Abstract
We describe some results on approximation of convex bodies by polytopes. Best and random approximations are considered and compared. The geometric quantities related to the convex body, that appear naturally in such approximation questions are the affine surface areas. Those, and their relation to floating bodies, will be discussed as well.
In this survey we give only a very selective collection of results on approximation by polytopes.
Funding Statement
Partially supported by NSF grants DMS-1811146 and DMS-2103482 and by a Simons Fellowship
Acknowledgments
The author wants to thank the referees for the careful reading and suggestions for improvement.
Citation
Elisabeth M. Werner. "Floating bodies and approximation of convex bodies by polytopes." Probab. Surveys 19 113 - 128, 2022. https://doi.org/10.1214/22-PS5
Information
