![]() ![]() Thus the Fibonacci sequence and Fibonacci numbers can be defined recursively as:įn+2= fn + fn+1 where n>0 or n=0. After one year, let us calculate the pairs of Rabbit produced? Fibonacci Solution: Solution provided is the Sequence given by Fibonacci:Ġ,1,1,2,3,5,8,13,21,34,55,89,114 Thus, after completion of one year, pairs of rabbits produced will be 144. after reaching two months age, each pair produces another pair (one female and one male), and then mixed pairs are produced every month thereafter and no rabbit dies in between. Assuming all the months have same number of days and rabbit starts producing young rabbits exactly after two months they were born i.e. This sequence appears in numerous mathematical problems.įibonacci problem: Let us assume 2 rabbits (one male and one female) are born on 1st January. The Fibonacci sequence is the best example of any recursive sequence. By definition, the numbers in the Fibonacci sequence starts with either 0 and 1, or 1and1, and each subsequent number is the sum of the previous two numbers. The Fibonacci sequence has remarkable characteristics it can be applied to various fields like discrete mathematics, number theory and geometry. The Fibonacci number and sequence proposed by him gives a clear indication that mathematics can be connected to many things that may seem unrelated to it. One of these concepts is the “Fibonacci sequence” that was developed by Leonardo Pisano during the 13th century. The Fibonacci sequence may simply express the most efficient packing of the seeds (or scales) in the space available.In the realm of Mathematics, there are many concepts that can be applied to multiple fields of mathematics. ![]() ![]() As each row of seeds in a sunflower or each row of scales in a pine cone grows radially away from the center, it tries to grow the maximum number of seeds (or scales) in the smallest space. That is, these phenomena may be an expression of nature's efficiency. The same conditions may also apply to the propagation of seeds or petals in flowers. ![]() Given his time frame and growth cycle, Fibonacci's sequence represented the most efficient rate of breeding that the rabbits could have if other conditions were ideal. Why are Fibonacci numbers in plant growth so common? One clue appears in Fibonacci's original ideas about the rate of increase in rabbit populations. The number of rows of the scales in the spirals that radiate upwards in opposite directions from the base in a pine cone are almost always the lower numbers in the Fibonacci sequence-3, 5, and 8. The corkscrew spirals of seeds that radiate outward from the center of a sunflower are most often 34 and 55 rows of seeds in opposite directions, or 55 and 89 rows of seeds in opposite directions, or even 89 and 144 rows of seeds in opposite directions. Similarly, the configurations of seeds in a giant sunflower and the configuration of rigid, spiny scales in pine cones also conform with the Fibonacci series. All of these numbers observed in the flower petals-3, 5, 8, 13, 21, 34, 55, 89-appear in the Fibonacci series. There are exceptions and variations in these patterns, but they are comparatively few. Some flowers have 3 petals others have 5 petals still others have 8 petals and others have 13, 21, 34, 55, or 89 petals. For example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers. ![]()
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