The complement of a knot is everything in three-dimensional space that isn’t the knot. It’s a topological object—if you wiggle the knot around, then its complement also squishes around. In ...

We'll address those ambiguities later. For the time being, when we think about shape, we're referring to the geometry of space. For example, on a flat surface, the angles of a triangle always add ...

A new degree of polarization to control topological photonic states based on the spin of Möbius rings is provided and a way to tune the topological phase in non-Euclidean space is opened.

It is opportune to remember that Thales Theorem is also a consequence of the famous Postulate 5 of Euclid Book 1: That, if a straight line falling on two straight lines make the interior angles on the ...

A particle’s straight-line path through space can be understood as the sum of all its possible paths. Kristina Armitage/Quanta Magazine. Introduction. By Charlie Wood ... Some physicists dislike ...

Lénárt, I. (2022) The Right Triangle as the Simplex in 2D Euclidean Space, Generalized to n Dimensions. Journal of Applied Mathematics and Physics, 10, 2837-2850. doi: 10.4236/jamp.2022.109189. 1.

The second curve is called “Double Continuous Curvature 3D Curve (DCC3D)” which is built as a concatenation of three straight line segments and two ECb3D curves, allowing to reach an arbitrary ...

A straight line becomes impossible without puncturing the surface of the sphere. Think of it like tunneling through the earth to reach the other side. Even if it were possible, it’s just not practical ...