Reach (mathematics)

In mathematics, the reach of a subset of Euclidean space Rn is a real number that roughly describes how curved the boundary of the set is.

Definition

Let X be a subset of Rn. Then reach of X is defined as

Examples

Shapes that have reach infinity include

The graph of ƒ(x) = |x| has reach zero.

A circle of radius r has reach r.

References

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