![]() ![]() The mystery of Fibonacci sequence and the golden ratio as common patterns in nature. Patternsand Regularities Mathematics helps organize patternsand regularities in the world Patterns have underlying mathematical structures Every living or nonliving thing in the world may seem to follow a certain pattern on their own. ![]() Fibonacci inHuman %2Fsymmetryprojectm-100429072518-phpapp02%2F95%2Fsymmetry-presentationby-manali-3728.jpg%3Fcb%3D1272526366&imgrefurl=https%3A%2F%2Fcrystal4%2Fsymmetry-presentation-bymanali&tbnid=ItIywG9uXTIjTM&vet=12ahUKEwiEsX1z8byAhVZxosBHbmBBLwQMygAegUIARCvAQ.i&docid=nMMztRMrr6ES_M&w=7 28&h=546&q=symmetry%20in%20nature%20ppt&ved=2ahUKEwiEsX1z8byAhVZxosBHbmBBLwQMygAegUIARCvAQ 3. The eyes, fins and tail of the dolphin fall at golden sections along the body. Fibonacci inAnimals The shell of the chambered Nautilus has Golden proportions. Fibonacci inPlants Fibonacci inFruits Inside the fruit of many plants we can observe the presence of Fibonacci order. ![]() The numbers 8 and 13 are consecutive Fibonacci numbers. The nubs on many pineapples form 8 spirals that rotate diagonally upward to the left and 13 spirals that rotate diagonally upward to the right. The Snail Fibonacci inPineapple Pineapples have spirals formed by their hexagonal nubs. is TheSunflower Seed patterns of sunflower All the sunflowers in the world show a number of spirals that are within the Fibonacci sequence. The number of clockwise spirals is 34 and the number of counterclockwise spirals 55. In many sunflowers, the number of clockwise spirals and the number of counterclockwise spirals are consecutive Fibonacci numbers. Fibonacci inSunflower The seeds on a sunflower are arranged in spirals that curve both clockwise and counterclockwise from the center of the sunflower’s head to its outer edge. For instance, the number of pairs of rabbits at the start of the sixth month is 3 + 5 = 8. TABAN, UNP Fibonacci discovered that the number of pairs of rabbits for any month after the first two months can be determined by adding the numbers of pairs of rabbits in each of the two previous months. If none of the rabbits dies, how many pairs of rabbits will there be at the start of each succeeding month? At the start of 4th month, how many pairs of rabbits will there be? How about at the start of the 5th and 6th months? Solution: JOSEPH G. The offspring reproduce in exactly the same manner. After a month the rabbits have produced no offspring however, every month thereafter, the pair of rabbits produces another pair of rabbits. The Fibonacci Sequence Think of this! At the beginning of a month, you are given a pair of newborn rabbits. The snowflake The honeycomb The sunflower The snail’s shell Flower’s petals Weather The Snowflakes Petals of flowers FLOWERS NUMBER OF PETALS Lilies Buttercups Delphiniums Marigolds Asters Daisies 3 5 8 13 21 34, 55, 89 2. Patterns and Numbers in Nature and the World We live in a universe of patterns! 1. By using Mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature’s patterns are not just there to be admired, they are vital clues to the rules that governs natural processes. Patterns and Numbers in Nature and the World Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns called Mathematics. ![]()
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