The link between mathematics and kirigami

In a recent study, researchers at Harvard University set out to understand the mathematical principles underlying kirigami, which is a variation of origami and an old Japanese cultural tradition. They were able to come up with a mathematical model allowing them to cut a kirigami sheet of paper in a way in which it ‘can be moulded into just about any 3D shape’.

Kirigami, also known as origami’s lesser-known cousin, relies on cutting paper instead of folding it, with ‘kiri’ meaning ‘cut’ and ‘kami’ standing for ‘paper’. The study’s team sought to uncover the basic mathematical principles underlying kirigami, using them to create algorithms which allowed for the design of the number, size and orientation of the cuts in a flat sheet, thus ensuring it could morph into any given shape. For the study, they solved this problem by first identifying the constraints which must be satisfied in order to achieve such a cut pattern, using a numerical optimisation approach to determine the patterns, and finally verifying this experimentally.

Their mathematical framework is thought to be able to turn any sheet of material into any shape using kirigami cuts. The team is confident their work is ‘just the beginning of a class of new ways to engineer shape in the digital age using geometry, topology, and computation’. Further, they believe their work may potentially be used to ‘apply the tradition of kirigami to engineering by creating flexible construction shapes’. Such work is said to draw ‘on inspiration from art, tempered by the rigor of mathematics, and the challenges of engineering shape’.

Applicants for Mathematics, as well as those applying for Engineering might reflect on how such a peculiar link, between the topics of art, design, and mathematical principles, might be beneficial for future innovative applications, for example by using such findings for concepts such as ‘creating foldable shelter and housing’.