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A ternary flammability diagram, showing which mixtures of methane, oxygen gas, and inert nitrogen gas will burn
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant.[1] It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory, it is often called a simplex plot.[2] Ternary plots are tools for analyzing compositional data in the three-dimensional case.
In a ternary plot, the values of the three variables a, b, and c must sum to some constant, K. Usually, this constant is represented as 1.0 or 100%. Because a + b + c = K for all substances being graphed, any one variable is not independent of the others, so only two variables must be known to find a sample's point on the graph: for instance, c must be equal to K − a − b. Because the three numerical values cannot vary independently—there are only two degrees of freedom—it is possible to graph the combinations of all three variables in only two dimensions.
The advantage of using a ternary plot for depicting chemical compositions is that three variables can be conveniently plotted in a two-dimensional graph. Ternary plots can also be used to create phase diagrams by outlining the composition regions on the plot where different phases exist.
The values of a point on a ternary plot correspond (up to a constant) to its trilinear coordinates or barycentric coordinates.
^Weisstein, Eric W. "Ternary Diagram". mathworld.wolfram.com. Retrieved 2021-06-05.
^Karl Tuyls, "An evolutionary game-theoretic analysis of poker strategies", Entertainment Computing January 2009 doi:10.1016/j.entcom.2009.09.002, p. 9
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