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A lost opportunity

It was in eighth grade, when directly in front of me and to the left of the blackboard was a diagram that looked like this :


There was no explanation, just a simple diagram, the bottom square marked into a grid of 5 squares, the left square a grid of 3 squares, and the right square a grid of 4 squares. There was no explanation and no labeling of the length of the squares -it had to be seen as obvious as to what the lengths were. The result : 180 days of staring at the diagram before me, wondering what lay beneath the surface.

All through high school there was little said about the diagram aside from it appearing in occasional algebraic or geometric exercises. Then in senior year, in a trigonometry class, the diagram appeared again. It looked like this :


But this time the diagram was used in an actual proof, that with difficulty could be followed, but seemed too difficult to retain, and I managed to ignore the proof for years.

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