Notice that the lengths of the squares are all Fibonacci numbers.Īny rectangle in the picture is composed of squares with lengths that are Fibonacci numbers. The numbers inside each square indicate the length of one side of the square. The rectangle is called a Fibonacci rectangle, which is further described in Fibonacci Numbers in Nature. Such spiral is called the Fibonacci spiral, and it can be seen in sea shells, snails, the spirals of the galaxy, and other parts of nature, as shown in Image 6 and Image 7. We can build Fibonacci rectangles by continuing to draw new squares that have the same length as the sum of the length of the latest two squares.Īfter building Fibonacci rectangles, we can draw a spiral in the squares, each square containing a quarter of a circle. We draw another square with length 3 that is touching one unit square and the latest square with length 2. Then, we draw a new square with length 2 that is touching the sides of the original two squares. We can build Fibonacci rectangles first by drawing two squares with length 1 next to each other. Fibonacci rectangles are rectangles that are built so that the ratio of the length to the width is the proportion of two consecutive Fibonacci numbers. It was coincidence that the number of rabbits followed a certain pattern which people later named as the Fibonacci sequence.įibonacci numbers can be seen in nature through spiral forms that can be constructed by Fibonacci rectangles as shown in Image 5. This problem was originally intended to introduce the Hindu-Arabic numerals to Western Europe, where people were still using Roman numerals, and to help people practice addition. The population continues to match the Fibonacci sequence no matter how many months out you go.Īn interesting fact is that this problem of rabbit population was not intended to explain the Fibonacci numbers. , which is the same as the beginning of the Fibonacci sequence. As you can see in the image, the population by month begins: 1, 1, 2, 3, 5, 8. This is exactly the rule that defines the Fibonacci sequence. This same reasoning can be applied to any month, March or later, so the number of rabbits pairs in any month is the same as the sum of the number of rabbit pairs in the two previous months. This means that on June 1st, there are 5 + 3 = 8 pairs of rabbits. ![]() ![]() Furthermore, there are 3 new pairs of rabbits born in June, one for each pair that was alive in April (and are therefore old enough to reproduce in June). As you can see in Image 2, all 5 pairs of rabbits that were alive in May continue to be alive in June. On February 1st, this baby rabbits matured to be grown up rabbits, but they have not reproduced, so there will only be the original pair present. The problem was to find out how many pairs of rabbits there will be after one year. the rabbits never die, so after they mature, the rabbits produce a new pair of baby rabbits every month.each new pair will mature for one month and produce a new pair of rabbits on the first day of their third month.this pair will grow for one month before reproducing and produce a new pair of baby rabbits on the first day of March.there is one pair of baby rabbits placed in an enclosed place on the first day of January. ![]() In his work Liber Abacci, he introduced a problem involving the growth of the rabbit population. The Fibonacci sequence was studied by Leonardo of Pisa, or Fibonacci (1770-1240). For more information about Fibonacci patterns in nature, see Fibonacci Numbers in Nature Nature prefers this way of arranging seeds because it seems to allow the seeds to be uniformly distributed. The two numbers of spirals are always consecutive numbers in the Fibonacci sequence. Different patterns of spirals are formed depending on whether one is looking at a clockwise or counterclockwise way thus, the number of spirals also differ depending on the counting direction, as shown by Image 1. The seeds at the head of the sunflower, for instance, are arranged so that one can find a collection of spirals in both clockwise and counterclockwise ways. The Fibonacci numbers can be discovered in nature, such as the spiral of the Nautilus sea shell, the petals of the flowers, the seed head of a sunflower, and many other parts. So, given two 's as the first two terms, the next terms of the sequence follows as : The Fibonacci sequence is the sequence where the first two numbers are 1s and every later number is the sum of the two previous numbers. ![]()
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