Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



SO(2)-congruent projections of convex bodies with rotation about the origin

Author: Benjamin Mackey
Journal: Proc. Amer. Math. Soc. 143 (2015), 1739-1744
MSC (2010): Primary 52A15
Published electronically: December 9, 2014
MathSciNet review: 3314085
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if two convex bodies $K, L \subset \mathbb {R}^3$ satisfy the property that the orthogonal projections of $K$ and $L$ onto every plane containing the origin are rotations of each other, then either $K$ and $L$ coincide or $L$ is the image of $K$ under a reflection about the origin.

References [Enhancements On Off] (What's this?)

  • Richard J. Gardner, Geometric tomography, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, New York, 2006. MR 2251886
  • V. P. Golubyatnikov, Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data, VSP, 2000.
  • Don Koks, Explorations in mathematical physics, Springer, New York, 2006. The concepts behind an elegant language. MR 2253604
  • Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 52A15

Retrieve articles in all journals with MSC (2010): 52A15

Additional Information

Benjamin Mackey
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Received by editor(s): September 18, 2013
Published electronically: December 9, 2014
Additional Notes: This research was supported in part by the NSF Grant, DMS-1101636
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society