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Curvature, Radius of curvature

The curvature of a parametric curve (x(t), y(t)) is

MATHand its radius of curvature is r = 1/k.

This is the radius of a circle that is the best fit to the curve at the point (x(t), y(t)).

circle of best
              fit
r = 1 - 2 cos θ



A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Osculating circle


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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