Question

What's the relationship between $\frac{\text{d}^n\gamma}{\text{d}s^n}$ and $\left(\gamma\circ s^{-1}\right)^{(n)}|_{s(t)}$?

score 87 · Answer 1 · 2018-01-12 20:51:19

87

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What's the relationship between $\frac{\text{d}^n\gamma}{\text{d}s^n}$ and $\left(\gamma\circ s^{-1}\right)^{(n)}|_{s(t)}$?

Published on 12 Jan 2018 - 20:51

score 7.5k · Answer 2 · 2010-11-01 02:29:09

7.5k

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Calculating the height of a circular segment at all points provided only chord and arc lengths

Published on 01 Nov 2010 - 2:29

score 62.8k · Answer 3 · 2011-06-13 11:22:45

62.8k

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What is the length of a sine wave from $0$ to $2\pi$?

Published on 13 Jun 2011 - 11:22

score 459 · Answer 4 · 2011-10-06 01:57:04

459

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Can anyone tell me why the arclength integral is an uppersemicontinuous function on the set of continuously differentiable real-valued functions?

Published on 06 Oct 2011 - 1:57

score 1.2k · Answer 5 · 2011-10-07 03:10:00

1.2k

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Can anyone tell me why the arclength integral is a lower semicontinuous function on the set of continuously differentiable real-valued functions?

Published on 07 Oct 2011 - 3:10

score 4.3k · Answer 6 · 2011-12-12 05:58:19

4.3k

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Rectifiability of a curve

Published on 12 Dec 2011 - 5:58

score 133 · Answer 7 · 2012-02-24 01:34:41

133

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Examples of functions whose arc-length from the origin is given by their derivative

Published on 24 Feb 2012 - 1:34

score 1.1k · Answer 8 · 2013-02-11 08:43:06

1.1k

Views

Helix's arc length

Published on 11 Feb 2013 - 8:43

score 143 · Answer 9 · 2020-08-02 19:08:24

143

Views

Arc length of function - confused about particular u-substitution in integral

Published on 02 Aug 2020 - 19:08

score 53 · Answer 10 · 2020-08-05 21:28:36

53

Views

Finding the function that satisfies to condition that the length of the curve is the same as the volume of rotation around the x-axis

Published on 05 Aug 2020 - 21:28

score 124 · Answer 11 · 2020-08-10 11:56:11

124

Views

Prove: For a smooth curve $C$ parameterized by $r(s)$ where $s$ is arc length,$r′(s)$ satisfies $|r′(s)| = 1$.

Published on 10 Aug 2020 - 11:56

score 1.2k · Answer 12 · 2020-08-11 20:40:19

1.2k

Views

Understanding the formula for curvature

Published on 11 Aug 2020 - 20:40

score 328 · Answer 13 · 2020-08-21 21:27:31

328

Views

Finding coordinates on cubic polynomial with a given arc length and start point

Published on 21 Aug 2020 - 21:27

score 63 · Answer 14 · 2020-08-24 08:08:38

63

Views

Arc length of the curve $x^1=2a\cos t$, $x^2=sint$.

Published on 24 Aug 2020 - 8:08

score 28 · Answer 15 · 2020-08-27 02:34:04

28

Views

For the straight line between points with position vectors a and b, find an explicit unit-speed parameterization.

Published on 27 Aug 2020 - 2:34

List Question

What's the relationship between $\frac{\text{d}^n\gamma}{\text{d}s^n}$ and $\left(\gamma\circ s^{-1}\right)^{(n)}|_{s(t)}$?

Calculating the height of a circular segment at all points provided only chord and arc lengths

What is the length of a sine wave from $0$ to $2\pi$?

Can anyone tell me why the arclength integral is an uppersemicontinuous function on the set of continuously differentiable real-valued functions?

Can anyone tell me why the arclength integral is a lower semicontinuous function on the set of continuously differentiable real-valued functions?

Rectifiability of a curve

Examples of functions whose arc-length from the origin is given by their derivative

Helix's arc length

Arc length of function - confused about particular u-substitution in integral

Finding the function that satisfies to condition that the length of the curve is the same as the volume of rotation around the x-axis

Prove: For a smooth curve $C$ parameterized by $r(s)$ where $s$ is arc length,$r′(s)$ satisfies $|r′(s)| = 1$.

Understanding the formula for curvature

Finding coordinates on cubic polynomial with a given arc length and start point

Arc length of the curve $x^1=2a\cos t$, $x^2=sint$.

For the straight line between points with position vectors a and b, find an explicit unit-speed parameterization.

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