trigonometry - What is the connection and the difference between the ...
4 Dec 2025 at 4:06pm
Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618.
Fibonacci Sequence, Golden Ratio - Mathematics Stack Exchange
7 Dec 2025 at 6:52am
Explore related questions sequences-and-series convergence-divergence fibonacci-numbers golden-ratio See similar questions with these tags.
How to show that this binomial sum satisfies the Fibonacci relation?
6 Dec 2025 at 5:16pm
Since we already demonstrated that the number of ways to sum $1$ s and $2$ s to get the natural numbers $n$ is a Fibonacci sequence shifted, we now have the basic connection in hand.
geometry - Where is the pentagon in the Fibonacci sequence ...
8 Dec 2025 at 8:23am
The Fibonacci sequence is related to, but not equal to the golden ratio. There is no reason to expect that the sequence mimics the geometric series $\varphi^n$ than there is to expect that the Fibonacci spiral is the same as the golden spiral.
How to express the approximate CURVE of the Fibonacci sequence in a ...
2 Dec 2025 at 2:33am
Is there a way to derive a curve function for the Fibonacci sequence to plot an approximation of the increase in value for each iteration? Please bear with me if I'm using the wrong terminology when
Fibonacci nth term - Mathematics Stack Exchange
9 Dec 2025 at 1:34am
Explore related questions sequences-and-series fibonacci-numbers See similar questions with these tags.
Continuous Fibonacci number F (n) - Mathematics Stack Exchange
6 Dec 2025 at 12:01pm
FibonRatio[n_] = N[Fibonacci[n + 1]/Fibonacci[n]]; Plot[{FibonRatio[n], N[GoldenRatio], 1.7}, {n, 3., 12.}, GridLines -> Automatic] Also using this continuous function definition how is it proved that $$\lim _ {n\rightarrow \infty}\dfrac {F_ {n+1}} {F_n} = \phi$$ ( where $\phi$ is the GoldenRatio) ? Appreciate your comments.
recurrence relations - Fibonacci, tribonacci and other similar ...
5 Dec 2025 at 8:27am
Whoever invented "tribonacci" must have deliberately ignored the etymology of Fibonacci's name - which was bestowed on him quite a bit after his death. Leonardo da Pisa's grandfather had the name Bonaccio (the benevolent), which was also used by his father. The name "filius bonacii" or "figlio di Bonaccio" (son of Bonaccio) was contracted to give Fibonacci. By the way: the Fibonacci sequence ...
Applications of the Fibonacci sequence - Mathematics Stack Exchange
1 Dec 2025 at 7:59pm
Fibonacci numbers have a property that the ratio of two consecutive numbers tends to the Golden ratio as numbers get bigger and bigger. The Golden ratio is a number and it happens to be approximately 1.618.
Is the Fibonacci sequence exponential? - Mathematics Stack Exchange
7 Dec 2025 at 5:00pm
Because the Fibonacci sequence is bounded between two exponential functions, it's effectively an exponential function with the base somewhere between 1.41 and 2.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
4 Dec 2025 at 4:06pm
Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618.
Fibonacci Sequence, Golden Ratio - Mathematics Stack Exchange
7 Dec 2025 at 6:52am
Explore related questions sequences-and-series convergence-divergence fibonacci-numbers golden-ratio See similar questions with these tags.
How to show that this binomial sum satisfies the Fibonacci relation?
6 Dec 2025 at 5:16pm
Since we already demonstrated that the number of ways to sum $1$ s and $2$ s to get the natural numbers $n$ is a Fibonacci sequence shifted, we now have the basic connection in hand.
geometry - Where is the pentagon in the Fibonacci sequence ...
8 Dec 2025 at 8:23am
The Fibonacci sequence is related to, but not equal to the golden ratio. There is no reason to expect that the sequence mimics the geometric series $\varphi^n$ than there is to expect that the Fibonacci spiral is the same as the golden spiral.
How to express the approximate CURVE of the Fibonacci sequence in a ...
2 Dec 2025 at 2:33am
Is there a way to derive a curve function for the Fibonacci sequence to plot an approximation of the increase in value for each iteration? Please bear with me if I'm using the wrong terminology when
Fibonacci nth term - Mathematics Stack Exchange
9 Dec 2025 at 1:34am
Explore related questions sequences-and-series fibonacci-numbers See similar questions with these tags.
Continuous Fibonacci number F (n) - Mathematics Stack Exchange
6 Dec 2025 at 12:01pm
FibonRatio[n_] = N[Fibonacci[n + 1]/Fibonacci[n]]; Plot[{FibonRatio[n], N[GoldenRatio], 1.7}, {n, 3., 12.}, GridLines -> Automatic] Also using this continuous function definition how is it proved that $$\lim _ {n\rightarrow \infty}\dfrac {F_ {n+1}} {F_n} = \phi$$ ( where $\phi$ is the GoldenRatio) ? Appreciate your comments.
recurrence relations - Fibonacci, tribonacci and other similar ...
5 Dec 2025 at 8:27am
Whoever invented "tribonacci" must have deliberately ignored the etymology of Fibonacci's name - which was bestowed on him quite a bit after his death. Leonardo da Pisa's grandfather had the name Bonaccio (the benevolent), which was also used by his father. The name "filius bonacii" or "figlio di Bonaccio" (son of Bonaccio) was contracted to give Fibonacci. By the way: the Fibonacci sequence ...
Applications of the Fibonacci sequence - Mathematics Stack Exchange
1 Dec 2025 at 7:59pm
Fibonacci numbers have a property that the ratio of two consecutive numbers tends to the Golden ratio as numbers get bigger and bigger. The Golden ratio is a number and it happens to be approximately 1.618.
Is the Fibonacci sequence exponential? - Mathematics Stack Exchange
7 Dec 2025 at 5:00pm
Because the Fibonacci sequence is bounded between two exponential functions, it's effectively an exponential function with the base somewhere between 1.41 and 2.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
