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
3.14159265358979323846 are the first 20 digits of pi.
The first eleven digits of pi are:3.141592653
3.14159265358979323846264338327 are the first 30 digits of pi.
The first 160 digits ( including the 3 ) are... 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128
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