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On Surfaces Traced out by the Motion of an Invariable Curve

Published online by Cambridge University Press:  03 November 2016

Harold Hilton
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Extract

Suppose that a curve Г of constant shape moves in space so as to trace out a surface Σ. The problem has suggested itself to various authors whether it is possible for Г to be always a line of curvature, geodesic, asymptotic line, etc., on Σ. The following elementary method of solving such problems may be of interest.

Type
Research Article
Information
The Mathematical Gazette , Volume 7 , Issue 103: Special Commemorative Issue , 1913 , pp. 36 - 38
Copyright
Copyright © Mathematical Association 1913

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References

page 37 of note * See Frost’s Solid Geometry, Ch. XXIV

page 37 of note † See Bianchi’s Geometria Differenziale, § 317.