NATURE AND FIBONACCI SEQUENCE SERIES

Rows of seeds in opposite directions, or even 89 and 144 rows of seeds in opposite directions. Radially -Diverging outward from a center, as spokes do from a wagon wheel or as light does from the sun. Phyllotaxis -The arrangement of the leaves of a plant on a stem or axis. 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 KEY TERMS 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.

The Fibonacci sequence appears in unexpected places such as in the growth of plants, especially in the number of petals on flowers, in the arrangement of leaves on a plant stem, and in the number of rows of seeds in a sunflower.įor example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers.

NATURE AND FIBONACCI SEQUENCE SERIES

Thus, if a series begins with 3, then the subsequent series would be as follows: 3, 3, 6, 9, 15, 24, 39, 63, 102, and so on.Ī Fibonacci series can also be based on something other than an integer (a whole number). That means that the specific numbers in a Fibonacci series depend upon the initial numbers. Number (after the second) is the sum of the previous two. Other Fibonacci sequencesĪlthough the most famous Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55., a Fibonacci sequence may be any series of numbers in which each succeeding Table 1. The numbers in the “Total Pairs ” column represent the Fibonacci sequence. Beginning in the third month, the number in the “Mature Pairs ” column represents the number of pairs that can bear rabbits. Each pair of rabbits can only give birth after its first month of life. Each number in the table represents a pair of rabbits. Table 1 illustrates one way of looking at Fibonacci ’s solution to this problem. The problem was this: Beginning with a single pair of rabbits (one male and one female), how many pairs of rabbits will be born in a year, assuming that every month each male and female rabbit gives birth to a new pair of rabbits, and the new pair of rabbits itself starts giving birth to additional pairs of rabbits after the first month of their birth? The Fibonacci sequence was the outcome of a mathematical problem about rabbit breeding that was posed in the Liber Abaci. The Liber Abaci showed how superior the Hindu-Arabic arithmetic system was to the Roman numeral system, and it showed how the Hindu-Arabic system of arithmetic could be applied to benefit Italian merchants. In 1202, he published his knowledge in a famous book called the Liber Abaci (which means the “book of the abacus, ” even though it had nothing to do with the abacus). While growing up in North Africa, Fibonacci learned the more efficient Hindu-Arabic system of arithmetical notation (1, 2, 3, 4.) from an Arab teacher. Mathematical calculations were made using the Roman numeral system (I, II, III, IV, V, VI, etc.), but that system made it hard to do the addition, subtraction, multiplication, and division that merchants needed to keep track of their transactions. Italians were some of the western world ’s most proficient traders and merchants during the Middle Ages, and they needed arithmetic to keep track of their commercial transactions. Fibonacci, the son of an Italian businessman from the city of Pisa, grew up in a trading colony in North Africa during the Middle Ages. The Fibonacci sequence was invented by the Italian Leonardo Pisano Bigollo (1180 –1250), who is known in mathematical history by several names: Leonardo of Pisa (Pisano means “from Pisa ”) and Fibonacci (which means “son of Bonacci ”). This sequence expresses many naturally occurring relationships in the plant world. The Fibonacci sequence is a series of numbers in which each succeeding number (after the second) is the sum of the previous two.

Nature and fibonacci sequence