G2 shall be my favorite group! Well, for now. For a while. Or maybe for longer. It's the smallest of the exceptional Lie groups. Found 1893 by Élie Cartan. It was he who suggested to think about it in terms of rolling balls.

Picture two spheres, one three times larger than the other. Imagine them rolling on another without slipping nor twisting. Rolling surfaces have their own branch of mathematics: contact geometry!



Fun fact about G2: it's 5-dimensional, but the little ball has only two dimensions of infinitesimal freedom! You could get to any 5d point by navigating as if you were walking on a 2d surface! Orienting a ball by rolling it on the ground is similar...

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