What is the Pei Bonashi series? What's special about it?

1. Fibonacci series refers to 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144, 234. 6765,10946,1771,28657, 46368 ... This series starts with the third item, and each item is equal to the sum of the first two items.

Second, the Fibonacci number in Fibonacci sequence will often appear in front of our eyes-such as the arrangement of pinecones, pineapples and leaves, the number of petals of some flowers (typically sunflower petals), honeycombs, dragonfly wings, transcendental number E (more can be deduced), golden rectangle, golden section, equiangular spiral, and the law of twelve averages.

1, with the increase of the number of series items, the ratio of the former item to the latter item is getting closer and closer to the golden section value of 0.6 180339887. ...

2. The sum of squares of the first few terms of Fibonacci sequence can be regarded as squares with different sizes, and they can be combined into a large rectangle due to Fibonacci recurrence formula. So the sum of the areas of all the small squares is equal to the area of the big rectangle. Then the following identities can be obtained:

3. The divisibility of Fibonacci sequence and prime number generation: one of every three consecutive numbers is divisible by 2, one of every four consecutive numbers is divisible by 3, one of every five consecutive numbers is divisible by 5, one of every six consecutive numbers is divisible by 8, and one of every seven consecutive numbers is divisible by 13. ...

Extended data:

Fibonacci sequence is widely known in Europe and America, so it often appears in the popular art of movies. For example, it appears as an important symbol and plot clue in the popular Da Vinci Code, and it is also a random question asked at the job fair for shopkeepers in Magic Toy City.

It can be seen that this series is as popular as the golden section. However, although it is well known, most people have memorized the first few figures and haven't studied them deeply. Fibonacci series has also appeared in TV series. For example, in the fifth episode of the Japanese TV series Kao Shen, Izzy did the last math problem in the national mock exam, which was quoted countless times by Fox's hit American TV series mystery files, and even served as one of the design elements of the whole drama poster.

References:

Baidu encyclopedia Fibonacci sequence