I never really liked geometry in school—it was never as interesting to me as the equations-based parts of maths were. Fortunately, I was still rather good, as I finally had a need for it when marking out a piece of wood that would become both a shelf and top to the fitted wardrobe I’ve designed as part of my remodelled bedroom.
Had all the walls involved been perfectly vertical and perpendicular, and the wardrobe a simple rectangle, only the length and width would have been required. But in order to accommodate hangers, my wardrobe design is deeper on one side, and the walls are far from perfect, both in that they lean and are not at 90-degree angles to one another. These factors resulted in a top that was almost trapezoidal.
To recreate this unique shape accurately in wood, I recalled that a quadrilateral can be broken up into two different pairs of triangles, and that three specific lengths can only form two triangles, which are mirror images of each other. Putting this all together we measured all four sides plus the two diagonals. Back at the wood I marked out the front edge, then, from the two front corners, drew arcs with radii equal to the side and diagonal relevant to each point. The two resulting intersections represented the back two corners, which allowed me to mark in the remaining three edges.
At least that was the plan. In reality, measuring the diagonals was complicated by not being able to get the end of the tape measure right into the back corners, so the distance from front corner to the diagonally opposite corner formed by the 25mm-wide supports that were on the wall was measured instead. This didn’t cause too much added difficulty in marking the wood, however, since the ruler I used was also 25mm wide, allowing me to simply line up to one side of the ruler, and draw along the other.
This use for old-school geometry turned out to be far more accurate than previous attempts at marking out shelves, with only a few small adjustments needed afterwards—to account for the walls’ waviness—before it slotted into place perfectly. So now if anyone ever complains that maths has no use in the real world, I can correct them with evidence, and show them my lovely new shelf, which is so much better than a boring rectangular one.