Is You Is…

…or is you ain’t…

in this case – a simple triangle. Sum of internal angles is 180 degrees. Simple…

Learning geometry in junior school, pencil and paper. Ruler for straight lines. Pencils sharpened to the pointiest points. 180 degrees is the ‘answer’ we were supposed to get. Any more, any less, and we were wrong. More or less than 180 degrees, the lines don’t meet, except at infinity. But infinity was not given as an option. Only right and wrong.

We are given protractors, our first encounter with mathematical measuring tool beyond the simple rule – the key to measurement in one dimension. The protractor opened the possibilities on two, defined by an angle between lines. We drew triangles in our exercise books, and measured their angles. Our sharpest pencils, our most careful lines. We measured them. Their internal angles measured 179 or 181. We must have drawn them wrong! Out came the erasers and lines were redrawn. 179 and a bit, 182… Oh dear, we hadn’t drawn a proper triangle – perhaps the geometry of the exercise book precluded the perfection of the Greek ideal, or more likely – we had made a mistake. Rubbetty rub, the paper wore thin as we got closer and not quite closer to the triangle the teacher had told us  should be 180 degrees. We had drawn it wrong. We had failed. Not once did the teacher provide insight into the imperfection of measurement, and the idealness of ideals.

In the end, we cheated. We recorded one angle a little bigger, another a little smaller. One hundred and eighty! It took a whole lesson for us to get our ‘triangles’ perfect. We did not question the principles because we did not really understand them, but we understood our fallibility, believing in this above any lesson taught by the teacher. The greater lesson was missed by all. Maybe our imperfect triangles worked at infinity.

 

 

 

 

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