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Raynor talks with students at the MAA meeting. This means, if you stop to think about it, that the rate of change of the rate of change at any point (the second differential of a sine or cosine curve, to use the mathematical term) is always in negative proportion to its height at that point; it is as if it was being pushed towards the origin by a force proportional to its distance from it. The art and fun becomes everlasting with this trigonometry project.
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