- References
Weyl's tube formula gives the volume of an object defined as the set of all points within a small distance of a manifold.
Let 
be an oriented, closed, two-dimensional surface, and let 
denote the set of all points within a distance 
of the surface . Then, for sufficiently small, the volume of is
where 
is the area of the surface and 
is its Euler characteristic. This expression can be generalized to the case where is a 
-dimensional submanifold of 
-dimensional Euclidean space 
.
References
- {{cite journal|last=Weyl |first=Hermann |author-link=Hermann Weyl |title=On the volume of tubes |journal=American Journal of Mathematics |volume=61 |year=1939| pages=461–472 |jstor=2371513}}
- {{cite book|last=Gray |first=Alfred |title=Tubes |chapter=An introduction to Weyl's Tube Formula |publisher=Springer Science+Business Media |isbn=978-3-0348-9639-9 |year=2004 |series=Progress in Mathematics, volume 221 |doi=10.1007/978-3-0348-7966-8_1}}
- {{cite web|url=https://golem.ph.utexas.edu/category/2010/03/intrinsic_volumes_for_riemanni.html |first=Simon |last=Willerton |date=2010-03-12 |access-date=2018-03-10 |website=The n-Category Café |title=Intrinsic Volumes and Weyl's Tube Formula}}
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