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can some one give me the concept of arc and curvature( related to calculus 3)

Mathematics
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curvature is the rate where the unit vector T turns per unit of length. it is calculated \[k=|dT/ds|\]
if you are given a position, you can find T by dividing the derivative of position over the absolute value of it. it can be looked at as velocity over speed\[r'(t)/|r'(t)|\]
ds refers to arc length parameter for a curve. if you're given a curve r(t)=x(t)i+y(t)j+z(t)k, \[s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt\]

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now, k can be re written as \[k=|(dT/dt)(dt/ds)|\]
hmm.........ok thanx
elica?
the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning
i just finished this class so my explanation might not be detailed enough since i need to understand more but i shared what i can
in which class u r?
calc III just had the finals on monday

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