How do we interpret the fact that all these surprising relationships exist? Why are there so many that we’d never intuitively expect? And what does that tell us?
Beautiful relation between π and the Fibonacci sequence
The sum over the arctan of the odd terms in the Fibonacci sequence is equal to π/4pic.twitter.com/WsXl2zHmwL
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That’s a great question.. in a purely seductive system, shouldn’t coincidences be disturbing?
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Arctan of the reciprocal of the odd terms...
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didn't sound as sexy and the formula spoke for itself
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π/4 = arctan(1) = arctan(1/2) + arctan(1/3) = arctan(1/2) + arctan(1/5) + arctan(1/8) = arctan(1/2) + arctan(1/5) + arctan(1/13) + arctan(1/21) = arctan(1/2) + arctan(1/5) + arctan(1/13) + arctan(1/34) + arctan(1/55) =...
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arctan α + arctan β = arctan [(α+β) / (1-αβ)] arctan α - arctan β = arctan [(α-β) / (1+αβ)]
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Best thing I've seen today!
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Excluding the first odd Fibonacci number phi_1 = 1
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Look at index. Starts at n=1 i.e 3rd fibo number.
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