What is the Fibonacci Sequence? What are the Fibonacci Features?
What is the Fibonacci Sequence? What are the Fibonacci Features? His questions are investigated by those who are devoted to the science of mathematics and understanding logic.
Fibonacci sequence It is a very important concept for especially mathematicians, biologists, physicists, engineers and software developers. The fibonacci sequence, which you can use in the ordinary course of life and will take you to an accurate and fast determination in your transactions, has also been used in the Egyptian pyramids, which everyone admires. This series, which is quite difficult to grasp, turns into a very enjoyable and pleasant with the examples and procedures. Well, What is the Fibonacci Sequence? Let's see it all together.
What is the Fibonacci Sequence? What Are Their Numbers?
Fibonacci Sequence It is a sequence of numbers that operates according to a certain arithmetic order and is associated with the golden ratio in the interconnection. Nowadays, it is used in many account transactions and makes transactions very easy. Fibonacci series, which is usually given to students for homework, is followed and researched by many engineers, mathematicians, software developers, physicists and biologists. In this article, we will give you all the details you need to know about the Fibonacci sequence.
What is the Fibonacci Sequence?
What is the Fibonacci Sequence? We will share with you all the curious about the question. In mathematics, the Fibonacci sequence numbers, which are usually expressed as "Fot", reveal a sequence. For this sequence to be possible, each number in the array must start from 0 and 1 and be the sum of the previous number. Although this may seem a bit confusing at first, the information you will gain in our article will allow you to fully comprehend the Fibonacci sequence.
Request Fibonacci Sequence Formula;
- If we express our number as Fn for the Fibonacci sequence, the formula Fn = Fn-1 + Fn -2 is applied.
Fibonacci Sequence History
Fibonacci sequence history It is very old. The Fibonacci series first appeared in the Liber Abaci book, which is said to have been written in 1202. This book, which is an algebra book, contains many sequences, arithmetic numbers and logical operations and shows examples. The definition of the fibonacci sequence in the book shows an example that certain numbers are arranged according to a rule and expresses the arithmetic order of this sequence.
How the Fibonacci Sequence Was Found
How To Find The Fibonacci Sequence does not express the exact and correct source, but this series is the first Leonardo Fibonacci It is said to be found by. Coming to the story of how the Fibonacci sequence was found, it is said that Leonardo Fibonacci focused his attention on the Hindu - Arabic arithmetic system in his researches during his North Africa journey and found the Fibonacci sequence while continuing his studies.
Fibonacci Numbers - What Are Their Numbers?
Fibonacci numbers or numbers We have given you a tip on the Fibonacci Sequence definition. Again, to repeat, the Fibonacci sequence numbers start with 0 and 1 and give the sum of the previous two numbers. Let's give you some of the Fibonacci numbers and their formula and an example with solutions.
Request Fibonacci Numbers Formula;
- Fibonacci Sequence progresses as "0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...".
- The formula of these numbers continues as Fn = Fn-1 + Fn -2.
Solved Fibonacci Number Example;
- You can think of the concept we call Fn as any number in the array. We're going to base the number 5. We immediately return to the formula "The number of Fibonacci sequences gives the sum of the previous two numbers" Let's continue with "Fn = Fn-1 + Fn -2" ie 5-1 + 5-2 = 8 (Fn) 8-1 + 8-2 = 13 (Fn) and solve the last example with the number 13 you want the Fibonacci sequence. you can continue until.
Properties of the Fibonacci Sequence
Fibonacci Array properties It varies according to the area of use. But the basic concept to know is that the Fibonacci sequence is an analysis technique based on series of numbers. As we mentioned in our article, the Fibonacci numbers continue as 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144…. To find the last number of the series, it is necessary to continue by finding the sum of the previous two numbers. Besides, there are a few other features that you should know about.
Request Properties of the Fibonacci Sequence;
- In the Fibonacci Sequence, GCD of two consecutive terms is equal to 1.
- When each number in the Fibonacci sequence is divided by the number before it to the golden ratio ((1 + square root5) / 2 = 1.6118…) gives a close number.
- If you continue the Fibonacci sequence, you can see that every third number continues evenly, every fourth number is a multiple of three, and every fifth number continues as a multiple of five.
Fibonacci RabbitIs an example of Leonardo Fibonacci, an Italian mathematician from the 1200s, to provide a full grasp of the fibonacci sequence. In this rabbit example, Leonardo Fibonacci tried to determine how much male and female rabbit breeds in a year. We start the show with a newborn pair of rabbits. The gestation period of rabbits is one month and they are engaged in sexual maturity within a month. A pair of rabbits gives birth to a male and a female rabbit. The couple born after a month does not give birth immediately. This cycle continues like this. In the last year, we will have 233 pairs of rabbits. We will share pictures with you so that you can understand the event better. The numbers on the right of the picture are indicative. This process continues in this way.
Fibonacci SpiralIs a connected quarter circle drawn inside a square in the Fibonacci sequence. The squares in the figure show that the next number is equal to the previous two numbers. The ratio of each consecutive number in the Fibonacci sequence gives a value very close to the Golden Ratio (1.618034). The larger the numbers in the Fibonacci sequence, the closer to the golden ratio. This is one of the biggest indicators of how important the Fibonacci sequence is.
Fibonacci SequenceWhere s Used
Fibonacci sequence used in places is quite a lot. We will give the main areas and examples instead of explaining them separately. We have said that it is a very important concept for especially mathematicians, biologists, physicists, engineers and software developers. For example, you can see it in leaves, sunflower, pine cone, palm and spider web. In addition to these, it is known that there are Fibonacci Sequences in the written software, the Da Vinci cipher and the human body. It is said to have been built using the fibonacci sequence in the pyramids that are admired today.
Fibonacci Numbers and What is the Golden Ratio?
Fibonacci Numbers and the Golden Ratio We explained the link piece by piece in the article contents. The golden ratio is often used in mathematics and arts. It forms the geometric and numerical connections that reflect the harmony within the parts of a whole. The golden ratio was discovered by the Ancient Egyptians and Greeks and was widely used in architecture and art. The ratio of consecutive numbers in the Fibonacci sequence gives an approximate value to the Golden Ratio. This value is the number 1.618034, and the larger the numbers in the Fibonacci sequence, the closer to this ratio. Fibonacci numbers are used effectively in software and architecture, where the golden ratio is included.