Page:Popular Science Monthly Volume 38.djvu/51

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41
MY CLASS IN GEOMETRY.

truths set forth in the lines and figures I had conned as a boy; examples which, had they been presented at school, would certainly have somewhat diminished Euclid's unpopularity. In fullness of time it fell to my lot to be concerned in the instruction of three boys—one of fourteen, the second twelve, the third a few months younger. In thinking over how I might make attractive what had once been my best-enjoyed lessons, I took up my ink-stained Euclid—Playfair's edition. A glance at its pages dispossessed me of all notion of going systematically through the propositions—they took on at that moment a particularly rigid look, as if their connection with the world of fact and life was of the remotest. Why, I thought, not take a hint from the new mode of studying physics and chemistry? If a boy gets a better idea of a wheel and axle from a real wheel and axle than from a picture, or more clearly understands the chief characteristic of oxygen when he sees wood and iron burned in it than when he only hears about its combustive energy, why not give him geometry embodied in a fact before stating it in abstract principle? Deciding to try what could be done in putting book and blackboard last instead of first, I made a beginning. Taking the boys for a walk, I drew their attention to the shape of the lot on which their house stood. Its depth was nearly thrice its width, and a low fence surrounded it. As we went along the road, a suburban one near Montreal, we noticed the shapes of other fenced lots and fields. Counting our paces and noting their number, we walked around two of the latter. This established the fact that both fields were square, and that while the area of one was an acre and a half, that of the other was ten. When we returned home the boys were asked to make drawings of the house-lot and of the two square fields, showing to a scale how they differed in size. This task accomplished, they drew a diagram of the house-lot as it would be if square instead of oblong. With a foot-rule passed around the diagram it was soon clear to them that, if the four sides of the lot were equal, some fencing could be saved. The next question was whether any other form of lot having straight sides could be inclosed with as little fence as a square. Rectangles, triangles, and polygons were drawn in considerable variety and number and their areas calculated, only to confirm a suspicion the boys had entertained from the first—that of lots of practicable form square ones need least fencing. In comparing their notes of the number of paces taken in walking around the two square fields, a fact of some interest came out. While the larger field contained nearly seven times as much land as the other, it only needed about two and a half times the length of fencing to surround it. Taking a drawing of the larger inclosure, I divided it into four equal parts by two lines drawn at right angles to each other. It only needed a moment for the boys to