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Distance - Path Length

line segments indicates sign

The other meaning of distance is the length of a path. This is easily understood if the path consists entirely of line segments, such the perimeter of a pentagon. The distance is the sum of the lengths of the line segments that make up the perimeter. For curves that are not line segments, a continuous path can usually be approximated by a sequence of line segments. Using shorter line segments produces a better approximation. The limiting case, when the lengths of the line segments go to zero, is the distance. A common example would be the circumference of a circle, which is a distance.

Kristin Lewotsky

KEY TERMS

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Absolute distance

—The displacement between two points, independent of orientation.

Hessian normal form

—A definition of a line such that the line cuts the plane into positive and negative regions; this form attaches sign (+/-) to distance so that a distance measurement indicates displacement and orientation of the measured object from the line.

Oriented distance

—A distance that indicates direction by sign.

Path length

—The length of a path, generally determine by calculus.

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