| Date: | Tue, 19 Feb 2008 |
| From: | Denis Chebikin |
| Subject: | SPAMS Thursday 5pm in 4-231 |
Hi everybody,
This week Po-Ru will tell us about many fancy ways to bend a sheet of
paper - an exciting topic as I'm sure many of you remember from last
spring! There will be dinner after the talk in 2-349.
See you there!
Denis, on behalf of the 2007-08 SPAMS organizers
Non-Planar Paper: Flat with Flair
What kinds of surfaces can one form from a sheet of paper? If only
bending is allowed -- i.e., the paper must remain smooth -- the answer
is "developable surfaces." Such surfaces are well-studied in
differential geometry and not hard to characterize. On the other hand,
if arbitrary creasing is allowed, much more general behavior can occur;
hence, little can be said about these "applicable surfaces." To
convince yourself of this, find a paper you are tired of reading and
crumple it into a ball. (For added stress-relief, throw it in the trash
or at your office-mate.)
In between these two extremes lies the world of piecewise-developable
surfaces, which will be the main topic of this talk. We will begin by
reviewing the basic geometry of intrinsically flat surfaces which arises
in studying developables. Then, applying our tools, we will explore
some elementary but surprising results concerning the geometry of
straight and curved creases. Finally, we will view some curved origami
eye-candy that illustrates these effects in "real life."
Paper will be provided free of charge for a hands-on experience, though
attendees assume the risk of paper cuts and all complications thereof.