Fancy some Christmas ornaments that defy conventional Euclidean geometry? In these animations, created by mathematician and artist Jos Leys, you can see what Christmas ball patterns would look like in hyperbolic space, a “bizarro world” where parallel lines can intersect and the three angles of a triangle add up to less than 180 degrees.

The different ornament designs show various ways that 2D hyperbolic space can be tiled with polyhedron shapes by varying the Poincaré disc model. Developed by Henri Poincaré of Poincaré conjecture fame these tesselations have also been explored by artist MC Escher in a series of prints.

For more mathematical imagery, check out a gallery of art in the hyperbolic realm, hyperbolic home decoration or visit Leys’ web site. You may also like to watch our series of One-Minute Math animations.

View video here.

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