Why is 1.618034 So Important?
Summary
TLDRThe video script delves into the significance of the golden ratio, approximately 1.618, a mathematical constant found in art, architecture, and nature. It's linked to the Fibonacci sequence, where consecutive numbers' ratios approximate the golden ratio. Historically, it has influenced masterpieces from the Parthenon to the works of Da Vinci, and is believed to be present in human attractiveness and DNA. The video also explores the golden ratio in natural phenomena, suggesting a universal law that might hint at intelligent design.
Takeaways
- 🔢 The number 1.618033 is considered a perfect number, foundational to art, music, mathematics, and physics.
- 🌐 The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two, with applications in various fields including search algorithms and stock trading.
- 📚 Leonardo of Pisa introduced the Fibonacci sequence to the West in 1202, but it was known in India over a thousand years earlier.
- 🎨 The Golden Ratio, symbolized by the Greek letter Phi, is approximately 1.618033 and is associated with aesthetically pleasing proportions.
- 📏 A rectangle with dimensions in the Golden Ratio is considered perfectly proportioned, and this ratio can be found in various shapes and patterns.
- 🔗 The Golden Ratio is closely linked to the Fibonacci sequence, as the ratio between consecutive Fibonacci numbers approaches the Golden Ratio as the sequence progresses.
- 🏛 Historically, the Golden Ratio has been used in the design of significant structures like the Parthenon and the pyramids, and in the works of renowned artists like da Vinci and Dali.
- 🎼 The Golden Ratio is also found in music, with composers like Debussy, Bach, Mozart, and Chopin incorporating it into their compositions.
- 🌿 Evidence suggests that the Golden Ratio is a universal law in nature, appearing in the structure of DNA, the arrangement of seeds, and the spirals of galaxies.
- 🤔 The intentional use of the Golden Ratio in historical and modern works is debated, with some suggesting it's an inherently satisfying proportion for humans.
- 🧬 The Golden Ratio's presence in human bodies and its application in nature raises questions about intelligent design or a divine plan in the universe.
Q & A
What is the significance of the number 1.618033?
-The number 1.618033 is known as the golden ratio, a mathematical constant that is found to be aesthetically pleasing and is prevalent in art, architecture, and nature.
How is the Fibonacci sequence related to the golden ratio?
-The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. As the sequence progresses, the ratio of two consecutive Fibonacci numbers approximates the golden ratio.
Who introduced the Fibonacci sequence to the West?
-Leonardo of Pisa, also known as Fibonacci, introduced the sequence to the West in 1202, although it had been identified by Indian mathematicians over a thousand years before.
In what ways is the golden ratio applied in practical fields today?
-The golden ratio is applied in various fields such as search algorithms, stock trading, gambling odds, and more due to its fundamental importance in mathematics.
What is the connection between the golden ratio and the human body?
-The golden ratio is believed to be present in the proportions of the human body, with Leonardo da Vinci's works, such as the Vitruvian Man, illustrating this concept.
How is the golden ratio used in facial attractiveness?
-Psychologists have noted that people whose facial features adhere to the golden ratio are often perceived as more attractive, indicating an inherent preference for this proportion.
Can the golden ratio be found in DNA?
-Yes, the golden ratio is observed in the structure of DNA, both in the double helix spirals and the composition of a single DNA molecule.
What is the significance of the golden ratio in nature?
-The golden ratio appears in various natural phenomena such as the spirals of snail shells, the arrangement of seeds in pinecones, and the branching of trees, suggesting a universal law in nature's design.
How does the golden ratio relate to honeybee colonies?
-Honeybee colonies maintain a ratio of males to females that approximates the golden ratio, specifically at 1:2 1.618, indicating a natural application of this mathematical principle.
What is the historical significance of the golden ratio in architecture?
-The golden ratio has been used in the design of historical structures such as the Parthenon, the pyramids of Egypt, the Taj Mahal, Notre Dame, and the Great Mosque of Cordoba, reflecting its importance in architectural aesthetics.
How is the golden ratio connected to the works of famous artists?
-Artists like da Vinci and Dali incorporated the golden ratio in their paintings, and it can also be found in the music of composers such as Debussy, Bach, Mozart, and Chopin, indicating its influence across various art forms.
Outlines
🔢 The Golden Ratio and Fibonacci Sequence
This paragraph introduces the concept of a 'perfect number', which is the Golden Ratio, approximately 1.618034. It's a number that underpins art, music, mathematics, and physics, and is believed to influence the natural world and the universe. The explanation begins with the Fibonacci sequence, a series of numbers starting with 0 and 1, where each subsequent number is the sum of the two preceding ones. This sequence was introduced to the West by Leonardo of Pisa, known as Fibonacci, but was known to Indian mathematicians much earlier. The paragraph highlights the practical applications of the Fibonacci sequence in various fields such as search algorithms, stock trading, and gambling odds. It then connects the sequence to the Golden Ratio, a mathematical concept that describes a pleasing ratio between two quantities, represented by the Greek letter Phi. The ratio is approximately 1.618034, and objects or compositions that approximate this ratio are considered to have perfect proportions. The paragraph also explains how the Golden Ratio is derived from the Fibonacci sequence by examining the ratio between consecutive Fibonacci numbers, which converge towards the Golden Ratio as the sequence progresses.
