The Search for the Perfect Ruler/Protractor/Set Square/Magic Measuring Device, or A Love Letter to the Aristo TZ-Dreieck 1650


It is the September of 2007, a few days into my first year of undergraduate studies, and I am in the basement of the Sanford Fleming Building at the University of Toronto. I am holding something that will change my life, though I do not know it yet. I tear into the paper packaging sleeve, and rip out an Aristo TZ-Dreieck 1650.

The Aristo TZ-Dreieck 1650 is a set square. It is an isosceles right triangle (“dreieck” is triangle in German) made of transparent plexiglass. It has a removable yellow handle and bumpy feet on the bottom (to make it glide along on a surface). The hypotenuse is 225 mm long and has 1 mm gradations going from -10 mm to +10 mm (with the zero at the midpoint). A 1 cm square grid is inscribed over its face. Along the two equal sides of the isosceles triangle are 1 degree gradations going from 0 to 180 degrees (and back again from 180 to 0), denoting the angle from the hypotenuse at its midpoint. Two lines of sans font proclaim its name and place of origin: “ARISTO TZ-DREIECK 1650 AUSTRIA”.

The TZ-Dreieck is a ruler, a protractor, a square. You can use it to draw parallel lines a set distance apart. You can use it to draw lines of any length at any angle. You can use it to draw rectangles of set width and length. You can use it to bisect angles of unknown magnitude. And you can, obviously, measure distances and angles. Now, you can do all these things with any regular ruler and protractor set; but the TZ-Dreieck is both a ruler and a protractor, it allows you to do these things so much faster, without having to switch tools, without even having to lift it off the surface.

I was required to have the TZ-Dreieck for Professor Michael P. Collins’s CIV102 course on structural engineering. At the time, I was mildly annoyed at the inconvenience of having to purchase yet another useless piece of equipment for a course, oblivious to how much I would come to depend on this little plastic triangle. I owe Professor Collins many wondrous years of plotting and measuring with this tool. (The list of things I owe Michael P. Collins is quite long and ought to be the subject of a future blog.)

I work on the folding and unfolding of thin sheet-like structures. I need to draw and measure lengths and angles on flat surfaces constantly. And with the TZ-Dreieck, I can draw and measure lengths and angles effortlessly. It is a joy to use. It is a marvelous object and volumes of beautiful poetry need to be written about it.

But, like any good love story, this one ends badly. It ends in a ruined TZ-Dreieck — its measuring edge notched and marred. For in my ignorance and stupidity, I used the ruled edge as a guide for a blade. I did this over and over again, ripping out chunks of the TZ-Dreieck every time. I did not know better; to me, it was the most natural thing to line up the edge with where I wanted to cut, press the blade right up against the edge, and… slice. Ugh.

I have lived with my notched set square for seven years, not because I’m the sort of depraved person that enjoys seeing a little squiggle in every attempt at a straight line, but because of the three following reasons. First, a sentimental attachment to the object I purchased seven years ago (I still have the paper packaging sleeve that I tore into the first day I bought it). Second, I could never find anything better. The Rotring Centro Professional Set Square (made by a German competitor) comes close, but it is not the same. Third, the TZ-Dreieck is very difficult to acquire in North America. It’s made in Austria, and sold, it seems, exclusively in Europe.

But at some point last week, something flipped, and I finally bought a new TZ-Dreieck. I had to get it from, and have it be shipped across the Atlantic. It should be here in a few days. And this time, I’ll treat it with the care and attention it deserves.


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