## Plus Advent Calendar Door #2: Symmetry

Submitted by Rachel on December 2, 2010When you saw us outside building snow-mathematicians and throwing snowballs we weren't just larking about, honestly! We were actually conducting in-depth research into symmetry and trajectories — and here our results are behind door number 2...

Symmetry rules

Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how the symmetry we admire in a snow flake might also explain the workings of the Universe.

Through the looking-glass

When Alice stepped through the looking glass in Lewis Carroll's *Through the Looking-Glass and What Alice Found There*, she would have found that more than just the writing was back to front. The very molecules that made up her body would have been the wrong way around in the looking-glass world, and their
interaction with the looking-glass molecules would have led to a very confusing — and possibly dangerous — adventure!

Beautiful symmetry provides glimpse into quantum world

A complex symmetric structure known as the *exceptional Lie group E8*, which has so far only existed in the minds of mathematicians, seems to have turned up in real life for the first time in 2010.

They never saw it coming

Borrow mathematical stealth from the military (and insects) to win in your next snowball fight!