Lissajous Curve
Lissajous curves are the family of curves described by the parametric equations
 |  |  | (1) |
 | |  | (2) |
sometimes also written in the form
| |  | (3) |
| |  | (4) |
They are sometimes known as Bowditch Curves after Nathaniel Bowditch, who studied them in 1815. Theywere studied in more detail (independently) by Jules-Antoine Lissajous in 1857 (MacTutor Archive). Lissajous curves haveapplications in physics, astronomy, and other sciences. The curves close Iff
isRational.
References
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 53-54, 1993. Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 178-179 and 181-183, 1972. MacTutor History of Mathematics Archive. ``Lissajous Curves.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Lissajous.html.
- Cylindrical Coordinates
- Cylindrical Equal-Area Projection
- Cylindrical Equidistant Projection
- Cylindrical Function
- Cylindrical Harmonics
- Cylindrical Hoof
- Cylindrical Projection
- Cylindrical Segment
- Cylindrical Wedge
- Cylindroid
- Daisy
- d'Alembertian Operator
- d'Alembert Ratio Test
- d'Alembert's Equation
- d'Alembert's Solution
- d'Alembert's Theorem
- Damped Exponential Cosine Integral
- d-Analog
- Dandelin Spheres
- Danielson-Lanczos Lemma
- Darboux Integral
- Darboux-Stieltjes Integral
- Darboux Vector
- Darling's Products
- Dart