What is the arclength between two points on a curve? How does it differ from the distance?

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What is the arclength between two points on a curve? How does it differ from the distance?

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Answer 1 · 2015-11-08T20:35:02

The distance is the arc length on a straight line. The arc length is the distance along the arc.

Explanation:

Example

For the points $(- 1, 0)$ $(-1,0)$ and $(1, 0)$ $(1,0)$ ,

the distance between the points (the length of the straight line joining them) is $2$ $2$ .

The length of the arc on the unit circle: $x^{2} + y^{2} = 1$ $x^2+y^2=1$ is half the circumference, so it is $π$ $pi$ . (More completely, the lengths of both the upper and lower arcs are $π$ $pi$ .)

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What is the arclength between two points on a curve? How does it differ from the distance?

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