HP42s first major program (Double Integral) Best way to approach?

[ijabbott]

(06-01-2020 04:46 PM)DM48 Wrote:  Albert, thank you for posting that update. That is over my head but it allowed Werner to create a noticeably faster implementation of Bore on my DM42 and for that I am grateful to the both of you.

I have the "coupon" that was "tapped" from ductile iron pipe on my desk. I have always assumed, when flattened, it would be an ellipse. Is that correct?

I don't think so. If you define variables \(R_p\) for the pipe radius and \(R_h\) for the hole radius, the parametric equations for the "coupon" would be:

\[\begin{cases}
X_c = R_p \arctan\left(\frac{R_h \cos(t)}{\sqrt{{R_p}^2 - (R_h \cos(t))^2}}\right) \\
Y_c = R_h \sin(t)
\end{cases}
t \in [0, 2\pi)\]

EDIT: Corrected it, I think.

But the parametric equations for an ellipse with the same axes would be:

\[\begin{cases}
X_e = R_p \arcsin\left(\frac{R_h}{R_p}\right) \cos(t) \\
Y_e = R_h \sin(t)
\end{cases}
t \in [0, 2\pi)\]