Advertisement

Curvature of Curves

  • Silvanus P. Thompson
  • Martin Gardner
Chapter

Abstract

Returning to the process of successive differentiation, it may be asked: Why does anybody want to differentiate twice over? We know that when the variable quantities are space and time, by differentiating twice over we get the acceleration of a moving body, and that in the geometrical interpretation, as applied to curves, \(\frac{{dy}}{{dx}}\) means the slope of the curve. But what can \(\frac{{{d^2}y}}{{d{x^2}}}\) mean in this case? Clearly it means the rate (per unit of length x) at which the slope is changing—in brief, it is an indication of the manner in which the slope of the portion of curve considered varies, that is, whether the slope of the curve increases or decreases when x increases, or, in other words, whether the curve curves up or down towards the right.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Martin Gardner 1998

Authors and Affiliations

  • Silvanus P. Thompson
  • Martin Gardner

There are no affiliations available

Personalised recommendations