Sturm curves

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[edit]

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

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#### Comments[edit]

Replacing "rolls along a straight line" by "rolls along another fixed curve" , the point will describe a roulette.

#### References[edit]

[a1] |  J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)

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[a2] |  F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971)