0
How does the Fibonacci sequence apply to the golden ratio im in lower ks3 easy to understand answer please?
Wiki User
∙ 10y ago
phi, the Golden ratio is [1 + sqrt(5)]/2 = approx 1.6180...
The Fibonacci sequence is defined as follows:
U1 = 1, U2 = 1 and Un =Un-1 + Un-2 for n = 3, 4, 5, ...
that is, the first two terms are 1 and after that, each term is the sum of the previous two terms.
Now consider the sequence Un+1/Un for n = 1, 2, 3, ... that is, the sequence of each Fibonacci number divided by the one before it. This goes
U2/U1 = 1/1 = 1
U3/U2 = 2/1 = 2
and so on.
Then
U7/U6 = 13/8 = 1.6250 which is less than 1% away from phi.
U9/U8 = 34/21 = 1.6190 which is less than 0.1% away.
U16/U15 = 987/610 = 1.6180 which is less than 1 in a million away.
Thus, after the first few, terms of the Fibonacci sequence increase in approximately the Golden ratio.
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
What does Fibonacci and the golden ratio have in common?
The ratio of dividing the larger Fibonacci number into the smaller Fibonacci number gives you the golden ratio (1.618 to 1). -------- The Golden Ratio is the number (1+sqrt(5))/2~=1.618 The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . Skipping the first two terms, if you divide one term in this sequence by the previous term the resulting sequence converges to the Golden Ratio: 1.0000 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 Please see the link for more information.
What is a18 in arithmetic sequence?
There is insufficient information for us to even begin to understand this question. Please edit the question to include more context or relevant information.
What does sequental mean?
In sequence: happening in chronological order, or forming a sequence. ^_^ Please tell me if that was useful.
What is the next fraction in this sequence?
Without seeing the sequence, we'd just be guessing.
What is the geometric sequence formula?
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
What does Fibonacci and the golden ratio have in common?
The ratio of dividing the larger Fibonacci number into the smaller Fibonacci number gives you the golden ratio (1.618 to 1). -------- The Golden Ratio is the number (1+sqrt(5))/2~=1.618 The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . Skipping the first two terms, if you divide one term in this sequence by the previous term the resulting sequence converges to the Golden Ratio: 1.0000 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 Please see the link for more information.
What is a18 in arithmetic sequence?
There is insufficient information for us to even begin to understand this question. Please edit the question to include more context or relevant information.
When was Please Understand Me created?
Please Understand Me was created in 1984.
What is the ISBN of Please Understand Me?
The ISBN of Please Understand Me is 0960695400.
Who is Leonardo Pisano Fibonacci?
He is a famous mathematician, He created the numbers we use today. He wrote a book also, called, Liber Abbaci. Meaning 'Book of Calculating'. He created a sequence. You can find this sequence in many places, Mostly in nature. You can also find Fibonacci numbers in nature. You can find Fibonacci in the human body too. The sequence is 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 13 You take the last two numbers and add them to get a new number and add those two this sequence never stops. Most people cannot recite the first 20 Fibonacci Numbers. This will help you find the correct answer if you try it and do not get these numbers you did something wrong. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368...You Welcome for this answer if you have trouble or any corrections please contact me. My user name is South031796. If you have any concerns or additions please tell me I am doing this for Science Fair and need to know any further information. Thank You South031796
How many pages does Please Understand Me have?
Please Understand Me has 210 pages.
Which is the next number in this logical sequence.?
There is no sequence, please add one and I'll help.
What does sequental mean?
In sequence: happening in chronological order, or forming a sequence. ^_^ Please tell me if that was useful.
What is the nth term for sequence 4 9 16 25?
Please note that (a) this is a sequence of square numbes, and (b) the sequence starts at 22.
What are mr golden sun lyrics?
Oh, Mr. Sun, Sun, Mr. Golden Sun, Please shine down on me. Oh Mr. Sun, Sun, Mr. Golden Sun, Hiding behind a tree These little children are asking you To please come out so we can play with you. Oh Mr. Sun, Sun, Mr. Golden Sun, Please shine down on, please shine down on, Please shine down on me
What is the next fraction in this sequence?
Without seeing the sequence, we'd just be guessing.
What sequence do the intake and exhaust valves go in on the head?
Please restate your question.
