The determination of convex bodies from the size and shape of their projections and sections

Volume 84 / 2009

Paul Goodey Banach Center Publications 84 (2009), 13-30 MSC: Primary 52A20; Secondary 52A22, 52A38. DOI: 10.4064/bc84-0-1


We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur but appear to be sporadic. In a rather different direction, we will see that combining information about the size of projections or sections with other information such as Steiner points or centres of gravity also leads to complete determination of the original body.


  • Paul GoodeyDepartment of Mathematics
    University of Oklahoma
    Norman, Oklahoma 73019, USA

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