Understanding the natural geometry of crystals has long fascinated scientists, especially when studying how materials behave at different temperatures and pressures. One major question in this area is ...

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Ф-function technique, a ...

They are commonplace because we learn about two-dimensional versions of these shapes as children: triangles, squares, dodecahedrons, and other convex polygons [a polygon is any flat shape made ...

With this final piece in place, the geometry of convex bodies in high dimensions is now a little less mysterious—although, as always in mathematics, each new slice reveals more questions to explore.

Roger Koenker, Ivan Mizera, Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules, Journal of the American Statistical Association ...

But unlike granular systems, the jamming transition in chain mail can occur on bending or under tensile loading, because of the non-convex shape and interlocking of its structural elements.