this is Gareth Manfred graph with
restore the planet and today I'm here to
share with you about the Fibonacci
sequence and spiral the Fibonacci
sequence is a series of numbers that go
from 1 to 1 to 2 to 3 to 5 to 8 and then
to 13 and 21 and on and on in fact it
will continue like that forever
you might wonder is this some sort of
arcane mathematics that doesn't make any
sense absolutely not this number
sequence is very easy to understand you
simply add back the last two numbers for
example we start with 1 the smallest
total unit that we can have there's
nothing before 1 so we simply have to
duplicate it so we get another one but
the next time we perform this process we
get 1 + 1 which makes 2 to perform this
process again you'll have to add 2 + 1
to produce 3 then 2 + 3 to produce 5
then 3 + 5 to make 8 + 8 + 5 to make 13
and so on unto infinity nature uses this
extraordinarily simple number sequence
to construct so many of her forms
everything from galaxies to sunflowers
and now I'm going to show you how this
number sequence translates into actual
physical geometry if you're just
starting out it's best to begin with a
surface like graph paper meaning that
it's easiest if you draw on something
that has evenly and symmetrically placed
square units of measurement that are all
of the same size to make it simple we'll
have one of these units represent one
and we'll trace it out in red then we
need another 1 unit so we'll draw that
one next to the first one then on the
top or in this case the bottom we can
draw a line connecting both of the two
squares that we made we can then
duplicate that line three more times and
produce a perfect square then we can
duplicate that process as
many times as we like or as many times
as the canvas that we're using will
allow and as you can see the five square
is five units by five units the eight
square is eight units by eight units and
so on now I'm going to show you how to
add the more feminine curving lines
there are various ways that I've seen
different artists do this but I'm going
to show you the method that I like the
best because I feel that it most closely
matches nature this method allows you to
use circles to construct the spiral to
begin with draw a perfect cross who's
every arm is the exact length of the
square that you're working in the center
of this cross should be placed furthest
from where the spiral will end up being
now all you've got to do is draw a
perfect circle which by virtue of its
size and positioning is cut into four
equal pieces by the cross this means
that the square that you're working on
should take up 1/4 of the circle that
you're using to produce a spiral within
it now all we've got to do is erase the
other 3/4 that we don't need but in this
case either side is the same so we can
simply add back in 1/4 now all we've got
to do is repeat this process again and
again until all of the zero curvature
scaffolding for a Fibonacci spiral is
filled and as you can see in its
completed form it very closely matches
the twisting motions of a galaxy thanks
so much for watching and wanting to
understand our universe have by far the
absolute best day ever
