Each circumsinusoidal region has two vertices, but the two paths connecting them are distinct curves. Until and unless I find that such regions already have a different name, I am naming these two-dimensional curved shapes “circumsinusoidal regions.” There are four of them per wavelength of the wave, and two per semicircle. Then, however, I became more interested in the discrepancy between the two, represented by the yellow regions which are outside the true wave, and inside the semicircles which contain that wave. My goal was to compare the two curves, simply to see how well one simulates the other (answer: not very well at all). In this case, semicircles could used because I adjusted the wavelength, making it exactly four times the amplitude of the wave. The two sets of curves cross each other at the rest position, and are tangent to each other at each peak and trough, producing four of these yellow regions per wavelength. In addition, each semicircle involved must have a radius equal to one-fourth the wavelength of the sine or cosine wave. (I’m resorting to use of some physics terminology here, simply because I don’t know the corresponding mathematical terms). In order for this to work, to form these yellow regions, the semicircle centers (centers of the circles they are each half of) must be directly below peaks, and above troughs, of the sine (or cosine) curve, and vertically positioned at what would be called the rest position in physics. The inner boundary of the yellow regions above is a sine curve (technically, a cosine curve, but that’s the same thing, just with a phase shift).
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