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YouTubeThe WE-Heraeus International Winter School o…
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Walk a vector around a triangle on a sphere. 🌐➡️↩️ It comes back ROTATED 90°. But the vector never turned — the SPACE did. This is called parallel transport, and the rotation angle measures something profound: curvature itself. On a flat plane, a vector always returns unchanged. On a sphere, it doesn't. That gap IS Gaussian curvature. This one idea underlies general relativity, gauge theory, and the entire field of differential geometry. ✨ #math #mathematics #differentialgeometry #curvature #pa
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Walk a vector around a triangle on a sphere. 🌐➡️↩️ It comes back ROTATED 90°. But the vector never turned — the SPACE did. This is called parallel transport, and the rotation angle measures something profound: curvature itself. On a flat plane, a vector always returns unchanged. On a sphere, it doesn't. That gap IS Gaussian curvature. This one idea underlies general relativity, gauge theory, and the entire field of differential geometry. ✨ #math #mathematics #differentialgeometry #curvature #pa
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