Places You Won’t Believe The Golden Ratio & Fibonacci Sequence Appears

Places You Won’t Believe The Golden Ratio & Fibonacci Sequence Appears

– You’ve probably heard
of the golden rule, and you might even be using
it in your daily life, but there is another little bit of gold that is playing a role in your daily life that you might not know about. The Golden Ratio, or 1.618. The Golden Ratio is a proportion based on the Fibonacci
Sequence and can be found almost anywhere in life,
probably even in the room where you are sitting. For those who do not know
the Fibonacci Sequence, it’s a series of numbers where each number is the sum of the two previous numbers. For example, one, one,
two, three, five, eight is a basic example of
the Fibonacci Sequence. The sums are all called Fibonacci Numbers. These special little numbers
can be found in architecture, art, music, and even in nature. Here we will explore
some of the many places where you can find the Golden Ratio, and the Fibonacci Sequence. – Amazing! Number 10: the Great Pyramids of Giza. The ancient Egyptians have
intrigued the human race for thousands of years,
possibly the most famous point of interest in Egyptian culture are The Great Pyramids of Giza. The most popular question
about the pyramids is how they were built,
but maybe the question should be why they were built, specifically why they were built in such a specific orientation. When ariel photographs
first became available of the Great Pyramids, it became apparent that there is a pattern
to they’re placement. The first place that the ratio is seen is in the geometry of the pyramids. When applying the Pythagorean Theorem to the height of the base of
one of he internal triangles, you will notice that the
hypotenuse is just .025% off of a perfect Golden Ratio triangle, otherwise known as a Kepler Triangle. While this could be a happy accident, we are guessing that these
ancient mathematicians were attempting to be as exact as possible when dragging these eight
ton blocks across the desert. The next place you can
find the golden ratio in the pyramids is their
placement next to each other. Most of the pyramids have been placed in the exact orientation
of a phi matrix grid, which is based on the Golden Ratio. This can be seen in
the Pyramids of Queens, and the Pyramids of Khufu and Khafre. While the Golden Ratio can
be found in many more places in the complex of the pyramids,
maybe the most astounding can only be seen from above. When drawing lines
through the base corners of the pyramids, you will notice that they begin to intersect
at a specific point, mathematicians then began
to notice a familiar shape form when looking at the
illustration from above. The spiral shape hat is
seen in so many Golden Ratio related figures is seen
once again in the placement and orientation of the
Great Pyramids of Giza. Just to clarify, a
golden spiral is a spiral that grows by a factor of
Phi as it increases in size. These spirals can also be
fit into the Phi matrix. Number nine: The Taj Mahal. One more wonder of the world
that successfully implemented the Golden Ration into it’s
architecture, the Taj Mahal. It’s no big secret that
the Indian people have made a great contribution to
the field of mathematics, so it should come as
no surprise that their most famous building is rich
with mathematical references. The first and most obvious
place you see the Golden Ratio on the Taj Mahal is on
it’s rectangular base where the Phi matrix can be seen. In addition to this, you
can see other buildings on the Taj Mahal premises
that also implement the Phi matrix into it’s architecture. Number eight: The Mona Lisa. One of the most famous pieces
of art in human history is also one of the most famous examples of the use of the Golden
Ratio, the Mona Lisa. Leonardo Da Vinci was a
polymath who held talents is subjects from
architecture to astronomy. What is best known for
his contributions to art in many of his works he was
able to combine his talents in mathematics with his artistic ability. The Mona Lisa was no exception. Throughout the picture, you
can draw the Golden Rectangle, for example the space between
her eyes can be divided into a Golden Rectangle,
meaning that a Golden Rectangle exists around her head,
furthermore her entire body can be fit into a Golden Rectangle. You can even draw a Golden Spiral from the center of her nose over her head and through her shoulders. Many of Da Vinci’s works
where the Golden Ratio can be found is within
the famous Vitruvian Man, as well as The Last Supper. Nowadays, artists look to
incorporate the Golden Ratio within their works in
an attempt to emulate the masterpieces of Renaissance. Number seven: Spiral Galaxies. The examples of the Fibonacci Sequence and the Golden Ratio that
we have provided so far may lead you to think
that this is some man made and contrived conspiracy
theory put forth by mathematicians around the world, but when we look to nature, we can see that this is no accident. It almost seems divine. One of the most astounding
places that we find the Golden Ration in nature
is at it’s most grand scale. The cosmos. The Golden Spiral can be
seen across the universe in the shape of spiral galaxies, and even in our milky way galaxy. If you look at our
galaxy, you can calculate the familiar logarithmic
growth by a factor of phi as the galaxy expands, but
the galactic implementation of the Golden Ratio doesn’t end here. The shape of the earth and moon are also related to the Golden Ratio. When placed next to each other, the radius of the moon plus
the radius of the earth equal the square root of phi. In addition to this, the
