Given a fixed point A(a,0) and a constant b > 0, let a line (PQ) vary in such a way that P describes Ox and Q describes Oy, with ; Dürer's shell curve, that the engraver had designed from an articulated system, is the locus of the points M on the line (PQ) such that PM = b.
 

Parametric system:  (). Cartesian parametrization 1: . Cartesian parametrization 2:  (). Cartesian equation: . Rational bicircular quartic.

The parametric system above shows that Dürer's shell curve is the projection on xOy of the biquadratic, intersection of the elliptic cylinder  with the hyperbolic cylinder .
 

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© Robert FERRÉOL  2017