These curves appear in Dürer's work *Instruction in Measurement with Compasses and Straight Edge* (1525) and arose in
investigations of perspective. Dürer constructed the curve by drawing lines and of length 16 units through
and , where . The locus of and is the curve, although Dürer found only one of the two
branches of the curve.

The Envelope of the lines and is a Parabola, and the curve is therefore a Glissette of a point on a line segment sliding between a Parabola and one of its Tangents.

Dürer called the curve ``Muschellini,'' which means Conchoid. However, it is not a true Conchoid and so is sometimes called Dürer's Shell Curve. The Cartesian equation is

The above curves are for , , . There are a number of interesting special cases. If , the curve becomes two coincident straight lines . For , the curve becomes the line pair , , together with the Circle . If , the curve has a Cusp at .

**References**

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 157-159, 1972.

Lockwood, E. H. *A Book of Curves.* Cambridge, England: Cambridge University Press, p. 163, 1967.

MacTutor History of Mathematics Archive. ``Dürer's Shell Curves.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Durers.html.

© 1996-9

1999-05-24