Namespaces
Variants
Actions

Difference between revisions of "Roulette"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
m (→‎References: expand bibliodata)
Line 10: Line 10:
  
 
====References====
 
====References====
<table><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, reprint (1972)</TD></TR></table>
+
<table>
 +
<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>

Revision as of 16:41, 11 December 2017

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

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


Comments

References

[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
How to Cite This Entry:
Roulette. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Roulette&oldid=42495
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article