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Math Help - don't understand the value of a sum in a curve that has arc length

  1. #1
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    don't understand the value of a sum in a curve that has arc length

    Hi there

    I've got a curve in \mathbb{R}^3:  \gamma(x):=(f(u),0,h(u)) I know that f(x) is always bigger than zero and the parameter x is between 0 and 1.

    Now \gamma has arc length which means

    \int_0^1 |\gamma'| dx=\int_0^1  \sqrt{ f'(x)^2+h'(x)^2 } dx = 1. Well somenone today told me that then

    \sqrt{f'(x)^2+h'(x)^2}=1 must be true. Can someone please explain me why this is true or isn't it true? Yet I don't understand why this has to be equal to 1...

    Regards
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  2. #2
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    Re: don't understand the value of a sum in a curve that has arc length

    a curve is said to be parameterized by arc length if its tangent vector is of unit length.
    Thanks from topsquark
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