List questions from curves

Published on 29 Sep 2015 - 22:03

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Easy derivation to show that the curvature is $k(t)=\frac{|\alpha'\wedge\alpha''|}{{|\alpha'|}^3}$?

Published on 30 Mar 2026 - 8:58

448

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Do we have to show it for both cases?

Published on 01 Oct 2015 - 16:46

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Curvature of a regular curve is a smooth function of parameter if it does not vanish

Published on 30 Mar 2026 - 8:58

395

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How can the vectors be non-zero and linearly independent?

Published on 02 Oct 2015 - 13:25

291

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Prove that for two continuous curves that "touch" in a single point, the two tangents in that point are equal

Published on 07 Oct 2015 - 8:16

53

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The definition of curve

Published on 07 Oct 2015 - 14:40

823

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Signed curvatures

Published on 28 Mar 2026 - 10:36

10.2k

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Curves with constant curvature and constant torsion

Published on 30 Mar 2026 - 12:23

173

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How to relate between tangents of two parallel curves?

Published on 28 Mar 2026 - 6:15

55

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Published on 08 Oct 2015 - 20:31

66

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Parametrization of intersection of curves

Published on 03 Apr 2026 - 17:36

1.1k

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Parametric line segment in 3-space

Published on 02 Apr 2026 - 21:54

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Published on 01 Apr 2026 - 17:52

225

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Derive curve and equation from points

Published on 13 Oct 2015 - 4:24

List Question

Finding Area under Curve Bounded by both x and y axis.

Easy derivation to show that the curvature is $k(t)=\frac{|\alpha'\wedge\alpha''|}{{|\alpha'|}^3}$?

Do we have to show it for both cases?

Curvature of a regular curve is a smooth function of parameter if it does not vanish

How can the vectors be non-zero and linearly independent?

Prove that for two continuous curves that "touch" in a single point, the two tangents in that point are equal

The definition of curve

Signed curvatures

Curves with constant curvature and constant torsion

How to relate between tangents of two parallel curves?

I want to display a parabola defined by a line and a focus point but I don't get what is expected.

Parametrization of intersection of curves

Parametric line segment in 3-space

Closed periodic curve

Derive curve and equation from points

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