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Chord of Curvature, Math, Marketing Management

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Definition: If C be the circle of curvature at any point P on a curve, then a chord of C through P in a given direction is called the chord of curvature in that direction.

The Lengths of Chords of Curvature

Case I: Let y = ƒ(x) be any cartesian curve. Draw the circle of curvature at any point P on the curve. Let the tangent at P make and angle ? with the x-axis. Let PQ and PS be the chords of curvature parallel to x-axis and y-axis respectively. Complete the rectangle PQRS. We have PR = 2?. Now,

PQ = 2? cos (90 - ?) = 2? sin ?,

And PS = 2? cos ?.

Hence

The chord of curvature parallel to the x-axis = 2? sin ?,

The chord of curvature parallel to the y-axis = 2? cos ?.

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