Rational Approximations for Phi

“If I get the next two digits right, I’ll be ecstatic!” Simon says, as he hurries on with a φ (Phi) approximation algorithm using Fibonacci numbers. He keeps dividing every following Fibonacci number by the previous one and eventually gets quite a good Phi approximation a precision of 6 digits! This experiment is inspired by Mathologer, who applied this algorithm to approximate both Pi and Phi and show how “wildly less irrational Pi is than Phi”, Simon says. Simon calculated more terms for Phi though.

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