If you mean the golden ratio, that's approximately 1.618033988749894848204586834... The exact value is (1 + (square root of 5)) / 2.
The first 10 digits of phi (the golden ratio) are 1.6180339887. Phi is an irrational number, meaning its decimal representation goes on forever without repeating. It is often denoted by the Greek letter φ and can be expressed as (1 + √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.
The first 10 digits of phi (the golden ratio) are 1.6180339887. Phi is an irrational number, meaning its decimal representation goes on forever without repeating. It is often denoted by the Greek letter φ and can be expressed as (1 + √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
Become an initiated brother into Phi Delta Theta and you will learn.
Phi, or the Golden Ratio, is approximately 1.618033988749895. It is an irrational number, meaning its decimal representation is infinite and non-repeating. This value is often encountered in mathematics, art, and nature due to its unique properties.
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.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647 Those are the first 120 digits of Pi
The first 160 digits ( including the 3 ) are... 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128