DescriptionThe Japanese techniques of paper folding (origami) and cutting (kirigami) offer means to approximate complex curved shapes in 3 dimensions. This technique has gathered momentum recently because it has become possible to transform planar sheets to 3-dimensional shapes across a range of scales, with a variety of industrial applications. For instance, self-folding robots and stretchable electronics.Although origami techniques have been exploited in engineering for quite a while, the great potential of kirigami has only started being appreciated. A deep understanding of the underlying mathematics and mechanics of kirigami structures remains to be achieved to unnlock the full potential of kirigami structures. This project starts by exploring the links between differential geometry, origami and kirigami, in particular the precise notion of surface curvature. The emphasis of the project will be tailored to each student. For instance, one could ask about the advantages and disadvantages of the two techniques in developing new materials, study lattice kirigami or explore geodesics and isometric immersions in kirigami.
PrerequisitesThe core Mathematics modules are prerequisites, and choosing Differential Geometry III (MATH3021) is a good idea.Resources- N. Wolchover, Scientists conjure curves from flatness, Quanta magazine.- S. Callens and A. Zadpoor, From flat sheets to curved geometries, Materials Today, Volume 21, Number 3 (April 2018); available online from DU Library. - Dudte, L., Vouga, E., Tachi, T. et al. Programming curvature using origami tessellations. Nature Materials 15, 583–588 (2016); available online from DU Library. - Choi, G.P.T., Dudte, L.H. & Mahadevan, L. Programming shape using kirigami tessellations. Nature Materials 18, 999–1004 (2019); available online from DU Library. - J. Conway, P. Doyle, J. Gilman and B. Thurston, Geometry and the Imagination, Section 35 on curvature of surfaces. - D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, Chelsea Publishing, 2nd edition (Section 28 on the curvature of surfaces); book available at DU Main Library but no online access. - Q. Han, M. Lewicka and L. Mahadevan, Geodesics and isometric immersions in Kirigami Further resources will be avaible to those choosing this project. |
email: Anne Taormina