If you mean the golden ratio, that's approximately 1.618033988749894848204586834... The exact value is (1 + (square root of 5)) / 2.
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.
talic pablo
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
Become an initiated brother into Phi Delta Theta and you will learn.
Which of the following would be considered PHI
phi
The first eleven digits of pi are:3.141592653
3.14159265358979323846 are the first 20 digits of pi.
The first 160 digits ( including the 3 ) are... 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128
3.14159265358979323846264338327 are the first 30 digits of pi.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647 Those are the first 120 digits of Pi
It was digits followed by zero
The first 55 digits of pi after the decimal point are: 3.1415926535897932384626433832795028841971693993751058209