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The profiles of the edge of rectangular sheets of paper folded so as to join opposite edges were measured and compared with the profiles calculated with the theory of elasticity. I show how the calculation can be accomplished by using the aspect ratio of the loops as the only input parameter. [ABSTRACT FROM AUTHOR]

A quandle is a set with a self-distributive binary operation satisfying a certain condition. Here we construct a monoid (a semi-group with the identity) associated with a quandle. This monoid has a structure of a quandle, which contains the original quandle as a sub-quandle. We call it the enveloping monoidal quandle. The purpose of this paper is to introduce the notion of the enveloping monoidal quandle, and to investigate it. [Copyright &y& Elsevier]