🏛️ Cultural and Natural Significance of the Golden Ratio
The second paragraph delves into the historical and cultural significance of the Golden Ratio, noting its presence in the design of iconic structures like the Parthenon, Egyptian pyramids, the Taj Mahal, Notre Dame, and the Great Mosque of Cordoba. It also mentions the use of the Golden Ratio by renowned artists such as da Vinci and Dali, and composers like Debussy, Bach, Mozart, and Chopin. The paragraph raises the question of whether the use of the Golden Ratio was deliberate or inherent to human satisfaction. It then shifts to the natural world, suggesting that the Golden Ratio is a universal law applied by nature, as evidenced by its presence in the human body, the structure of DNA, and various aspects of the natural environment, including the arrangement of seeds, tree branches, and even the organization of honeybee colonies. The paragraph concludes by pondering whether the prevalence of the Golden Ratio is evidence of intelligent design in nature, hinting at a deeper exploration in a bonus video available on Patreon.
Mindmap
Keywords
💡Perfect Number
💡Fibonacci Sequence
💡Golden Ratio
💡Phi
💡Proportion
💡Da Vinci
💡Parthenon
💡DNA
💡Nature's Design
💡Intelligent Design
💡Quantum Level
Highlights
The concept of a 'perfect number' that influences art, music, mathematics, and physics is introduced as 1.618033.
The Fibonacci sequence is explained, starting with 0 and 1, and its infinite extension by adding consecutive numbers.
The Fibonacci sequence's importance in various practical applications such as search algorithms, stock trading, and gambling odds.
The golden ratio is defined as a mathematical term describing the relationship between two figures in a complimentary ratio.
The golden ratio, symbolized by Phi, is closely approximated to 1.618033 and is associated with perfect proportions.
The connection between the Fibonacci sequence and the golden ratio is revealed through the ratio of consecutive Fibonacci numbers.
Historical and cultural significance of the golden ratio in architecture and art, including the Parthenon and the pyramids.
Artists like da Vinci and Dali incorporated the golden ratio in their work, and its presence in music by composers like Debussy and Beethoven.
The golden ratio's occurrence in natural designs, such as the human body, facial structures, and DNA.
The golden ratio's presence in the natural world, including snail shells, flower petals, and the arrangement of seeds and tree branches.
The ratio's application in the behavior of honeybee colonies, maintaining a specific male to female ratio.
The golden ratio's appearance in phenomena like hurricanes, spiral galaxies, and quantum-level objects.
The debate on whether the golden ratio's prevalence is evidence of intelligent design in nature.
The golden ratio's potential origins and its significance in ancient and modern human culture and architecture.
The possibility that the golden ratio is inherently satisfying to humans and may be applied unconsciously.
A bonus video exploring the golden ratio as potential evidence of intelligent design available on Patreon.
Transcripts
imagine if there was a perfect number a
single number so flawless had formed the
basis for all art and music a number so
important that it could be used across
the disciplines of mathematics and
physics and a number so profoundly
purposeful that the natural world and
the universe would bend to its whims
that number is one point six one eight
oh three four so let's find out why it's
so important
[Music]
at number five an explanation the
Fibonacci sequence is a string of
numbers that begins with 0 and 1 which
can be extended infinitely by adding up
any two consecutive numbers to find the
next in the sequence when we add 0 and 1
we get 1 which is the third Fibonacci
number then we add 1 and 1 to obtain our
fourth Fibonacci number which is 2 and
if we continue with this elementary
exercise in addition we get the numbers
3 5 8 13 21 34 55 89 etc in a pattern
that can be extended all the way to
infinity the sequence was introduced to
the West in 1202 by Leonardo of Pisa
also known as Fibonacci although it had
already been identified by Indian
mathematicians over a thousand years
beforehand but this guy from Pisa
shouted first so he gets to name it
after himself that's just how things
work as the world began to develop its
understanding of mathematics we soon
realised this string of digits was of
fundamental importance and today we
apply this knowledge in all manner of
practical ways search algorithms stock
trading gambling odds all make use of
the Fibonacci sequence but the way in
which you have most likely encountered
it is via the mysterious golden ratio
which appears in more random stuff than
MSG and Jessie Hyman combined at for the
golden ratio
the golden ratio is a mathematical term
used to describe the relationship of two
figures whereby the numbers seem to be
in some form of complimentary ratio if
you have a number a and a lower number B
then the two are in the golden ratio if
the ratio between a versus B is similar
to the ratio between the sum of a plus B
versus a the Greek letter ascribed to
this ratio is Phi and its value was
contracted to one point six one eight oh
three four basically anything which
comes close to this value in terms of
its ratio is said to be perfectly
proportioned for example a rectangle
that measures twelve point nine four by
eight centimeters is in the golden ratio
because twelve point nine four divided
by eight is one point six one seven five
and if we add the width and length of