triangle that can be drawn using the radius of the earth as the base will create a triangle with
the hypotonus measuring phi. Another example of this Golden
Spiral that can only be seen from space is the shape of hurricanes. Loot at any satellite
picture of a hurricane, and you can once again see the spiral form in the raging winds of nature’s
most destructive force. Number six: Flower Petals. One of the most famous examples
where the Fibonacci Series and the Golden Ratio are seen
in nature is within plants. The Fibonacci Series can often be found in the number of seeds or
petals in many flowers and the Golden Spiral can be found within the shape of the entire flower. Many flower petals come
in quantities that are Fibonacci Numbers, for
example, lilies and irises have three petals, butter
cups have five peals, and daisies can be found
with 34, 55, and 89 petals. If you look at pine cones and pineapples from the bottom, you
will notice that spines of these two plants are
oriented in clockwise, and counterclockwise spirals. The number of lines
that make these spirals are both Fibonacci numbers. Flowers like roses have petal arrangements that are golden ratios. Nest time you’re out in
the garden, see how many of your own plants follow
these Fibonacci trends. Number five: DNA. The Golden Ratio is so
abundant, it even exists within your DNA. You can find the Golden Ratio
and the Fibonacci Sequence in numerous places throughout the Deoxyribonucleic Acid that
makes up the human body. Maybe the most obvious
example is the actual size of human DNA which
measures 34 angstrom units long by 21 angstrom units wide. Both of these are Fibonacci Numbers. It is even reported that
a cross sectional view of a DNA molecule shows a decagonal shape. A decagon can be created
by rotating a pentagon by 36 degrees using the
diagonals of the pentagons that can be found in the fractals of a DNA cross section, you
can see the Golden Ratio within the proportions of
the diagonals and the sides which would be phi, too. Number four: music. As we’ve said before,
the Golden Ratio exists across all subjects including music. In some of the world’s most
popular pieces of music, the golden ratio is seen
in timing and pacing. It is speculated that
such pieces that implement a Golden Ratio based pattern
are more pleasing to the ear. In most of these examples,
mathematicians have broken songs down by the Golden Mean, .618. One of the most famous examples of this is Beethoven’s Fifth Symphony
where the Golden Ratio is used in multiple sections
throughout the song. Mozart has also been reported
using the Golden Ratio in many of his Sonatas. Nowadays, you can find many composers, musicians, artists, trying
to implement the Golden Ratio into their songs. Number three: Human Facial Construction. You’ve probably heard people saying that humans are naturally attracted to facial symmetry. That symmetry is created
by the Golden Ratio. People often say the Mona
Lisa is one of the most pleasing paintings to look at, and it’s not coincidence
that the Golden Spiral that shapes her face is
similar to that of most humans. Many of the people that
society deems most attractive are the ones whose face most closely fits into the phi matrix that
a person’s face fits into. Plastic surgeons even
use programs that help to digitally alter
someone’s face so it better fits the golden ratio. This allows them to show their patients how their face can be surgically altered to look more attractive. Facial recognition
software is also based on the Golden Ratio. Number two: Advertising. Companies are always looking
for the best ways to advertise to their potential customers, and the use of the Golden Ratio is one of
the most effective techniques. We already know that faces that loosely associated to the Golden
Ratio, or found most appealing, and you will find that these
are the types of people that are being sold. You can also find the
Golden Ratio in the logos of some of the world’s
most popular brands, such as Toyota or Pepsi. The Golden Ratio is a powerful tool for website and graphic designers. Many of your favorite sites will be based around the Golden Matrix,
or the Golden Rectangle. Take a look at the most basic templates on some free web builders,
and you will notice that most of them share
a very similar look to the Golden Ratio grids. Number one: Anatomy of Living Things. Earlier we mentioned one
of Leonardo Da Vinci’s most famous works, the Vitruvian Man. One of the reasons that
it was such a famous drawing is because it outlined the immense proportionality
of the human body. For example, you can
see the Golden Ratio in the length of the human head,
the breadth of the shoulders, the distance from the top of the head to the fingertips, and even
the length of your forearm. The consistency of the
number five in the human body is also related to the Golden Ratio. We have five appendages on our torso, two arms, two legs, one head. On each of our arms and legs, we have five appendages in fingers and toes. On our head we have five protruding appendages in two ears,
two eyes, and a nose. Finally, as we all know,
we have five senses. Other groups in the
Animal Kingdom also have body proportions based on the Golden Rule. The most visibly obvious example are insects and their segmented bodies. From the galaxies above
us, right down to our DNA, you can find the Golden
Ratio in almost every aspect. There are plenty of
other examples out there of how the Golden Ratio plays a role in your day to day
activities, but we just listed some of our favorites. Let us know some of your favorite ways the Golden Ratio affects your
life in the comments below. Thanks for watching.


