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CHAPTER – SEQUENCE AND SERIES FIBONACCI SEQUENCE BY C.RAM MUKILAN XI A 1 KENDRIYA VIDYALAYA NARIMEDU, MADURAI
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When there is a staircase with three steps how many ways can you reach the top?Case a Case b Case c
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There is a staircase, number of ways one can reach Zero step –1 First step -1 Second step –2 Third step –3 Fourth step - 5 When we observe…….. 1 1 2 3 5 8 13 ………..
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The number pattern is known as the Fibonacci sequence. 1 1 2 3 5 8 13 21 34 55
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On many plants, the number of petals is a Fibonaccinumber:Buttercups have 5 petals; lilies and iris have 3 petals;some delphiniums have 8; corn marigolds have 13petals; some asters have 21 whereas daisies can be foundwith 34, 55 or even 89 petals.13 petals: ragwort, corn marigold, cineraria, some daisies21 petals: aster, black-eyed Susan, chicory34 petals: plantain, pyrethrum55, 89 petals: michaelmas daisies, the asteraceae family.Some species are very precise about the number ofpetals they have - e.g. buttercups, but others have petalsthat are very near those above, with the average being aFibonacci number.
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A Fibonacci word is a specific sequence of binary digits. The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. Fibonacci based constructions are currently used to model physical systems with aperiodic order such as quasicrystals. Crystal growth techniques have been used to grow Fibonacci layered crystals and study their light scattering properties
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