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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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?Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.?
Shakuntala Devi

1. ## Fibonacci number - Wikipedia

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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

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2. ## Celebrate numbers, patterns, and trippy visuals on ...

https://mashable.com/article/fibonacci-day-2019翻譯此頁

Nov 23, 2019 · It's a big day for number nerds. The date Nov. 23 – really 11/23, since formatting makes a difference here – marks Fibonacci Day, a time when people on the internet take a …

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
How to calculate Fibonacci numbers?

How to Calculate the Fibonacci Sequence - Method 2 Using Binet's Formula and the Golden Ratio

• Set up the formula xn{\displaystyle x_{n}}=?n?(1??)n5{\displaystyle {\frac...
• Plug the number for n{\displaystyle n} into the formula.
• Substitute the golden ratio into the formula.
• Complete the calculations in parentheses.
• Calculate the exponents.
www.wikihow.com/Calculate-the-Fibonacci-Sequence
What are the first 20 Fibonacci numbers?
The first 20 Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181. Fibonacci numbers appear unexpectedly often in mathematics, and also in biological settings. The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence),...
0-1-1-2-3-5-8-13-21-34-55-89-144-233-377-610-987-159…
What are some examples of the Fibonacci numbers?

7 Beautiful Examples Of The Fibonacci Sequence In Nature

1. Shells. As you may have guessed by the curve in the box example above,...
2. Trees. Tree -- we see them everywhere, but do you look and analyse the structure...
3. Flower Pistils. The part of the flower in the middle of the petals (the pistil)...
4. Flower Petals. Flowers of all kinds follow...
www.theodysseyonline.com/7-beautiful-examples-fibonac…
What are some examples of the Fibonacci sequence in nature?

18 Amazing Examples of the Fibonacci Sequence in Nature

• 1) Chicken Egg. Image originally found at www.holistichouseplans.com.
• 2) Romanesque Broccoli. Picture of a Romanesque Cauliflower. Red / Flickr.
• 3) Aloe Plant. Spiral within an aloe plant. brewbooks / Flickr...
• 4) Buena Mulata Pepper. Add a comment... This pepper has grown...
5. ## Fibonacci - Simple English Wikipedia, the free encyclopedia

https://simple.wikipedia.org/wiki/Fibonacci翻譯此頁

Fibonacci, also known as Leonardo Bonacci, Leonardo Fibonacci and Leonardo of Pisa, lived c. 1170–1250.He was an Italian mathematician. He was thought "the most talented Western mathematician of the Middle Ages".. Fibonacci popularized the Hindu–Arabic numeral system to the Western World. He did this in his composition in 1202 of Liber Abaci (Book of Calculation).

6. ## THE FIBONACCI SEQUENCE - What Is the Fibonacci Sequence ...

Dec 09, 2019 · THE FIBONACCI SEQUENCE - What Is the Fibonacci Sequence? The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is ...

7. ## 斐波那契數列_百度百科

https://baike.baidu.com/item/斐波那契數列/99145

斐波那契數列的定義者，是意大利數學家列昂納多·斐波那契（Leonardo Fibonacci），生于公元1170年，卒于1250年，籍貫是比薩。 他被人稱作“比薩的列昂納多”。 1202年，他撰寫了《算盤全書》（Liber Abacci）一書。他是第一個研究了印度和阿拉伯數學理論的歐洲人。 他的父親被比薩的一家商業團體聘任 ...

8. ## Amicable numbers - Wikipedia

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Demonstration, with rods, of the amicability of the pair of numbers (220,284) nism|Pythagoreans]], who credited them with many mystical properties. A general formula by which some of these numbers could be derived was invented circa 850 by the Iraqi mathematician Thābit ibn Qurra (826–901). Other Arab mathematicians who studied amicable numbers are al-Majriti (died 1007), al-Baghdadi (980 ...

9. ## I - NJUST OnlineJudge

icpc.njust.edu.cn/Contest/406/I

The input consists of several instances, each of them consisting of a single line. Each line of the input contains two numbers X and Y in Fibonacci base separated by a single space.