Roulette

The name of a planar curve considered as the trajectory of a point which is rigidly connected with some curve rolling upon another fixed curve. In case a circle rolls upon a straight line, the roulette is a cycloid; if a circle rolls upon another circle it is a cycloidal curve; if a hyperbola, an ellipse or a parabola rolls upon a straight line it is a Sturm curve (cf. Sturm curves). The trajectory of an ellipse rolling upon another ellipse is called an epi-ellipse. Each planar curve can be considered as a roulette in many ways; for example, any curve can be formed by rolling a straight line upon its evolute.

#### References[edit]

[1] |  A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

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[a1] |  M. Berger, "Geometry" , I , Springer (1987)
[a2] |  H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
[a3] |  M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976) pp. 145
[a4] |  J.D. Lawrence, "A catalog of special plane curves" , Dover (1972) ISBN 0-486-60288-5 Zbl 0257.50002