A helix is also called a Curve of Constant Slope. It can be defined as a curve for which the Tangent makes
a constant Angle with a fixed line. The helix is a Space Curve with parametric equations

(1) | |||

(2) | |||

(3) |

where and are constants. The Curvature of the helix is given by

(4) |

(5) |

(6) |

so

(7) |

(8) |

(9) |

The Minimal Surface of a helix is a Helicoid.

**References**

Geometry Center. ``The Helix.'' http://www.geom.umn.edu/zoo/diffgeom/surfspace/helicoid/helix.html.

Gray, A. ``The Helix and Its Generalizations.'' §7.5 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 138-140, 1993.

Isenberg, C. Plate 4.11 in *The Science of Soap Films and Soap Bubbles.* New York: Dover, 1992.

Pappas, T. ``The Helix--Mathematics & Genetics.'' *The Joy of Mathematics.* San Carlos, CA: Wide World Publ./Tetra,
pp. 166-168, 1989.

Wolfram, S. *The Mathematica Book, 3rd ed.* Champaign, IL: Wolfram Media, p. 163, 1996.

© 1996-9

1999-05-25