Fibonacci Numbers

As early as we can know, the term Fibonacci was first used in Indian mathematics around 200 BC. Fibonacci numbers are numbers in the Fibonacci sequence where every number is the sum of the former two numbers. The Fibonacci numbers are as follows: 0, 1, 1, 2, 3, 5, 8, 13, and so on. The application of the Fibonacci series can be seen mainly in nature or biological settings, mathematics, and sometimes in human anatomy as well. In this article we will try to understand some basic concepts related to Fibonacci numbers such as the occurrence of Fibonacci numbers in nature and geometry, what is Fibonacci sequence, and much more.

Fibonacci Numbers in Nature

The pattern of Fibonacci number has been mostly seen in nature in the form of the pattern of a plant, the stem, or the arrangement of a plant. As mentioned above these numbers or sequences are also seen in human anatomy. Let us now look into the examples and understand where we can see the Fibonacci numbers. 

  1. Occurrence of Fibonacci number in Plants: The occurrence of these numbers/sequences has been seen in various arrangements such as their branches and stems, different flowers, and plants. The leaves present on the stem get exposed to the sunlight and capture it the most. When these stems develop, a spiral pattern is generally seen on these plants. Similarly, various fruits such as pineapples also give us evidence of the spiral pattern which is related to Fibonacci numbers.
  2. Occurrence of Fibonacci numbers in Bees: The most nail-biting fact about the Fibonacci numbers is the way it is generally seen in the development of the dynamic system. The family tree of the bees, both male and female forms a sequence and their total gives us the Fibonacci number. 
  3. Fibonacci numbers in Human Anatomy: When we study human anatomy, we study the different parts and structures of the human body. The unique fact about these numbers is that they also occur in the human hand. If we deeply examine our hand, we will get to know that our hand is also a member of the Fibonacci series.
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Fibonacci Number in Geometry

Along with the occurrence of Fibonacci numbers in the natural world, we can also see that these numbers also occur in the mathematical world or geometry. In the next paragraph, we will briefly examine the occurrence of the numbers through some examples.

  1. Rectangle: We can see the appearance of the Fibonacci Rectangle in the plane geometry. It is defined as the sides of two successive numbers (Fibonacci) in length, also generated through squares with sides that are Fibonacci numbers.
  2. Fibonacci Numbers and Prime Numbers: There are a lot of prime numbers in the Fibonacci sequence. It is also said and accepted that many such(prime)numbers are Fibonacci.
  3. Occurrence of Fibonacci number in Pascal Triangle: One of the greatest known mathematicians and physicists, Blaise Pascal developed a triangle which he named as Pascal Triangle. The Fibonacci number is found by the addition of diagonal numbers in the Pascal Triangle.

Fibonacci Sequence

The Fibonacci numbers result in the formation of a sequence, this sequence is known as the Fibonacci sequence. The Fibonacci sequence can be also defined as the horizontal line of numbers that gets started with a one or zero and further gets carried on based on the Fibonacci number rule. This term, Fibonacci has been derived from the name of an Italian mathematician who survived for around 80 years. His name was Leonardo Pisano or Leonardo Fibonacci. This sequence is also related to a natural proportion or phenomenon that generally occurs in the natural world.

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