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ORTHOPOLAR OF A CURVE WITH RESPECT TO TWO LINES
Notion studied by Henri Lazennec in 2015.
Homemade name. |
Given two secant lines When the point In the following, we take the orthogonal lines Therefore, we have the simple result in polar coordinates: |
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The orthopolar with respect to the axes of the curve |
Examples (initial curve in blue, orthopolar in red):
The orthopolars of lines that do not pass by O are the strophoids.
More precisely, the orthopolar with respect to the axes of the line |
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The orthopolar of a circle centred on O is a quadrifolium. |
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The orthopolar with respect to the axes of the circle passing by O For |
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... and for |
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An example with a circle that does not pass through O. |
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The orthopolar of the cross-curve |
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© Robert FERRÉOL 2017