Recently, my friend Nick Ridge and I took on a job in Northern California that had an interesting challenge — an elliptical staircase with a self-supporting inside stringer. To make things trickier, the major axis of the ellipse paralleled a back wall that ran at an angle to the two side walls enclosing the staircase. I had to figure out a way to size the ellipse so that it hit the walls at three unknown tangent points.

The architect's drawing was of little use and I couldn't figure out a way to do the layout with math, so I resorted to the tried-and-true caveman method — trial and error — in hopes of eventually finding the correct-size ellipse to fit the space. Working in an open area elsewhere in the house so that the proliferation of trial lines wouldn't...

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