Question

I dont understand when to use which of the following Formulas for computing the signed curvature. As far as I understand there are two different foruma:

$イ^$

but how do we know when to use which formula?

det (γ', γ" ) イ^

Answer 1

• The first formula is to be used when the curve is given parametrically in Cartesian co-ordinates as γ(t) = (x(t),y(t)).
• And the 2nd formula is to be used when the curve is given in polar co-ordinates as γ= r(θ), where the prime in the formula refers to differentiation with respect to θ.