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#### 为何1.618034如此重要

Why is 1.618034 So Important?

Imagine if there was a perfect number,

a single number so flawless,

it 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 1.618034.

So let’s find out why it’s so important.
[音乐]
[music]

At number five, an explanation.
[音乐]
[music]

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 elementary exercise in addition, we get numbers
3 5 8 13 21 34 55 89等等
3 5 8 13 21 34 55 89, et cetera,

in a pattern that can be extended all the way to infinity.

This sequence was introduced to the West in 1202

by Leonardo of Pisa, also known as Fibonacci,

over a thousand years beforehand.

But this guy from Pisa shouted it 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 in Jesse Heiman combined.
[音乐]
[music]

At four, 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 complementary ratio.

If you have a number a and a lower number b,

Then they two are in the golden ratio if the ratio between a versus b

is similar to the ratio between the sum of a+b versus a.

The Greek letter ascribed to this ratio is Φ.

And its value is contracted to 1.618034.

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 12.94 by 8 centimeters

is in the golden ratio.

Because 12.94 divided by 8 is 1.6175.

And if we add the width and length of the rectangle together

to get 20.94.

The ratio between this and the longer side, 12.94,

is 1.6182.

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?
[音乐]
[music]

To link the Fibonacci sequence and the golden ratio,

we must look at the ratio between two consecutive Fibonacci numbers,

and observe the pattern in 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.
3和2的比值是1.5
The ratio between 3 and 2 is 1.5.
5和3的比值是1.66
The ratio between 5 and 3 is 1.66.

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 1.6179.

The ratio between 144 and 233 is 1.6180.

And so on and so forth.

As we mentioned earlier,

the golden ratio is 1.618034.

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.
[音乐]
[music]

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 Kairouan,

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 1.618034

limited only to humans?
[音乐]
[music]

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.
《Divina proportione》是一本在1498年
The ‘Divina proportione’ 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 the 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 demontrated in the shells of snails,

the number of petals in a flower,

and the arrangement of individual seeds within seed heads,

pine cones, tree branches, and root systems

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 the ratio of males to females
1到1.618之间
at 1 to 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, too.

We are going to explore this idea in our bonus video,
《黄金比例：智能设计的证明？》
“The Golden Ratio: Evidence of Intelligent Design?”,

which you can watch on our Patreon page atpatreon.com/strangemysteries.

For a \$2 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 that 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

As you’ll see, if you watch our recent video
《人类过去的缺失部分》 你就会看到
on missing pieces of humanity’s past.

##### 译制信息

1.618034被认为是完美的数字，自然界以及人类的设计中无不蕴含着这一数字，本视频带你一同探索为何1.618034如此重要。