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NOTCHED CURVE
How to notch a curve?
Let h be an nondecreasing odd function on This indentation is then curved as follow: |
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If the central curve is parametrized on Opposite, the case of a circle; the corresponding curve, with polar equation |
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If the parameter t is not proportional to the curvilinear abscissa, the dents do not have the same lengths, as it can be seen in the case of an eight.
Therefore, to get equal dents, the curve has to be parametrized by the curvilinear abscissa. |
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Here is the example of the cycloid, that can easily be parametrized by the curvilinear abscissa. The dents are equal. | ![]() |
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© Robert FERRÉOL 2017