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Fibonacci Numbers Essay

2277 words - 10 pages

Fibonacci numbers are numbers in the Fibonacci sequence. In this paper, you will find out what Fibonacci numbers are related to. You will also find out how Fibonacci numbers are everywhere in the world. Though Fibonacci numbers are found in mathematical subjects, they are also found in other concepts.
According to the Merriam-Webster Dictionary “Fibonacci Numbers are integers in the infinite sequence 1, 1, 2, 3, 5, 8, 13 … of which the first two terms are 1 and 1 and each succeeding term is the sum of the two immediately preceding.” This is also known as a recursive sequence, because each number is a function of the preceding two numbers. Fibonacci numbers are contained in a few formulas. They are also numbers in shapes, such as triangles and rectangles. Fibonacci number is found throughout nature, art, music, and science.
Fibonacci Numbers originated from India hundreds of years ago. Though Fibonacci Numbers came from India, Leonardo of Pisa, better known as Fibonacci, made it known to the world. Leonardo came from a wealthy Italian family and traveled to North America to join his father. He was educated by the Moors and sent on business trips. “After returning to Pisa around 1200, Leonardo wrote his most famous literature, Liber Abaci” (Pearson). Leonardo featured a rabbit question in the book. The question was asked in a mathematical competition, he appeared in when he was young. Leonardo Fibonacci used the Fibonacci Numbers to solve it. Fibonacci Numbers is now used throughout our society.
The question that Leonardo Fibonacci solved with Fibonacci Numbers was about rabbit reproduction. The question was asking, “Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was…How many pairs will there be in one year?” (Knott). Leonardo Fibonacci had to figure out how much rabbits were going to be reproduced in one year. The answer to this question was 233 pairs of rabbits after the first year has passed. Leonardo Fibonacci got this answer by adding the first pair of rabbits to the next one. Then he kept on adding the two previous pairs to get the next pair. Leonardo Fibonacci kept on doing this, until he got to a year and he solved the problem. (Refer to diagram 1) This is one of the first questions in the world, which introduced the use of Fibonacci Numbers.
Fibonacci Numbers can be solved by using a rule. The rule is xn = xn-1 + xn-2. Xn is the term “n”; Xn-1 is the term right before “n”; Xn-2 is the term right before xn-1. (Refer to diagram 2). For example, if n equals 8, xn-1 equals x7, and xn -2 equals x6, you solve this problem by finding out what x8, x7, and x6 equals. When looking at the chart, x8 equals 21,...

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