View source for 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|cycloid]]; if a circle rolls upon another circle it is a [[Cycloidal curve|cycloidal curve]]; if a hyperbola, an ellipse or a parabola rolls upon a straight line it is a Sturm curve (cf. [[Sturm curves|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|evolute]].

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Savelov, "Planar curves" , Moscow  (1960) (In Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''I''' , Springer (1987)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR>
<TR><TD valign="top">[a3]</TD> <TD valign="top"> M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall  (1976)  pp. 145</TD></TR>
<TR><TD valign="top">[a4]</TD> <TD valign="top"> J.D. Lawrence, "A catalog of special plane curves" , Dover (1972) {{ISBN|0-486-60288-5}} {{ZBL|0257.50002}}</TD></TR>
</table>