Last
time...
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