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From where did the Fibonacci sequence come from?
The Fibonacci sequence, was first known by the ancient people of India. When Fibonacci travelled there in the 1200's he learnt it from them and then passed on his learning to the rest of Europe through his book, Liber Abaci.
Did pascals triangle or fibonaccis sequence come first?
Fibonacci lived about 400 years before Pascal did.
Which number should come next 3-5-8-13-21?
This is a Fibonacci sequence. Each number in the sequence is the sum of the previous two numbers:3+5=85+8=138+13=2113+21=34
How did the Fibonacci pattern of numbers come about?
the fibonacci pattern of numbers came round about in the 1980's
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.
