Equidistant Curve

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Equidistant Curve

 

The set of the ends of equal segments laid off in a fixed direction along the normals to a given plane curve L is known as an equidistant curve of L. For example, an equidistant curve of a circle is a circle. In Lobachevskian geometry an equidistant curve of a straight line—that is, the locus of points at a given distance from the line—is called an equidistant curve (with that line as base) or, less frequently, a hypercycle. In Euclidean geometry an equidistant curve of a straight line is a straight line.