Nash embedding theorem
- Yuki
- Jul 22
- 1 min read
"Curved space can be embedded into a higher-dimensional, ordinary Euclidean space without disrupting its distance or curvature."
C1 Embedding Theorem
Within the range of first-order differentiability, it can be embedded in surprisingly low dimensions. However, very fine waves and wrinkles may appear on the surface.
Smooth embedding theorem
While it's always possible to embed the image while maintaining smoothness, it requires a higher level of precision.
A theory that translates the unique distances, circulation paths, and curvatures set within a building into the complex three-dimensional shapes of the external space.
A cultural hall whose outer shell has acquired an almost infinite number of folds in order to maintain internal distance.
A cross-section that connects the different distance relationships between the external shape and the internal space through subtle vibrations of the outer shell.
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