# Approximation of total curvature

fishingspree2
Hello, I am trying to find an interpolating curve between a few points that has minimal curvature. That means, as close to a straight line as possible.

$$\kappa \left ( x \right )=\frac{|f''\left ( x \right )|}{\left ( 1+\left [ f'\left ( x \right )^{2} \right ] \right )^{\frac{3}{2}}}\approx |f''\left ( x \right )|$$

Why are they able to say that? Is there any proof or explanation? Thank you very much