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BALANCE SPRING CURVE
Curve presented in the magazine of the Palais de la Découverte without reference, where it is written that it approximates the shape of a balance spring in a clock.
According to Wikipedia, it is rather an Archimedean spiral... 
Polar equation: .
Transcendental curve. 

We get a curve the two ends of which have an asymptotic point, for one of them, and an asymptotic circle for the other.
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© Robert FERRÉOL
2017