SHAPES OF RECTANGULAR PRISMS AFTER REPEATED

The shape of a rectangular prism in (d + 1)-dimensions is defined as Y= (Yls Y2, *, Yd), Yn=Ln/Ln+l where the Ln are the prism's edge lengths, in ascending order. We investigate shape distributions that are invariant when the prism is cut into two, also rectangular, prisms, with one prism retained for measurement and the other discarded. Interesting new distributions on [0, l]d arise.