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Into my limited mathematical capacity has finally dawned the connection between a sine wave and a circle. Though my husband, who speaks fluent calculus, cannot grasp the possibility that anyone could grow up without knowing about this, I toddled happily through most of my life so far without any apparent deficit. It was brought home to me not by a need for a trigonometric function, but by a study of sound waves.
Want to see? Draw plus sign (+, or, “x and y axes,” if you will). Now, stick a right triangle with one of its corners at the intersection of those two lines. Next, imagine that triangle stuck (at the origin, (0,0), that intersection) with a brad so it can spin freely (wheee, a pinwheel!). Pick one of the free corners to keep your eye on as it hits the y axis. The circle that it makes, if plotted out to the right over time (watch that corner rise toward the vertical, then lower toward the horizontal, then rise again as the triangle returns to its original position), undulates gracefully over, through, and under the horizontal x axis with perfect regularity, as each high and low point (where the triangle hits the vertical axis as it passes, spinning, through it) is plotted. The ‘hills’ and ‘valleys’ of that wave keep making perfect copies of the circle described by that triangle – stretched out over time (put a hill on top of a valley for a circle, and imagine that triangle spinning around pinned at its center.
Anyway, like it or not, as mathematics, this can still sing to you as poetry! Alex Bellos’s The Grapes of Math will help!
As we go round and round in our daily lives (stuck in a particular place, maybe?), a lovely wave is described that could rightly be called our song (because sound waves have this pattern, remember?). Slow turning = deeper sound, longer stretches of time before the circle pattern repeats. Have patience with slowness, please, because through it, the deep, bass notes of your being are cultivated and the profound and hidden riches of your song are issuing forth into the world.
Do take time to get your mind out of the math classroom, and contemplate this!