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Curves of Constant Diameter

Published online by Cambridge University Press:  03 November 2016

M. J. Kearsley
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Extract

The literature dealing with curves of constant diameter is not very extensive, and the following notes may be of general interest.

If the distance between parallel tangents to any curve is constant, whatever their common direction, then the curve is a corve of constant diameter. Thus, if p (ψ) is the perpendicular distance from the origin to the tangent to the curve, where ψ is the angle the tangent makes with the positive x-axis, and D(ψ) is the diameter of the curve, that is, the distance between parallel tangents, then

Type
Research Article
Information
The Mathematical Gazette , Volume 36 , Issue 317 , September 1952 , pp. 176 - 179
Copyright
Copyright © Mathematical Association 1952

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