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Results tagged with curves-and-surfaces
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user 32389
A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
14
votes
If a triangle can be displaced without distortion, must the surface have constant curvature?
Already Riemann in his famous "On the Hypotheses Which Lie at the Bases of Geometry" concludes that the spaces of constant curvature are precisely those in which figures can move without distortion. H …
- 16.5k
1
vote
Surfaces contained in a ball
Sufficient conditions, in terms of geometric invariants of the domains, such as volumes, surface areas and curvature integrals of the boundaries of domains, under which one domain can be moved by an …
- 16.5k