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.
en.wikipedia.org/wiki/G2_%28ma

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!

en.wikipedia.org/wiki/Contact_

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I'm indebted to @johncarlosbaez for his talk about the relation of G2 to the octonions, from which I learned all I know about G2. Find out more here:

math.ucr.edu/home/baez/ball/in

Thanks, John!

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