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Why Are Fibonacci Numbers Important in Nature? : Math Problems & Trigonometry

hi my name is Eugenia and I'm a math

tutor today we're going to talk about

wife of a nachi numbers are important in

nature to review the Bonacci numbers are

a sequence of numbers starting with 0

and 1 where each of the following

numbers is a sum of the previous two so

we have 0 plus 1 is 1

1 plus 1 is 2 1 plus 2 is 3 2 plus 3 is

5 and then we have 8 13 21 34 and 55 and

so the list continues the fascinating

thing about this sequence is that it is

naturally found throughout the whole

universe from the formation of galaxies

and hurricanes to the way leaves grow on

a stem one of the most common ways we

see that the Bonacci sequence in nature

is in spirals take a look at this

pattern it may not be obvious at first

but if you take a close look you will

find that there are multiple spirals

here in different directions if this is

a truth of a dachi pattern then the

number of spirals when added up will

always be a Fibonacci number for example

if we count the number of spirals going

in this direction we will find that

there are 21 of them when we add them up

and 21 is one of our numbers or we could

count the spirals going in this

direction in which case we would get 34

total spirals and that of course is also

one of our numbers or there's a third

way we could count it going this way in

which case we would get 55 total spirals

which is also one of our numbers now

that you know what if Fibonacci spiral

is and what it looks like take a look at

this pine cone do you see how it

resembles the same spirals the same is

true of almost all pine cones if you

count their spirals in any direction you

will get a Fibonacci number

another way that Fibonacci numbers

appear in nature is in the way animals

reproduce like rabbits and honeybees for

example if a female honeybee lays an egg

and

is unfertilized than a male will hatch

so each male bee has one only one parent

if the egg is fertilized then a female

will hatch so all female bees have two

parents now let's imagine one male bee

since he's a male he has only one parent

a female since this is a female she has

two parents a female and a male

this female also has two parents

but this male only has one let's do one

more row of parents this female has a

female and a male parent this male only

has one female parent and this female

has a female and a male parent can you

tell where this is going if we add up

the B's in each generation we get 1 1 2

3 & 5 which is the beginning of our list

of Fibonacci numbers and if you continue

drawing the parents the list will

continue that's just 2 examples of how

the Fibonacci numbers are important in

nature and there are many more my name

is Eugenia and thanks for watching