You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
\$ n >= 5\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 39
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 39
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
\$ n >= 5\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 39
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 3039
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 30
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 39
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 30
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.
You want to see how quickly the ratio of two consecutive Fibonacci numbers converges on φ.
Phi, known by the nickname "the golden ratio" and written as \$φ\$, is an irrational number, almost as popular as π and e. The exact value of \$φ\$ is \$\frac {1 + \sqrt 5} 2 = 1.618...\$
The Fibonacci sequence is a recursive series of integers calculated by
$$F_n = F_{n-1} + F_{n-2} \\ F_0 = 0 \\ F_1 = 1$$
Calculate \$φ\$'s value and the ratio \$\frac {F_n} {F_{n-1}}\$. How closely does \$φ\$ match the ratio?
Examples
\$n = 2\$, ratio: \$\frac 1 1 = 1.000\$, compared to \1ドル.618...\$, 0 decimal spots match
\$n = 5\$, ratio: \$\frac 5 3 = 1.666...\$, compared to \1ドル.618...\$, 1 decimal spot matches
Input
1 integer \$n\$ to calculate \$\frac{F_n}{F_{n-1}}\$
Output
1 integer \$x\$, indicating the number of decimal places that match the value of \$φ\$
It is acceptable that the program only works accurately until the float precision limit of the language.
Test Cases
Input -> Output
5 -> 1
10 -> 2
12 -> 2
15 -> 5
20 -> 7
23 -> 7
25 -> 9
50 -> 18
100 -> 30
Tips
Do not round the ratio of \$\frac{F_n}{F_{n-1}}\$
Rounding will give you errors.
Let's look at \$n = 5\$ again.
\1ドル.666...\$ rounds to \1ドル.7\$ and \1ドル.618...\$ rounds to \1ドル.6\$, so 0 is the wrong answer.
Useful information and math.
The limit of the ratios of the consecutive Fibonacci terms as \$n\$ tends to infinity is the golden number \$φ\$. The inverse of this ratio is \$\frac 1 φ\$ which equals to \$φ−1\$.
\$\frac 1 φ = φ -1 \$
\$ \lim_{n \to \infty} \frac{F_n}{F_{n-1}} = φ\$
Winning criterion
Code Golf.