When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

Abstract: The average distance problem asks to find a good way to approximate a high-dimensional object, represented as a measure, by a one-dimensional object. We will discuss two variants of the ...

There's a good explanation for the eight-foot pit in the center of the lab in Fronczak Hall, UB physicist Sambandamurthy Ganapathy tells a visitor from the Reporter. Slated for installation beneath ...

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to ...

The fields of finite-element analysis, failure analysis, and solid mechanics all express stresses in terms of tensors. Engineering literature usually treats a tensor as a symbol dressed with indices ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

Scheme illustration of object identification and all-optical 3D reconstruction system. (a) A contour surface image of the object can be obtained in a single processing of the system. (b) High-contrast ...

Black holes have a complex shape. Inside, gravity exists in three dimensions. But black holes are also connected to outside particles and magnetic fields that only exist in two dimensions. So how can ...

In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man ...