>From: [EMAIL PROTECTED] (Donald Burrill)
>There must be constraints on the values of the three variables.
>Commonly used for situations like a chemical mixture of 3 components.
>Each component can have a relative concentration between 0% and 100%,
>but if component A is at 100%, components B and C must both be at 0%,
>and the point (100%, 0%, 0%) falls at one apex of the triangle. The
>formal restriction, of course, is that the sum of all three
>concentrations equals 100%, so that there are really only two dimensions'
>worth of information available: (A, B, (100%-A-B)), (A, (100%-A-C), C),
>or ((100%-B-C), B, C). Since there is usually no reason to treat any
>component as more (or less) important than any other, triangular
>coordinates are often displayed on an equilateral triangle, and special
>graph paper can be purchased that has such a grid. In the absence of
>such paper, one can plot, say, A and B at right angles to each other and
>let the 45-degree line from (100,0) to (0,100) represent the C axis (and
>the upper boundary of the space of possible points).
<Snip>
> -- DFB.
These ternary plots are common in petrology, where the vertices are % sand, %
clay, % silt and in population genetics, where the 3 vertices are AA aa and Aa
(individuals from a population in Hardy-Weinberg equilibrium fall along a curve
on this plot; departures from H-W equilibrium are readily evident).
Middleton's (2000, p. 181-185); "Data Analysis in the earth sciences using
Matlab") provides Matlab code for plotting these ternary diagrams.
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