Nicomedes

Conchoid of Nicomedes

1) Draw a straight line a.
2) Fix a point A, not on a.
3) Fix a segment of length d.
4) Consider a point B, moving on a.
5) Construct the points X, Y , on AB, such that XB=BY = d.
6) The locus of X, Y , for B moving on a, is the conchoid of Nicomedes.

Modify the length of segment d, to see the various shapes this curve takes.

Its polar equation: r = a*sec(u) + k.
Its Cartesian equation: k^2*x^2 = (a-x)^2(x^2+y^2).

More General Conchoids: Replace the line a with an arbitrary curve and make the same constructions. F.e. a circle, a conic section, etc.

For the construction of the conchoid through the [implicit function tool] look at file: Nicomedes2.html .

http://users.math.uoc.gr/~pamfilos/