(x2 + xy + ax - b2)2 = (b2 - x2)(x - y + a)2 Dürer calls the
curve 'ein muschellini' which means a conchoid, but since it is
not a true conchoid we have called it Dürer's shell curve
(muschellini = conchoid = shell). This curve arose from Dürer's
work on perspective. He constructed the curve in the following
way. He drew lines QRP and P'QR of length 16 units through Q (q,
0) and R (0, r) where q + r = 13. The locus of P and P' as Q and
R move on the axes is the curve. Dürer only found one of the two
branches of the curve. The envelope of the line P'QRP 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.
There are a number of interesting special cases: In the above
formula we have: b = 0 : Curve becomes two coincident straight
lines x2 = 0. a = 0 : Curve becomes the line pair x = b/√2, x =
-b/√2 together with the circle x2 + y2 = b2. a = b/2 : The curve
has a cusp at (-2a, a). |Main index||Famous curves index|
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