Renaissance Banff: Mathematics, Music, Art, Culture (2005)

Pages 339–342

Venn diagrams are familiar to anyone who has taken high school algebra. The standard two- and three-circle Venn diagrams have a pleasing look. This stems partly from their symmetries. As customarily drawn, each has a horizontal mirror symmetry. The two-circle diagram also has a second, vertical mirror symmetry. In addition to these, each diagram also has rotational symmetry: The two-circle diagram is invariant under rotation by 180 degrees around a point inside the lens-shaped intersection of the circles, while the three-circle diagram is invariant under rotation by 120 degrees around a point inside its triple-intersection region.

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