# Contour plots for three-ingredient mixing problems

In this worksheet, I consider a class of experiments where the "independent" variables are the relative proportions of three ingredients in a mixture. I put "independent" in quotes because we have the constraint that the proportions sum to unity, so there are really only two independent variables. Let me define three-ingredient space as that portion of the plane x + y + z = 1 that lies in the first octant. This is an equilateral triangle with vertices at (1,0,0), (0,1,0), and (0,0,1). We measure some response, Y, at a variety points in the space and attempt to statistically fit a function to the data. The level curves (also known as contours) of this function will be plotted in three-ingredient space.