Two tree frogs folded from uncut squares.
Mathematics is an essential tool in creating origami. The problem of turning paper into body parts of animals can often be expressed as circle packing problems. One can also use optimisation algorithms to determine the best ways to arrange creases such that it is both physically possible to fold the paper, as well as ensuring the final model is aesthetically pleasing. For example, in the frogs, surprisingly, the centre of the square becomes the tip of the nose – as it is most effective to allocate paper at the corners to the limbs.
The models were designed by the artist Satoshi Kamiya and folded by Maximilian Purewal, from Kamiya’s diagrams.
Max is a Mathematics Undergraduate in the Mathematical Institute, University of Oxford.