A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look ...

In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions ...

One of differential geometry’s most challenging problems has finally been solved after 150 years, with a closed surface Bonnet pair.

#OctopusEffects, #Blender Here is a tutorial for making a cartoon cupcake for Blender 3.2. Use basic operations to create cups and cakes. The part about the star using the procedure in Geometry Nodes.

In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be overemphasized. Differential geometry ...

Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

Abstract: Geometric algebra has been called a “unified language for mathematics and physics.” Sometimes known as Clifford algebra, it is based on the notion of an invertible product of vectors that ...

Abstract: This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Itô diffusions) can be defined and studied on manifolds. No knowledge is assumed of either ...

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg, and Haudenosaunee peoples. Our main campus is situated on the ...

ABSTRACT: This paper proposes a gauge field theory of gravitation and electromagnetism based on principal and associated bundles, aiming to realize mutual transformations between electromagnetic and ...