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I'm trying to put the following equation in determinant form: $12h^3 - 6ah^2 + ha^2 - V = 0$, where $h, a, V$ are variables (this is a volume for a pyramid frustum with $1:3$ slope, $h$ is the height and $a$ is the side of the base, $V$ is the volume).

The purpose of identifying the determinant is to construct a nomogram. I'm not sure if it actually can be placed in determinant form, and I'm curious if there is a Mathematica function that can do this? I've been trying a pen and pencil approach as listed here. But this approach has hopefully been automated.

Any tips are appreciated!

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    I can see how to do two of the three terms in a determinant; doing all three seems like it might be pretty complicated. You might try pitching your question at nomography.org; it's a small discussion board but the question is likely to get more interest.2012-12-15
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    Do you mind explaining what you want the nomogram for? There are a variety of ways to achieve an approximate nomogram (or in some cases perhaps an exact one), even if a standard algebraic determinant leading to a three-variable alignment nomogram turns out to be difficult or impossible (which I suspect is the case).2012-12-22

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