Analogies from 2D to 3D Exercises in Disciplined Creativity

Carlo H. Séquin

Visual Mathematics, Tome 3 (2001) no. 1.

Résumé

Human creativity reliesto a large part on our ability to recognize and match patterns, to transposethese patterns into different domains, and to find analogies in new domainsto known facts in old domains. In the realm of geometrical proofs and geometricalart, such analogies can carry concepts and methods from spaces that areeasy to deal with, e.g. drawings in a 2-dimensional plane, into higher dimensions where model making and visualization are much harder to carryout. Students in a graduate course on geometric modeling are challengedwith open-ended design exercises that introduce them to this analogicalreasoning and, hopefully, enhance their creative thinking abilities. Examplesinclude: constructing a Hilbert curve in 3D-space, finding an analogousconstellation to the Borromean rings with four or more loops, or developing3D shapes that capture the essence of the 2D Yin-Yang figure or of a logarithmicspiral. The proffered solutions lead to interesting discussions of fundamentalissues concerning acceptable analogies, the role of symmetry, degrees offreedom, and evaluation criteria to compare the relative merits of thedifferent proposals. In many cases, the solutions can also be developedinto attractive geometrical sculptures.

Détail

Classification : 00A66