the rectangle together to get twenty
point nine four the ratio between this
and the longer side twelve point nine
four is one point six one eight to the
golden ratio can be used to calculate
perfect spirals golden triangles and
other shapes and patterns too but what
does this have to do with the Fibonacci
sequence
[Music]
at 3:00 the link to link the Fibonacci
sequence and the golden ratio we must
look at the ratio between two
consecutive Fibonacci numbers and
observe the pattern this ratio takes as
you go on because it turns out that the
further along the Fibonacci sequence you
go the closer the ratio between any two
numbers is to the golden ratio the ratio
between three and two is 1.5 the ratio
between five and three is one point six
six and if we skip along a few to see
the ratio between the 12th and 13th
Fibonacci numbers we'll see that their
ratio is one point six one seven nine
the ratio between 144 and 233 is one
point six one eight zero and so on and
so forth as we mentioned earlier the
golden ratio is one point six one eight
oh three four so clearly the golden
ratio and the Fibonacci sequence have
some sort of link which we haven't
worked out yet and that is why so many
smart folks have become absolutely
obsessed with it at number two the uses
the golden ratio has fascinated the
world's most knowledgeable people for
millennia since its discovery and we
have seen its influence in some of the
finest works mankind has ever produced
plato's study into the golden ratio was
used in the designs of the parthenon the
egyptians displayed it in the planning
and construction of the pyramids and the
likes of the Taj Mahal Notre Dame and
the Great Mosque of care who odd were
also built according to this important
mathematical law artists from da Vinci
to Dali also incorporated the golden
ratio in the layout of their paintings
and the ratio can also be detected in
the music of Debussy Bach Mozart Chopin
and Beethoven even the Bible mentions
things being constructed in the golden
ratio with Noah's Ark and the Ark of the
Covenant both built in accordance with
the ratio driven Commandments laid down
by God
however the one thing we're not entirely
sure about is whether any or all of this
was deliberate modern artists and
architects know about the golden ratio
and are known to apply it purposefully
to their works and we know that at least
some historical buildings and artworks
were created by people who knew of the
golden ratio and its value but this
inexplicably pleasing proportion has
been used by people ignorant of its
existence too so is the golden ratio
merely something which all human beings
are attracted to is it something that we
find inherently satisfying and is this
love of the number 1.618 o3 for limited
only to humans and at number one
nature's design is the golden ratio a
universal law applied by nature the
evidence seems to suggest so and the
aforementioned Leonardo da Vinci may
have alluded to this in some of his most
famous works the Davina proporciona was
a mathematical textbook illustrated by
da Vinci in 1498 and in both this and
his drawing of the Vitruvian Man
he points out examples of the golden
ratio found within the human body
psychologists have also noted that
people whose facial body and bone
structures adhere to the golden ratio
are often deemed to be more attractive
than their non-proportional
counterparts and if you'd like to pause
the video to go measure your face right
now we totally understand but you might
want to hold on a second because the
most shocking example of the golden
ratio within human beings is far more
interesting did you know that the golden
ratio even applies to our DNA it's true
as both our double helix spirals and the
composition of a single DNA molecule
both seem to have been made in
accordance with the divine proportion of
the golden ratio and it's not just
humans either as we've seen the ratio
demonstrated in the shells of snails the
number of petals in a flower and the
arrangement of individual seeds
seedheads pinecones tree branches and
root systems also follow the golden
ratio as do some forms of algae and the
bodies of certain animals some creatures
even live according to the golden ratio
with honeybee colonies known to maintain
a ratio of males to females at 1:2 1.618
so is this ratio evidence that Nature
has been somehow designed was everything
on earth created by a God or advanced
extraterrestrial race to adhere to a
certain number it does look a little
suspicious especially when you also find
out that the golden ratio also applies
to hurricanes spiral galaxies and
objects at the quantum level - we're
going to explore this idea in our bonus
video the golden ratio evidence of
intelligent design which you can watch
on our patreon page at patreon.com
forward slash strange mysteries for a
$2.00 a month pledge which you can
cancel at any time you'll get to watch
this and indeed all of our bonus content
which goes deeper and darker into every
topic than YouTube allows if you don't
want to donate then it's cool we still
love you and we'll continue to provide
the best content we can under YouTube's
restrictions as you'll see if you watch
our recent video on missing pieces of
humanity's past
浏览更多相关视频
What is the Fibonacci Sequence & the Golden Ratio? Simple Explanation and Examples in Everyday Life
Fibonacci and the Golden Mean
Mathematics - Fibonacci Sequence and the Golden Ratio
The Golden Ratio: Nature's Favorite Number
P2- Fibonacci Sequence | Golden Ratio | Patterns and Numbers in Nature | Math1/GE3
The Golden Ratio: Is It Myth or Math?
5.0 / 5 (0 votes)