From a mathematical point of view the Japanese art of Origami is an art of finding isometric injections of subsets of . Objects obtained in this manner are developable surfaces and they are considered to be fully understood. Nevertheless, until now it was not known whether or not the local shape of the Origami model determines the maximum size and shape of the sheet of paper it can be made of. In the present paper we show that it does. We construct a set
containing the point
and an isometry
such that for every neighborhood
of the point
and for every
and
restricted to
cannot be extended to an isometry of the set
into
We also prove that all the singularities of an Origami model are of the same type -- there can appear only cones.
By: Tomasz Maszczyk, Grzegorz Swirszcz
Published in: RC24313 in 2007
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .