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Ternary and probability paper

Alongside the everyday grids sit a few specialist papers, each shaped to make one particular kind of data easy to read. Ternary paper handles mixtures of three ingredients; probability paper reveals whether data follows a bell curve. Both look strange at first and make perfect sense once you know what they are for.

Ternary paper: three parts that sum to one

A ternary diagram plots mixtures of three components that always add up to 100%, on an equilateral triangle. Each corner is a pure ingredient (100% of one, none of the others), and any point inside is a blend. Three families of lines run parallel to the three sides, so you can read each component straight off — slide along one set of lines to find how much A, another for B, the last for C. Because the three always total 100%, fixing two fixes the third automatically.

This is the standard tool wherever three ingredients combine: soil texture (sand, silt and clay), alloys and phase diagrams, petrology and mineralogy, and any three-component recipe or mixture design. The ternary paper generator sets the number of divisions along each edge. It takes a little practice to read three axes at once, so start by locating the three corners and working inward.

Probability paper: straightening the bell curve

Probability paper does something cleverer. Its vertical axis is stretched by the inverse normal distribution (a probit scale), running from about 0.1% to 99.9% and bunched in the middle. The payoff: when you plot the cumulative percentage of a sample against the measured value, normally distributed data falls on a straight line. A curve or an S-shape means the data is not normal. It is the classic pencil-and-paper test for a bell curve.

Once the points line up straight, the graph hands you two numbers: the mean is the value at the 50% line, and the standard deviation comes from the slope (the spread between the 50% and 84% points). Engineers use it for reliability and life-data, quality control and process capability, and particle-size distributions. Generate one on the probability paper page.

A family of “straightening” grids

Probability paper belongs to the same family as logarithmic paper: grids that reshape an axis so a particular pattern becomes a straight line you can read and measure. Semi-log straightens exponential growth; log-log straightens power laws; probability paper straightens the normal distribution. If one of these makes sense to you, the others will too — the guide to log, semi-log and log-log paper covers the logarithmic side in detail.

Printing specialty paper

Both papers depend on their proportions being exact — a ternary triangle must stay equilateral, and the probit spacing must not be squashed — so print at true scale with fit-to-page off. See how to print at the exact size.

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