Thursday, December 22, 2011

Bizarro-world math: Inside out Christmas decorations

If you could take a Christmas ball ornament and mathematically flip it inside out, you might end up with one of the fantastic shapes in this animation, created by mathematician and artist Jos Leys.
The space inside a sphere, as well as the space outside it, is filled with an infinite number of points. To perform an inversion, inside and outside points are matched up, then swapped. By tweaking various parameters, different shapes and patterns can be formed. For example, the shapes in this video assign values close to infinity to points near the centre of the sphere.
When a shape is inverted, it maintains all of the same angles as the original form. This makes the "bizarro" version useful for tackling geometric problems that are too difficult to solve using the original shape.
For more weird math, find out about an exotic seven-dimensional sphere, check out our archive of One-Minute Math animations or visit Leys' web site.

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