CHAPTER XII.
CURVATURE OF CURVES.
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,
Fig. 31. |
Fig. 32. |
as applied to curves, means the slope of the curve. But what can mean in this case? Clearly it means the rate (per unit of length ) at which the slope is changing—in brief, it is a measure of the curvature of the slope.
Suppose a slope constant, as in Fig. 31.
Here, is of constant value.