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The fibbonacci sequence is a sequence of numbers starting with one where each number is the sum of the two numbers before it. The sequence goes 1,1,2,3,5,8,13,21,34,55,89, and so in. The ratio of any number in the sequence to the number just before it (like 55/34, or 13/8) gets closer and closer to the golden ratio, 1.618033989.
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Who uses the Fibonacci sequence today?
The Fibonacci sequence is actually one of the most used mathematical ideas in the world! This is because the differences between the terms of the sequence give birth to the Golden Ratio (which is about 1:1.62). This 'magic' ratio is often said to hold the key to beauty, and is found throughout the natural world - including in the ratio of sizes in a human face. Today it is most commonly used by architects, artists, fashion designers and the like - for anyone that looks to create beauty the Fibonacci Sequence and the Golden Ratio is vital because it tells you how the size you need to make things to make them visually appealing.
How are pentagrams related to Fibonacci numbers?
The pentagram is related to the golden ratio, because the diagonals of a pentagram sections each other in the golden ratio. The Fibonacci numbers are also related to the golden ratio. Take two following Fibonacci numbers and divide them. So you have 2:1, 3:2, 5:3, 8:5 and so on. This sequence is going to the golden ratio
What is the Fibonacci like sequence?
Well a like sequence would follow the same rule as the sequence itself: Each number (after the first two) is the sum of the previous two numbers. Thus the sequence begins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc. The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).
What is Fibonacci sequence conclusion?
There is no conclusion to the Fibonacci sequence - it continues on infinitely. The conclusion is that successive terms tend to a constant ratio with one another. So if a is one term, the next is ar and the one after that is ar2. Then from the rule that any term is the sum of the previous two, ar2=ar +a, which means r2-r-1=0 so r =(1+sqrt5)/2 (the golden ratio). There is no end to this series.
What are some things in nature that have the Fibonacci sequence?
Obvious occurrences are in the number of "observable" spirals in the seeds of a sunflower, or on the outside of a pineapple, and in the number of leaves and petals on plants, for example clovers usually come with 3 leaves, daisies usually come with 55 petals. (3 & 55 are both Fibonacci numbers.) As the Fibonacci numbers increase, the ratio between them gets closer and closer to the "Golden Ratio" φ which is approx 1.618034 (exactly it is (1 + √5)/2). Each petal or leaf of a plant grows from primordia and if the reflex angle between successive primordia is measured it is approx 222.5°; the ratio of this to a full turn is 360/222.5 ≈ 1.618 - the Golden Ratio. In using this spacing it provides the densest packing (for example with the seeds in a sunflower) making it stronger than radial spokes; it also means that each successive primordium gets placed in the largest space available.
