Article July 16, 1904 Issue

Making our Demonstration

MORRIS WEBER.

At the end of a fruitful year of study in geometry, our teacher drew an unusual diagram on the blackboard and wrote down certain propositions connected therewith, and told us to prove them. None of us was equal to the task, so he gave us two weeks' time to work out the problem, and said, "Now I know those propositions are true, that they can be proven, and that you understand the principle of mathematics sufficiently to convince yourselves of their truth."

The first night we were all very eager to work. Forgetting all other lessons, we studied on that problem till midnight, looking up references and rules that we had forgotten, but all to no avail. The solution began to look impossible, and some ventured to affirm that our teacher had only played a huge joke on us, and was trying to make us study up our old lessons; that the conclusions he had drawn were false, hence could not be proven. For some days a few of us kept on trying, but finally only three remained who were convinced of the correctness of our teacher's assertions and that it was possible for us to work out the proof.

That day we three came together again and spent the better part of the night in trying to solve the problem by a united effort, but we failed again, this time because each of us thought that the methods of the others were erroneous, misleading, and fruitless, so each one of the three took up the task individually, and we finally did find the propositions to be true. Then the teacher asked us to prove them to the rest of the class. It was interesting to discover that, starting from the simplest propositions in geometry, we had reached one correct conclusion after another, and depending ever on the one basic law we had brought out the proof of the original proposition. It was a long and circuitous way, but the teacher let us alone till we had made the demostration after our own method. Then stepping to the blackboard, he solved the problem and made the diagram clear with a few well-defined lines.

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