A new nanoscale structure of carbon has joined the family. With no curve at all, carbon atoms form a flat sheet known as graphene, and a positive curvature creates the soccer ball-like structure ...

In a hypertorus model of the Universe, motion in a straight line will return you to your original location, even in an uncurved (flat) spacetime. The Universe could also be closed and positively ...

Nucleation and growth is the dominant relaxation mechanism driving first-order phase transitions. In two-dimensional flat systems, nucleation has been applied to a wide range of problems in physics, ...

THIS is an interesting contribution to the subject treated of by Riemann, Helmholtz, and others, and in this country by Prof. Clifford. The question is considered from the standpoint of elementary ...

Let G be a connected graph that is 2-cell embedded in some surface. For a vertex v and a face f of G, let deg(v) denote the degree of v and let deg(f) denote the size of f. We define the combinatorial ...

Try gift-wrapping a soccer ball, and you will quickly encounter the geometric abyss between paper’s inherent flatness and a sphere’s natural curves. “The very first bit seems to sort of match, but as ...