- Definition
- Examples
- References
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
- a single point,
- a straight line,
- a full square, and
- any convex set.
The graph of ƒ(x) = |x| has reach zero.
A circle of radius r has reach r.
References
- {{citation
| last = Federer
| first = Herbert
| authorlink = Herbert Federer
| title = Geometric measure theory
| publisher = Springer-Verlag New York Inc.
| location = New York
| year = 1969
| pages = xiv+676
| isbn = 978-3-540-60656-7
| zbl=0176.00801 | mr=0257325
| series = Die Grundlehren der mathematischen Wissenschaften
| volume = 153 }}
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