Margaret Wertheim speaks at TED about the beautiful mathematics of coral reefs, hyperbolic geometry, and more. In particular, I liked her bit (around the 8-minute mark) where she says that if zero and one are already possible answers, then mathematicians would become immediately suspicious that infinity might be one too (think, how many ways can two lines intersect). She also discusses the inability to see a principle when it is right in front of your face (like the hyperbolic geometry in leafy lettuce).
Margaret Wertheim on the Beautiful Mathematics of Coral Reefs
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