Places You Won't Believe The Golden Ratio & Fibonacci Sequence Appears
Summary
TLDRThe video script delves into the omnipresence of the Golden Ratio, 1.618, in various facets of life, from the architectural marvels of the Great Pyramids and Taj Mahal to the artistic genius of Leonardo da Vinci. It explores its presence in nature, from spiral galaxies to the arrangement of petals in flowers, and its influence on human aesthetics and facial proportions. The script also highlights the Golden Ratio's role in music, advertising, and even DNA, showcasing its universal significance and its integration into human creativity and the natural world.
Takeaways
- 📏 The Golden Ratio, approximately 1.618, is a mathematical proportion found extensively in nature, art, architecture, and even in human biology.
- 🏛 The Great Pyramids of Giza exhibit the Golden Ratio in their geometry and placement, suggesting a deliberate use of this mathematical concept in ancient Egyptian architecture.
- 🏰 The Taj Mahal incorporates the Golden Ratio in its design, reflecting the significant contribution of Indian mathematicians to the field.
- 🖼 The Mona Lisa by Leonardo da Vinci is a renowned example of the Golden Ratio's use in art, with the painting's composition and the subject's facial structure adhering to this proportion.
- 🌌 The Golden Ratio appears in the cosmos, with the spiral shapes of galaxies, including our Milky Way, following a logarithmic growth pattern based on the Golden Ratio.
- 🌼 In nature, the Fibonacci Sequence and the Golden Ratio are evident in the arrangement of flower petals and the spiral patterns of plants like pinecones and pineapples.
- 🧬 The Golden Ratio is present within human DNA, with the dimensions of DNA molecules and the structure of the DNA helix reflecting this mathematical ratio.
- 🎵 Music is another domain where the Golden Ratio is believed to enhance the aesthetic appeal, with composers like Beethoven and Mozart reportedly using it in their compositions.
- 🤩 The human face's attractiveness is often associated with the Golden Ratio, with facial symmetry and proportions that adhere to this ratio being perceived as more appealing.
- 📐 The use of the Golden Ratio in advertising and design is prevalent, with companies leveraging its aesthetic appeal to create more engaging logos, layouts, and advertisements.
- 🦋 The anatomy of living things, including humans and various animals, often reflects the Golden Ratio, indicating a universal pattern in biological structures.
Q & A
What is the Golden Ratio and what is its value?
-The Golden Ratio, often denoted by the Greek letter Phi (φ), is a mathematical proportion that is approximately 1.618. It is found in various aspects of art, architecture, and nature, and is based on the Fibonacci Sequence.
What is the Fibonacci Sequence and how does it relate to the Golden Ratio?
-The Fibonacci Sequence is a series of numbers where each number is the sum of the two preceding ones, typically starting with 0 and 1. It is closely related to the Golden Ratio because as the sequence progresses, the ratio of consecutive Fibonacci numbers approximates the Golden Ratio.
How is the Golden Ratio applied in the architecture of the Great Pyramids of Giza?
-The Golden Ratio is seen in the geometry of the pyramids, with the height to base ratio of the internal triangles being close to the Golden Ratio. Additionally, the placement of the pyramids follows a phi matrix grid, indicating a deliberate use of the Golden Ratio in their orientation.
What is the significance of the Golden Ratio in the Taj Mahal?
-The Taj Mahal incorporates the Golden Ratio in its architecture, with its rectangular base and other buildings on the premises following the phi matrix. This use of the Golden Ratio contributes to the aesthetic appeal and harmony of the structure.
How does Leonardo da Vinci utilize the Golden Ratio in his artwork, particularly in the Mona Lisa?
-Leonardo da Vinci used the Golden Ratio in the composition of the Mona Lisa, with the painting's dimensions and the positioning of the subject adhering to the Golden Rectangle. Additionally, a Golden Spiral can be drawn from the center of her nose over her head and through her shoulders.
In what way does the Golden Ratio manifest in spiral galaxies?
-The Golden Ratio appears in the form of the Golden Spiral, which is observed in the structure of spiral galaxies, including our own Milky Way. The spiral arms of these galaxies exhibit a logarithmic growth by a factor of phi as they expand.
Why are the Fibonacci Numbers and the Golden Ratio found in the arrangement of flower petals?
-Many flowers exhibit the Fibonacci Numbers in the number of their petals or seeds, and the Golden Spiral can be seen in the overall shape of the flower. This arrangement is believed to optimize the exposure to sunlight and resources for the plant.
How is the Golden Ratio present in human DNA?
-The Golden Ratio is found in the dimensions of human DNA, which measures 34 angstrom units long by 21 angstrom units wide, both Fibonacci Numbers. Additionally, the cross-sectional view of a DNA molecule shows a decagonal shape, which is related to the Golden Ratio.
How does the Golden Ratio influence music composition?
