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IEVref: | 102-04-18 | ID: | |

Language: | en | Status: backup | |

Term: | length (of a curve) | ||

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Definition: | least upper bound, if it exists, of the lengths of any polygonal lines determined by successive points of the curve between the two points corresponding to the limiting values of the parameter interval NOTE 1 For a curve from A to B defined by the position vector $r=f(u)$ as a function of the parameter NOTE 2 In the usual geometrical space, the length of a curve is a quantity of the dimension length. | ||

Publication date: | 2007-08 | ||

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NOTE 1 For a curve from A to B defined by the position vector $r=f(u)$ as a function of the parameter *u* in the given interval [*a*, *b*] where $a\le b$, the length of the curve is the line integral $\underset{\text{A}}{\overset{\text{B}}{\int}}\left|\mathrm{d}r\right|}={\displaystyle \underset{a}{\overset{b}{\int}}\left|\frac{\mathrm{d}f}{\mathrm{d}u}\right|\mathrm{d}u$.

NOTE 2 In the usual geometrical space, the length of a curve is a quantity of the dimension length.

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