One-dimensional curves from algebra, differential geometry and topology. Classic curves as well as new examples and counter-examples. Immersed curves and curves on surfaces. A parametrized curve c in a euclidean 3-space is a map

c : [a, b] -> R3

from an interval [a, b] of the real line into R3, which may have self-intersections or be knotted.

The curves in this model server are often specified as a polygon immersed in a euclidean space Rn.


  1. Egbert Brieskorn, Horst Knörrer: Plane Algebraic Curves, Birkhäuser Verlag, Basel-Boston (1986).
  2. J.D. Lawrence: A Catalog of Special Plane Curves, Dover Publications, New York (1972).
  3. R. J. Walker: Algebraic Curves, Springer Verlag, Berlin-New York (1978).
  4. Alfred Gray: Modern Differential Geometry of Curves and Surfaces, CRC Press (1994).
  5. V. Kommerell, K. Kommerell: Theorie der Raumkurven und krummen Flächen, Walter de Gruyter, Berlin (1931).
  6. MacTutor: Famous Curves Index, University of St. Andrews.

Technical Note

As a guide, polygons should be connected, no degenerate edges, no duplicate vertices.