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    November 23, 2019

    1, 1, 2, 3: It's Fibonacci Day!

    Today's date, November 23, can be represented as 11/23, or 1, 1, 2, 3—the beginning of the Fibonacci sequence of numbers. Likewise, as the leaves on the Queen Victoria agave in today's image spiral out from the center, they also express the Fibonacci sequence. This unique sequence of numbers was introduced to Europe in 1202 by the Italian mathematician Leonardo of Pisa (posthumously named Fibonacci) in his revolutionary work, the 'Liber Abaci.' The book begins by describing the Hindu-Arabic numeral system or 'Modus Indorum’—0 1 2 3 4 5 6 7 8 9—and shows how its application could simplify trade and make calculations faster and easier (most of Europe at this time used Roman numerals).

    In the third section of his book, Fibonacci goes on to describe various mathematical problems, including a thought experiment about increasing rabbit populations that results in the Fibonacci sequence. The sequence is determined by adding the previous two numbers together to establish the next number: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. Since then, mathematicians, scientists, and artists have been studying and applying the Fibonacci sequence and the Fibonacci numbers that make it up. While Fibonacci gets the credit for describing the number sequence, he wasn't the first to discover it. Research published in 1985 posits that ancient Indian mathematicians had been aware of and wrote about the sequence more than a thousand years before Fibonacci's work.

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  1. Fibonacci number - Wikipedia

    https://en.wikipedia.org/wiki/Fibonacci_number翻譯此頁

    In mathematics, the Fibonacci numbers, commonly denoted Fn form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is, and for n > 1. One has F2 = 1.

    In some books, and particularly in old ones, F0, the "0" is omitted, and the Fibonacci sequence starts with F1 = F2 = 1. The beginning of the sequence is thus:

    Fibonacci numbers are strongly related to the golden ratio: Binet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibona…

    In some books, and particularly in old ones, F0, the "0" is omitted, and the Fibonacci sequence starts with F1 = F2 = 1. The beginning of the sequence is thus:

    Fibonacci numbers are strongly related to the golden ratio: Binet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases.

    Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, later known as Fibonacci. They appear to have first arisen as early as 200 BC in work by Pingala on enumerating possible patterns of poetry formed from syllables of two lengths. In his 1202 book Liber Abaci, Fibonacci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics.

    Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems.

    They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone

    在 Wikipedia 上閱讀更多信息

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  2. Fibonacci Sequence - Math Is Fun

    https://www.mathsisfun.com/numbers/fibonacci-sequence翻譯此頁

    It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this! Using The Golden Ratio to Calculate Fibonacci Numbers. And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio: The answer always comes out as a whole number, exactly equal to the addition of the previous two ...

  3. Fibonacci series
    名詞
    Fibonacci numbers (復數名詞)
    1. a series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.
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    更多信息Fibonacci series
  4. People also ask
    What are the first 10 Fibonacci numbers?
    The first ten numbers in the Fibonacci Sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Fibonacci numbers also appear in many aspects of nature such as the arrangement of leaves on a stem and the branching of trees.
    www.quora.com/How-do-I-use-Fibonacci-in-Forex-trading
    What is the sequence of Fibonacci numbers?
    The Fibonacci sequence is a sequence of numbers in which each successive number in the sequence is obtained by adding the two previous numbers in the sequence. The sequence is named after the Italian mathematician Fibonacci. The sequence starts with zero and one, and proceeds forth as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on.
    www.techopedia.com/definition/15823/fibonacci-sequence
    Why are Fibonacci numbers interesting?
    These numbers have become important pivotal points when analyzing retracement of a trend. The Fibonacci numbers are the crucial numbers for the Elliott wave analysis. They play a major role in analyzing the way you think and how your emotions play a role in your investment decisions.
    How to determine the largest Fibonacci number?
    If you need to find the largest Fibonacci number that is less than a certain number N, you can also use the rounding calculation: phi^n / sqrt(5) < N which gives you: n < log(N x sqrt(5)) / log(phi) Then you can calculate the right hand side part for your chosen N, round it down to find n, and calculate the corresponding Fibonacci number with:
    stackoverflow.com/questions/13492807/how-to-determin…
  5. What Is the Fibonacci Sequence? | Live Science

    https://www.livescience.com/37470-fibonacci-sequence.html翻譯此頁

    The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it.

  6. Fibonacci Numbers Lines Definition and Uses

    https://www.investopedia.com/terms/f/fibonaccilines.asp翻譯此頁

    Fibonacci numbers/lines were discovered by Leonardo Fibonacci, who was an Italian mathematician born in the 12th century. These are a sequence of numbers where each successive number is …

  7. Fibonacci Numbers, the Golden section and the Golden String

    www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html翻譯此頁

    This string is a closely related to the golden section and the Fibonacci numbers. Fibonacci Rabbit Sequence See show how the golden string arises directly from the Rabbit problem and also is used by computers when they compute the Fibonacci numbers.

  8. Fibonacci Sequence | Series | Spiral | Number | Code ...

    https://www.scienceabc.com/eyeopeners/why-are...翻譯此頁
    The hint was a small, jumbled portion of numbers from the Fibonacci sequence. The sanctity arises from how innocuous, yet influential, these numbers are. A new number in the pattern can be generated by simply adding the previous two numbers. Starting from 0 and 1 (Fibonacci originally listed them starting from 1 and 1, but modern mathematicians prefer 0 and 1), we get:0,1,1,2,3,5,8,13,21,34,55,89,144…610,987,1597…We can find …
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  9. Fibonacci - Wikipedia

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    Fibonacci was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".
    The name he is commonly called, Fibonacci, was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for filius Bonacci ("son of Bonacci"). He is also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ("Leonardo the Traveller from Pisa").

    Wikipedia · CC-BY-SA 許可下的文字
  10. THE FIBONACCI SEQUENCE, SPIRALS AND THE GOLDEN MEAN

    https://math.temple.edu/~reich/Fib/fibo.html翻譯此頁

    THE FIBONACCI SEQUENCE, SPIRALS AND THE GOLDEN MEAN. The Fibonacci sequence exhibits a certain numerical pattern which originated as the answer …

  11. Fibonacci Number -- from Wolfram MathWorld

    mathworld.wolfram.com/FibonacciNumber.html翻譯此頁

    Dec 06, 2019 · with .As a result of the definition (), it is conventional to define .The Fibonacci numbers for , 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ...(OEIS A000045).. Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials with .. Fibonacci numbers are implemented in the Wolfram Language as Fibonacci[n].. The Fibonacci numbers are also a Lucas sequence, and are companions …

  12. Fibonacci numbers | mathematics | Britannica

    https://www.britannica.com/science/Fibonacci-number翻譯此頁

    Fibonacci numbers, the elements of the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, …, each of which, after the second, is the sum of the two previous numbers. These numbers were first noted by the medieval Italian mathematician Leonardo Pisano (“Fibonacci”) in his Liber abaci (1202; “Book of the

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