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DÜRER'S SHELL CURVE

Curve studied by Albrecht Dürer in 1525.
See also: http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Curves/Durers.html and K. Fladt p. 236. |

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