# What is a triangular graph with axes perpendicular to the sides called?

October 28, 2009 10:59 AM Subscribe

What is the graph or plot called which:
- is an equilateral triangle
- has three axes
- each axes is perpendicular to a side of the triangle?

Here is an example, but searching for "likelihood triangle" turns up nothing. I've never heard of that term before.

A triangle plot seems similar, but the axes are at 60 degree angles. Everyone in my laboratory agrees that they are difficult to easily interpret without practice.

Bonus question: Is there an R package which would create such a graph?

Thanks!

Here is an example, but searching for "likelihood triangle" turns up nothing. I've never heard of that term before.

A triangle plot seems similar, but the axes are at 60 degree angles. Everyone in my laboratory agrees that they are difficult to easily interpret without practice.

Bonus question: Is there an R package which would create such a graph?

Thanks!

Oh wait, sorry: my googling confused me. That's not quite what you want is it.

posted by pharm at 11:13 AM on October 28, 2009

posted by pharm at 11:13 AM on October 28, 2009

I'm definitely not looking for a triangle plot.

I can't find a good definition of what a De Finetti Diagram actually is, beyond the wikipedia definition and the (rather unhelpful and unlabeled) wikipedia diagram. Examining R packages for De Finetti Diagrams suggested to me that they were the same as triangle plots. I could be wrong on this last point, though.

posted by Peter Petridish at 11:19 AM on October 28, 2009

I can't find a good definition of what a De Finetti Diagram actually is, beyond the wikipedia definition and the (rather unhelpful and unlabeled) wikipedia diagram. Examining R packages for De Finetti Diagrams suggested to me that they were the same as triangle plots. I could be wrong on this last point, though.

posted by Peter Petridish at 11:19 AM on October 28, 2009

The diagram isn't unlabeled. x,y,z are all perpendicular to the sides and the text says "the three lines from that point that are perpendicular to the sides of the triangle." That sounds like what you want.

posted by DU at 11:27 AM on October 28, 2009

posted by DU at 11:27 AM on October 28, 2009

the article on Viviani's Theorem goes into more detail on the theory behind the Ternary plot of which a De Finetti Diagram is an example.

I guess the point is that the length of the lines (from any point in the triangle) always add up to 1. But I'm not sure what the benefit of showing information that way is. It's pretty confusing.

According to Wikipedia a triangle plot and a ternary plot are the same thing. Can you explain what the difference between the plot you want a ternary/triangle plot actually are? The example you gave certainly looks like a triangle plot, down to using an equilateral triangle.

posted by delmoi at 11:47 AM on October 28, 2009

I guess the point is that the length of the lines (from any point in the triangle) always add up to 1. But I'm not sure what the benefit of showing information that way is. It's pretty confusing.

According to Wikipedia a triangle plot and a ternary plot are the same thing. Can you explain what the difference between the plot you want a ternary/triangle plot actually are? The example you gave certainly looks like a triangle plot, down to using an equilateral triangle.

posted by delmoi at 11:47 AM on October 28, 2009

Whether or not it matters, that resembles a barycentric coordinate system.

posted by rlk at 12:10 PM on October 28, 2009

posted by rlk at 12:10 PM on October 28, 2009

Hmm. I may be confused here, and I am now realizing that this is more of a "data-presentation" issue than a "what kind of graph" issue.

Traditional triangle graphs look like this with data points added on top. This is what my lab was looking at as we discussed how such graphs are hard for the un-initiated to grasp. They're confusing!

I (now) believe that I am looking for a triangle graph with no guide lines and with axes labels within the graph, on a line perpendicular to the triangle side (I have no example of this online). Having the three axes on the inside of the triangle (with hash markings) will help people figure out the values of the plotted points.

I guess the solution is to manually add in these axes on a graph or keep on looking at R packages to find a good triangle graphing program.

Thanks for helping me figure this out!

posted by Peter Petridish at 12:13 PM on October 28, 2009

Traditional triangle graphs look like this with data points added on top. This is what my lab was looking at as we discussed how such graphs are hard for the un-initiated to grasp. They're confusing!

I (now) believe that I am looking for a triangle graph with no guide lines and with axes labels within the graph, on a line perpendicular to the triangle side (I have no example of this online). Having the three axes on the inside of the triangle (with hash markings) will help people figure out the values of the plotted points.

I guess the solution is to manually add in these axes on a graph or keep on looking at R packages to find a good triangle graphing program.

Thanks for helping me figure this out!

posted by Peter Petridish at 12:13 PM on October 28, 2009

No, I think a ternary plot is what you want. The three axes

In the wikipedia article, take a look at the three example drawings showing the individual variables (1 2 3). The lines which are shown are the lines along which each variable has a constant value. The axes are not explicitly shown, but are perpundicular to the constant-value lines which are shown. Just like in a standard x-y graph, the x axis is horizontal, which is perpundicular to (vertical) lines which have a constant x-value.

The benefit is showing three variables which have a constant sum, since the sum of distances to the three sides of an equilateral triangle is constant for all points within the triangle, but you don't have any reason to give preference to any two of the three variables over the third. You could just plot it on a standard x-y graph, arbitrarily picking two of the variables for x and y, since the third can be determined from the first two, but that gives prominence to those two variables at the expense of the third. It also makes the region covered by the graph a 90-45-45 triangle, rather than the equilateral triangle which gives equal prominence to all three variables.

For example, nutritiondata.com shows the ratio of calories from carbs, fats, and proteins for a given food on a ternary plot. I've often thought that the CIE chromaticity diagram ought to be plotted on a ternary plot, and I thought I had seen such a plot online somewhere, but I can't find it now and Googling shows only the xy-version, even though it meets the conditions for a ternary plot.

posted by DevilsAdvocate at 12:22 PM on October 28, 2009

*are*perpundicular to the three sides, it's just that the three axes aren't explicitly shown. The three axes are at 120° angles to each other, since the sides are at 60° angles.In the wikipedia article, take a look at the three example drawings showing the individual variables (1 2 3). The lines which are shown are the lines along which each variable has a constant value. The axes are not explicitly shown, but are perpundicular to the constant-value lines which are shown. Just like in a standard x-y graph, the x axis is horizontal, which is perpundicular to (vertical) lines which have a constant x-value.

*But I'm not sure what the benefit of showing information that way is. It's pretty confusing.*The benefit is showing three variables which have a constant sum, since the sum of distances to the three sides of an equilateral triangle is constant for all points within the triangle, but you don't have any reason to give preference to any two of the three variables over the third. You could just plot it on a standard x-y graph, arbitrarily picking two of the variables for x and y, since the third can be determined from the first two, but that gives prominence to those two variables at the expense of the third. It also makes the region covered by the graph a 90-45-45 triangle, rather than the equilateral triangle which gives equal prominence to all three variables.

For example, nutritiondata.com shows the ratio of calories from carbs, fats, and proteins for a given food on a ternary plot. I've often thought that the CIE chromaticity diagram ought to be plotted on a ternary plot, and I thought I had seen such a plot online somewhere, but I can't find it now and Googling shows only the xy-version, even though it meets the conditions for a ternary plot.

posted by DevilsAdvocate at 12:22 PM on October 28, 2009

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posted by pharm at 11:09 AM on October 28, 2009