Question

Can someone give me a few practical applications of curvature? (kappa)

Answer 1

ever see a bottle rocket go haywire? :)

Answer 2

\[\kappa = \frac{\left|| r'(t) \times r''(t) \right||}{\left|| r'(t) \right||^3}\]

Answer 3

Or, for a non-vector valued function:
\[\kappa = \frac{\left| f''(t) \right|}{(1+[f'(t)]^2)^{\frac{3}{2}}}\]

Answer 4

And, also, can you use anything like this for "tangent spaces"?

Answer 5

ive seen it, but I just aint got the time to recall it; good luck with it :)

Answer 6

All I really know about it is that 1/k=rho (radius of curvature) and you can use that in physics if something is traveling around a curved path that isn't circular.