Q&A for How to Calculate the Fibonacci Sequence

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Is "Fibonacci" an English word?

Danoyachtcapt

Top Answerer

No, it is the name of mathematician Leonardo of Pisa.

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How do I deduce Binet's fibonacci number formula?

Orangejews

Community Answer

One way is to interpret the recursion as a matrix multiplication. Take a vector of two consecutive terms like (13, 8), multiply by a transition matrix M = (1,1; 1,0) to get the next such vector (21,13). That gives a formula involving M^n, but if you diagonalize M, computing M^n is easy and that formula pops right out.

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Question

Who discovered this sequence?

WOOHP

Community Answer

Leonardo Bonacci

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What are ways to write a ratio?

Donagan

Top Answerer

A:B, A/B, or "A to B."

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Why does it have two 1's at the start?

Community Answer

This is just by definition. Some people even define the sequence to start with 0, 1. You'll still get the same numbers, though.

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Is it possible for -2,-2 could be the first two terms in a Fibonacci sequence?

Community Answer

No, because then you would get -4 for the third term. -2 + -2 = -4.

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What is the 40th term in the Fibonacci Sequence?

Community Answer

The answer is 102,334,155. Where 41 is used instead of 40 because we do not use f-zero in the sequence. You can work this out using any online Fibonacci calculator.

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What is the square root of minus one (-1)?

Community Answer

The answer is the portal to the world of "imaginary numbers". It is written as the letter "i".

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How is the Fibonacci sequence used in arts?

Community Answer

There may be more examples, but it is often used when you have spokes on a wheel. For instance, you'll often see wheels on a car with 3, 5, or 8 spokes, because it is visually appealing. You also may see fans with 3 or 5 blades. If you take into account the golden ration (Approx. 1.62) which is correlated to the Fibonacci sequence, (see method 2) then you have even more applications. One example is that a lot of rectangle portraits have side lengths with a ratio equal to the golden ratio. It is also often used in drawing composition, by placing the main focuses on a spiral that is defined by the golden ratio (This is called the Golden Spiral).

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