Difference between revisions of "Sturm curves"
From Encyclopedia of Mathematics
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| − | Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the | + | {{TEX|done}} |
| + | Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the $x$-axis — a [[Catenary|catenary]]. | ||
These curves were studied by J.Ch. Sturm. | These curves were studied by J.Ch. Sturm. | ||
Latest revision as of 11:44, 5 July 2014
Transcendental curves in the plane, described by a point associated with an ellipse, hyperbola or parabola, as it rolls along a straight line. An example of a Sturm curve is the trajectory of the focus of a parabola as it rolls along the $x$-axis — a catenary.
These curves were studied by J.Ch. Sturm.
References
| [1] | A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) |
Comments
Replacing "rolls along a straight line" by "rolls along another fixed curve" , the point will describe a roulette.
References
| [a1] | J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) |
| [a2] | F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |
How to Cite This Entry:
Sturm curves. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sturm_curves&oldid=32373
Sturm curves. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sturm_curves&oldid=32373
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article