Nafay Qazi

Proof of T-duality within Euclid's Geometry

Euclidean geometry contains an exact duality of scale. For the round 2-sphere S2R of radius R, both ends of the scale parameter R carry the Euclidean plane: as R → 0 the sphere collapses to a point whose tangent plane is Euclidean, and as R → ∞ the local geometry is Euclidean. Th...

Proof of T-duality within Euclid's Geometry

Euclidean geometry contains an exact duality of scale. For the round 2-sphere S2R of radius R, both ends of the scale parameter R carry the Euclidean plane: as R → 0 the sphere collapses to a point whose tangent plane is Euclidean, and as R → ∞ the local geometry is Euclidean. Th...