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FERMAT SPIRAL

Curve studied by Menelaus in the end of the first century and by Fermat in 1636.
Pierre Fermat (1601-1655): French mathematician.

 
Polar equation: .
Cartesian equation: .
Transcendental curve.
Curvilinear abscissa: .

The Fermat spiral is a special case of parabolic spiral.
 
It is a closed curve without double points dividing the plane into two connected regions, symmetrical about O.
The blue region opposite corresponds to .
If the curve is traced only for nonnegative values of , the area between two consecutive coils is constant equal to .

Its inverse with respect to O is the lituus.
 
The curve on which it rolls in such a way that the movement of its centre is linear is a cubic parabola.

Pre-Columbian work, museum of archaeology, Mexico City.


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© Robert FERRÉOL  2017