Fibonacci Sequence
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The Fibonacci sequence appears frequently in nature. It is seen in patterns of plant leaves, flower petals, pinecones, shells, and other biological settings. Many plants and flowers display spirals corresponding to Fibonacci numbers. The ratio of numbers in the sequence approaches the golden ratio, which is also found in natural patterns. The Fibonacci sequence has applications in mathematics, computer science, architecture, and art due to its prevalence in natural forms and patterns.
Fibonacci Sequence
- 2. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next) It is called the Fibonacci series after Leonardo Fibonacci.
- 3. The "shallow diagonals" of Pascal's triangle sum to Fibonacci numbers.
- 4. The Fibonacci numbers are studied as part of number theory and have applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science.
- 5. FIBONACCI SEQUENCE IS ALSO SEEN IN RABIT MULTIPLICATION
- 7. Every human has two hands, each one of these has five fingers, each finger has three parts which are separated by two knuckles. All of these fit into the sequence. Fibonacci Fingers?
- 9. •The Fibonacci numbers are Nature's numbering system. •They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, pinecone, or the scales of a pineapple. • The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees.
- 10. If we take the ratio of two successive numbers in Fibonacci's series, (1, 1, 2, 3, 5, 8, 13, ..) and we divide each by the number before it, we will find the following series of numbers: 1/1 = 1, 2/1 = 2, 3/2 = 1·5, 5/3 = 1·666..., 8/5 = 1·6, 13/8 = 1·625, 21/13 = 1·61538... The ratio is called the golden ratio. It has a value of approximately 1·618034 and is denoted by the Greek letter phi.
- 11. Flowers often have a Fibonacci number of petals, daisies can have 34, 55 or even as many as 89 petals!
- 12. Sunflower head displaying florets in spirals of 34 and 55 around the outside The beautiful spirals of the sun flower head reveal the astonishing double connection with the Fibonacci series
- 20. The florets within this cluster are arranged spirally. Typically each floret is oriented toward the next by approximately the golden angle, producing a pattern of interconnecting spirals where the number of left spirals and the number of right spirals are successive Fibonacci numbers.
- 26. This poppy seed head has 13 ridges on top. Fibonacci numbers can also be seen in the arrangement of seeds on flower heads.
- 27. some plants branch in such a way that they always have a Fibonacci number of growing points.
- 28. many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. FIBONACCI SEQUENCE IN PLANTS
- 29. Pine cones show the Fibonacci Spirals
- 31. The scales are spirally arranged in fibonacci number ratios.
- 33. Here is a curve which crosses the X- axis at the Fibonacci numbers
- 34. FIBONACCI SEQUENCE IN VEGETABLES
- 40. The adjacent picture shows a design featuring the pentagons and hexagons used in the Mosque. which were developed out of the connections between the Fibonacci series,and the Golden Proportion. The Fibonacci numbers play a significant role in nature and in art and architecture.
- 41. The sequence has been used in the design of a building,
- 45. The series can be extended and the numbers can be found directly by applying this formula-Fn-2=Fn-Fn-1