“Measuring Is The Enemy,” or, Truing A Triangle

One of the tools emerging from the recent Making Roubo Squares workshop was a diminutive 30-60-90 triangle.  This tool is integral to much of my/our shop life for areas ranging from cubic/pinwheel parquetry to laying out the dovetailed tenons of a Roubo bench leg-and-slab double mortise-and-tenon construction.

With the surplus rectangle of brass plate left over from the making of our nested set of cabinetmaker’s squares during the workshop there was plenty of brass plate left over for making other, smaller layout tools.  Included in these were some small triangles that were roughly laid out with a plastic drafting triangle and rough cut on the bandsaw.

I took the opportunity to demonstrate the truing of the triangle to the workshop students, reminding them of the simple truths they learned decades ago in seventh grade Geometry class.  Instead of using a micrometer or something similar to establish the tringle side lengths, a much easier, simpler, faster, and frankly more accurate method is only a compass or divider away.

After establishing the perfect square corner between the two shorter legs of the triangle it was possible to achieve a perfect set of 30-60 degree angles by using just a scrap piece of plywood, a pencil, and a set of dividers.  For work like this I almost always revert to a pair of dividers from an antique navigational drafting set that I bought for practically nothing many years ago.  These German Silver (alloy of brass plus nickel) tools are simply lovely and a pleasure to the eye and the hand.

First I traced the rough triangle onto a piece of scrap plywood, and set my dividers to the exact length of the shorter side adjacent to the right angle.

Then swinging the dividers to the hypotenuse I stepped off two of those lengths.  If you will recall, for a perfect 30-60-90 triangle the hypotenuse is exactly two time longer than the shorter side of the right angle.

Once I determined that two-times-longer distance along the hypotenuse I re-set my dividers to this exact distance then transferred it to the longer side of the right angle, redrew the hypotenuse on the plywood, then transferred it to the brass.

Five minutes later I had cut and filed the new hypotenuse and had a perfect 30-60-90 triangle ready to braze on the foot and put to use in a multitude of applications.

All with zero measuring, although to be honest I did grab my dial caliper afterwards to check.  I wound up being off by almost 0.002″ which probably amounts to a couple seconds or so of angle degree (or, about 1/1800th of a degree).   I can live with that.

To quote my mentor in the pattern shop, John Kuzma (cleaned up considerably for a family-friendly venue), “Measuring is the enemy.  Layout and transfer are your friends.”

I cannot recall my 7th grade Geometry teacher’s name but I do remember Mr. Fiske, who taught me Trigonometry in 11th grade almost fifty years ago.  Together these men impressed on me the importance of triangles in every-day life.  Thank you, gentlemen.