  1. This is an invitation to see a theory on the nature of time! In this theory we have an emergent uncertain future continuously coming into existence relative to the spontaneous absorption and emission of photon energy. In this process we even have an objective reason for the start of the Fibonacci numbers 0, 1, 1,… with the t = 0 and the positive +1 and negative –1 representing the positive and negative of electromagnetic waves with everything being based on one geometrical process. In this theory the future is not random it is based on a process of spherical symmetry forming and breaking. Spherical symmetry forms the low entropy that we see if we look back in time at the ‘big bang’ and also forms the potential for ever greater symmetry formation that we have in cell life with the Fibonacci spiral being visible almost everywhere in nature! This is because if the quantum wave particle function Ψ or probability function is reformulated as a linear vector then all the information I have found says that each new vector is formed by adding the two previous vectors together this forms the Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ∞ infinity!

  2. {Verily! In the creation of the heavens and the earth, and in the alternation of night and day, there are indeed signs for men of understanding.} (Al-Qur'aan; 3.190)

  3. Can any musicians explain to me how this is used in music? I heard him say with regards to timing and pacing..but can any1 give any examples? Thanks

  4. The golden ratio has nothing to do with (10) the Great Pyramids of Giza, or in (9) the Taj Mahal, or in (8) the Mona Lisa, or in (7) spiral galaxies (geometric spirals could have any ratio, the golden ratio is a specific ratio). It isn't until (6) that there's a valid example. Garbage channel.

  5. You've undermined a universal truth by forcing it onto ridiculous examples. The Toyota and Pepsi logos? Really???! I paused the video and tried and tried to 'get' your application. It's just a spiral plonked on top, in the Toyota example not precisely matching anything, and in teh Pepsi example not even nearly doing so. Given so many real examples, why be so ridiculous?

  6. Wtf has the golden ratio has to do with pepsi. You just put the spiral on top of things and say it is made with the golden ratio. I cannot really undertand what the golden ratio is but there is no symmetry in mona lisa, pepsi, most advertisements and other things. I cannot see where this spiral fits. I can say my computer screen is made from the golden ration because if i put the rectangle on top of and adjust the size of the sides it matches. The sides of the golden ratio form a rectangle.
    BONUS: The golden ratio number 5 fits in our 5 senses. NOPE, this is a myth. We have way more senses as the theory about the 5 senses has been FINAlly rejected.

  7. I have to do a project on this and I am fucking lost and am I only the one who thinks the mona lisa, the indian building, and the Last supper were not intended to have the golden ratio in them? I honestly just feel like people are looking way to deep into this. Us humans do tend to over complicate things

  8. Or it in painting and everything because it's proportional 3,6,9,rib of man womb of woman of rib man of womb two become one 3 ,man ,6 ,womb 9,self sum of the word a shall be as the sum of the word . 7 toes where you learn your letters 5 ,7 toes or meant hand 6 figures

  9. Fuck me ..!!! The amount of plp that can't understand or think it's bullshit ..!!!! HINT=if you can't understand that's ok but stop watching and leaving dumb arse comments …!!!! Stick to things you do understand like PLAY SCHOOL..!!!!!

  10. Funny how people doesn't “believe” in the golden ratio. And I say “believe” beacause it's not about beliving, it's just how it is. The Golden ratio is used not only in paintings, also in photography. Take your cellphone and activate the grid. Well that grid it's golden ratio based. Golden Ratio it's used in what photography is called composition, like in music. If you don't belive in it, just study a little about photography, and then you will feell stupid. And I say all of this beacause when I first started studding cinematography one day the teacher showed up in the calass and started talking about why the images in movies(some of them) look so good. And he started showing daiagonal lines in the images and the golden ratio and more things, and I was like, this is a joke, right? But hell no. And later on I learned that not only the golden ratio but there was a lot of types of composition.
    So basically, yes the golden ratio it's a thing.
    BTW, my english is not that good, so I apologize if there are errors.

  11. 2 eyes 2 ears , a nose & mouth is equal to appendages 6 …not 5 🙄 Your using your 6th appendage too much. Shut up

  12. Seems to me that this very forced application of the Fibonacci spiral on everything from the Mona Lisa to the pyramids is a just a bad case of pareidolia. Yep … there’s a spiral right here in my bowl of cereal …

  13. I found my phi moment whenever I beat my meat. Using fibonacci sequence each second I pump, I ejaculate at exactly 2 mins and 1 sec which is equivalent to 1 min and 61 secs = 1.61. That's weird.

  14. Please when you are recording the voice over please, just please use s pop filter. It's not nice on your ears when you don't.

  15. Fibonacci stole the idea in around 1200 centry from India were mathematics discovered this method a thousand years earlier!

  16. The overlay of a gr spiral on all of those photo examples are obviously bias; only like 50% of the intersecting points/lines/arcs apply to the gr. It doesn't fit like everyone portrays.

  17. Out of my own curiosity, do you know how many homeless families would $150.000 feed?
    That much is how much taxpayers, campaign money was used to buy high- end prostitute's silence. by the Bastard, fake resident. Awful!

  18. I dont know if anyone have noticed it but the singer and songwriter kim taehyung from korean boy band bts has a golden ratio from the right side of his face when he smiles and i dont know but you said in the video that every special thing had a golden ratio pattern and kim has been given the title of the most handsome face in 2018 from social media poll.

  19. Please, stop spreading a myth that golden ratio is based on Fibonacci sequence. You can take any starting numbers, not only 011. You can start the sequence with any two numbers and phi will always go closer to 1.618, because the method is the key, not the starting numbers.

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