}}
{{Color topics}}

[[Category:Color scales]]
[[Category:James Clerk Maxwell]]

Color triangle - Revision history

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