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. 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. Usually, this constant is represented as 1.0 or 100%. In a ternary plot, the values of the three variables a, b, and c must sum to some constant, K. Ternary plots are tools for analyzing compositional data in the three-dimensional case. In game theory, it is often called a simplex plot. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. Two ternary diagrams with matching axes can be joined at that axis to make a piper diagramĪ ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant.
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