-The Golden Ratio is used in the timing and pacing of some of the world's most popular music pieces, with the belief that compositions adhering to a Golden Ratio pattern are more pleasing to the ear. Examples include works by Beethoven and Mozart.
What role does the Golden Ratio play in human facial attractiveness?
-The Golden Ratio is believed to contribute to facial symmetry, which is often associated with attractiveness. The proportions of an attractive face often fit within the phi matrix, and this principle is used by plastic surgeons and in facial recognition software.
How is the Golden Ratio used in advertising and design?
-The Golden Ratio is employed in advertising and design to create visually appealing layouts and compositions. It can be found in logos of popular brands and is a fundamental aspect of web and graphic design, often used in template structures.
What is the connection between the Golden Ratio and the anatomy of living things?
-The Golden Ratio is observed in the proportions of the human body and other living organisms. For example, the Vitruvian Man by Leonardo da Vinci illustrates the human body's adherence to the Golden Ratio, and similar proportions can be seen in the segmented bodies of insects.
Outlines
🔍 The Golden Ratio in Architecture and Art
The script discusses the prevalence of the Golden Ratio, approximately 1.618, in various aspects of life, starting with its appearance in the Great Pyramids of Giza. It suggests that the pyramids' geometry and orientation are based on the Golden Ratio, as seen in the near-perfect Kepler Triangle and the phi matrix grid. The script also highlights the Taj Mahal's use of the Golden Ratio in its architecture, emphasizing the cultural significance of mathematics in Indian history. Additionally, the Mona Lisa by Leonardo da Vinci is noted for its use of the Golden Ratio, with the painting's composition and the artist's other works reflecting mathematical harmony.
🌌 The Golden Ratio in Nature and the Cosmos
This section of the script explores the Golden Ratio's presence in the natural world and the cosmos. It mentions the logarithmic growth pattern of spiral galaxies, including our Milky Way, and how the shapes of the Earth and Moon relate to the Golden Ratio. The script also describes the Golden Spiral seen in hurricanes from space and the Fibonacci Series' occurrence in the arrangement of flower petals and seeds. Pine cones and pineapples are highlighted for their Fibonacci spiral patterns, and the DNA's structure is noted for its Golden Ratio components, suggesting a fundamental role in life's design.
🎵 The Golden Ratio in Music, Human Anatomy, and Design
The script delves into the Golden Ratio's influence on music, suggesting that its use in timing and pacing contributes to the pleasing nature of certain compositions, with examples from Beethoven and Mozart. It also touches on the Golden Ratio's role in human facial attractiveness and the use of facial symmetry in advertising and design. The script further discusses the Golden Ratio in the anatomy of living things, referencing Leonardo da Vinci's Vitruvian Man and the proportionality of the human body. It concludes with a mention of the Golden Ratio in animal body proportions and an invitation for viewers to share their insights on the topic.
Mindmap
Keywords
💡Golden Rule
💡Golden Ratio
💡Fibonacci Sequence
💡Great Pyramids of Giza
💡Taj Mahal
💡Mona Lisa
💡Spiral Galaxies
💡Flower Petals
💡DNA
💡Music
💡Human Facial Construction
💡Advertising
💡Anatomy of Living Things
Highlights
The Golden Ratio, approximately 1.618, is a proportion found in various aspects of life based on the Fibonacci Sequence.
The Fibonacci Sequence is a series where each number is the sum of the two preceding ones, such as 1, 1, 2, 3, 5, 8.
The Golden Ratio is evident in architecture, art, music, and nature, including the Great Pyramids of Giza.
The geometry of the Great Pyramids and their orientation suggest intentional use of the Golden Ratio.
The Taj Mahal incorporates the Golden Ratio in its architecture, showcasing Indian contributions to mathematics.
Leonardo da Vinci utilized the Golden Ratio in his art, including the Mona Lisa and the Vitruvian Man.
Spiral galaxies, including the Milky Way, exhibit the Golden Ratio in their structure and expansion.
The Fibonacci Sequence is observed in the arrangement of flower petals and the spiral patterns of plants.
DNA structure contains the Golden Ratio and Fibonacci Numbers in its measurements and molecular geometry.
Musical compositions, such as Beethoven's Fifth Symphony, apply the Golden Ratio for aesthetic appeal.
Facial attractiveness is often associated with proportions that align with the Golden Ratio.
Advertising leverages the Golden Ratio to create appealing visuals and effective brand logos.
The human body's proportions, as depicted in the Vitruvian Man, reflect the Golden Ratio.
The Golden Ratio is present in the anatomy of various living organisms, including segmented bodies of insects.
The Golden Ratio's prevalence suggests a universal principle in design, from galaxies to DNA.
The video invites viewers to explore and share personal examples of the Golden Ratio's influence in daily life.
Transcripts
- 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.
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