I am looking for a determinant for a second order equation so that I can build a nomogram. The equation is simply: $$ x^{2} +2 a x-c = 0 $$ It can also be written in another format (which is more helpful to me), but I am not sure if it can be done in this format: $$ x^{2} +2 a x- \frac{D A^{2}...

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...

I'm trying to make a nomogram for finding the maximum pressure angle on cycloidal cams with radial followers. See image for the nomogram. I've obtained the paper from E.C. Varnum where he first created the nomogram. Reference is: "Varnum, E.C. Circular nomogram theory and construction techniqu...

I am trying to develop a nomogram which simultaneously shows the exact Fisher equation $(1+u) = (1+v)(1+w)$ and its linear approximation $u \approx v + w$. This amounts to finding twelve smooth curves such that the following equations hold: $$\det \begin{bmatrix}f_1(u) & f_2(u) & f_3(u) \\ g_1(v)&

I am attempting to make a nomogram for the equation $$\frac{z-x}{g} - \left(\frac{z-y}{g}\right)^2 =0$$ (here $g$ is a constant). You can use the quadratic formula to solve for $z$, in which case: $$z = \frac{g}{2} + y \,\pm \, \sqrt{g}\sqrt{\frac{g}{4} + y-x}$$ And we can take just the posit...