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DÜRER'S SHELL CURVE

Curve studied by Albrecht Dürer in 1525.
See also: mathshistory.st-andrews.ac.uk/Curves/Durers/ 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