The average number of normals through a point in a convex body and a related Euler-type identity

@article{Hann1993TheAN,
  title={The average number of normals through a point in a convex body and a related Euler-type identity},
  author={Kathy Hann},
  journal={Geometriae Dedicata},
  year={1993},
  volume={48},
  pages={27-55}
}
Anormal to a convex bodyK at a pointx in the boundary ofK is a ray with endpoint atx, perpendicular to support planeH ofK atx, and contained in the halfspace bounded byH that containsK. This work establishes bounds on the average number ofnormals through a point inK forK a polytope and forK with sufficiently smooth boundary. The integrals used to establish these bounds lead to an Euler-type relation. 

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