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thin material sheets embedded in
space
have preferred distance between
material points: metric
have energy cost S to alter this
distance
have energy cost B to bend: c1, c2
gaussian curvature (c1c2)
creates stretching
sheets ¨ unstretchable as thickness h ¨ 0: c1c2 ¨0
1/c2
1/c1
confinement of thin sheets
creates embedding singularities
vertex
ridge
ridges hold nearly all of
elastic energy
thickness << width
<< length
vertices: stretching lives in
core region
scaling of core size with
thickness is puzzling
ridges spawn boundary ridges