Plane to Torus

physicsstring theorytopologygeometryfundamental domainperiodicitysymmetriescompactificationtikz

Visualization of how a rectangular region of the plane becomes a torus through periodic boundary conditions. The diagram shows the identification of opposite edges and the resulting fundamental domain, a key concept in string theory compactification where spatial dimensions are "curled up" into compact geometries. This construction helps understand modular transformations and the origin of winding modes in string theory.