If you mean the golden ratio, that's approximately 1.618033988749894848204586834... The exact value is (1 + (square root of 5)) / 2.
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Pi is infinite & digits never end. 3.14159 are amongst the first. * * * * * The answer given above is for pi. The question was about phi - which is usually used to indicate the Golden Ratio! Like pi, phi is irrational - but unlike pi, is not transcendental. Phi = [1 + sqrt(5)]/2 = 1.61803 approx.
After the first few numbers in the Fib sequence, Fib(n) is very nearly equal to (phi)n / sqrt(5) where phi is the Golden Ratio = [1+sqrt(5)]/2 [The difference is around 0.00003 by Fib(20)] So you want the smallest n such that (phi)n / sqrt(5) ≥ 10999 Taking logs, n*log(phi) - 0.5*log(5) ≥ 999 n*log(phi) ≥ 999 + 0.5*log(5) = 999.349 n ≥ 999.349/log(phi) = 999.349/0.2090 So n = 4781
The first eleven digits of pi are:3.141592653
Check out the Joy of Pi link, for the first 10000 digits.
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