High Quality Content by WIKIPEDIA articles! In mathematics, the Loomis Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a d-dimensional set by the sizes of its (d 1)-dimensional projections. The inequality has applications in incidence geometry, the study of so-called "lattice animals", and other areas. The result is named after the American mathematicians L. H. Loomis and Hassler Whitney, and was published in 1949.