I was listening to someone talking about why mathematicians are so obsessed with pi the other day. They broke it down to what I thought was a fairly simple explanation. Pi is an infinitely complex, seemingly random, never-ending number, and it describes the ratio between the circumference of a circle and its diameter. Since a circle is one of the simplest shapes and pi is one of the most complex numbers, they feel that the complexity of pi must contain the hidden secrets to the simplicity of the universe.
I say that the square root of two is getting a bum rap here. If you measure diagonally, point-to-point across a square, and divide that "diameter" by the length of one side of the square, you get the square root of two. This is an infinitely complex, seemingly random, never-ending number that describes one of the simplest shapes known, and I've never heard of someone calculating the sqare root of two to billions of decimal places.
Don't even get me started on e...
Update: The square root of 2 was recently calculated to 1,000,082 digits. Still not billions, but quite impressive.
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