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Given a parametric curve $$x=t\cos t, y=t\sin t, z=at$$ I try to calculate the curvature by using I checked the calculations in WolframAlpha and everythings is ok. I get something like $$\frac{\sqrt{t^4 + 4t^2 + 4 + t^2 a^2 + 4 a^2}}{(t^2 + 2 + a^2)^\frac{3}{2}}$$ I found this exercise in two books and they say the result is $$\frac{2}{1+a^2}$$

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up vote 0 down vote accepted

What books? The curve is a helix whose radius increases over time... obviously this curve can't have constant curvature.

Your denominator should be $(t^2+1+a^2)^{3/2}$, but otherwise your answer matches mine.

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yes, you're right. – user20874 Dec 8 '11 at 15:19

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