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Using Playing Cards in the Study of Group Theory

Rotating & reflecting triangles, squares, and other geometrical objects is fun . . . for a minute or two. But, wouldn't you rather explore the amazing principles of Group theory in a far richer and infinitely more enjoyable venue? Showing your friend how rotating a square 90 degrees leaves it "unchanged" will elicit (at best) a shoulder shrug. Imagine, instead, showing your friend an “unmixable” packet of playing cards (despite countless random choices)—which will almost certainly elicit a "How is this even possible?!"

Symmetry group of a Square: The Dihedral Group of Order 8