Julia+&+Pelumi

__ The Fibonacci sequence!!! __ ​​ The Fibonacci sequence was named after an Italian Mathematician who lived in the 12th century. His name was Leonardo Fibonacci. The sequence was named after him because he founded the sequence. By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s. Some uses for the Fibonacci sequence is modelling the population growth in rabbits, and also the development of the spiral in a snail's shell. __Fibonacci sequence in nature__ __Development of a Snail's Shell__ The snail must grow in such a way that its body remains more or less the same size in relation to its shell, otherwise the shell would become too heavy to drag around. ​ The distribution of seeds in sunflower is spiral. The seeds of the sunflower spiral outwards in both clockwise and counterclockwise directions from the center of the flower. The number of clockwise and counterclockwise spirals are two consecutive numbers in the Fibonacci sequence. Pine cones are one of the well-known examples of Fibonacci sequence. All cones grow in spirals, starting from the base where the stalk was, and going round and round the sides until they reach the top.

__Counting a Family of Rabbit__ The Fibonacci sequence can be used to measure how fast rabbits can breed in ideal circumstances. Assume that there is one male rabbit and one female rabbit in a field and each time they breed, they have one male and one female bunny. Suppose these rabbits never die and they only breed once a month. The puzzle the fibonacci made was: How many pairs of rabbits will there be in a year?

1.At the end of the first month, a male an female rabbit mate, but there is still one only 1 pair of rabbits. 2.At the end of the second month the female has produced a new pair of rabbits, so now there are 2 pairs of rabbits on the field. 3.At the end of the third month, the original female produces a second pair, making 3 pairs of rabbit in all on the field. 4.At the end of the fourth month, the original female rabbit has produced yet another new pair, the female rabbit born two months ago also produces her first pair, making 5 pairs of rabbits.

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Can you see how the series is formed and how it continues? If not, look at the answer! The fibonacci series is formed by starting with 0 and 1 and then adding the previous two numbers to get the next one: 0 1 - the series starts like this. 0+1=1 so the series is now 0 1 1 1+1=2 so the series continues... 0 1 1 2 and the next term is 1+2=3 so we now have 0 1 1 2 3 and it continues as follows