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This article is made up of MSI Technology Commissioned, pan-scientific planning and execution.

Human beings are always attracted to shining things involuntarily. Adding the word “gold” when naming them seems to be able to increase their value and become popular. Whether it’s the Gold Coast, the golden location, the golden right foot, the golden kiwi fruit, the golden retriever, the golden crisp potato, the golden armor, the golden quicksand bag, the golden laugh (big mistake)… People use gold to describe all beautiful things, even ” “Proportion” is the same. The “golden ratio” is hailed as the most beautiful ratio. You must have heard the saying that the closer a person’s face, body or painting composition is to the golden ratio, the more fascinating it is. However, how can a number ratio have anything to do with aesthetics?

The history of human exploration of the golden ratio can be traced back to more than two thousand years…

In ancient Greece, about five hundred years ago, Pythagoras, who was obsessed with mathematics, believed that mathematics could explain everything in the world. His teaching attracted a group of enthusiastic followers, known as the Pythagoras school. In the eyes of others, the Pythagoras school may be a group of weird people: abide by extremely strict rules of life, do not eat meat and beans, and will also conduct high-intensity memory training and three provinces and so on. But the Pythagoras school is almost a fanatical cult of mathematics, especially the fascination with the number 5 and the pentagram, making them the first group in history to be exposed to the golden ratio. Divide the line segments that make up the five-pointed star and arrange them from short to long. Adding the two shortest line segments is exactly equal to the length of the third line segment; adding the second and third shortest line segments will also equal the fourth The line segments, in sequence, show the wonder of the golden ratio! However, they did not further explain, define and name this magical discovery.

It was not until 300 BC, when “Geometric Elements” by Euclid came out, that there was the earliest systematic exposition of the golden ratio. But you know what? Euclid never said the term “golden ratio” at all.The so-called “golden ratio” in later generations actually appeared in the fourth chapter of “Geometric Elements”“Limit to Mean Ratio”(Extreme and mean ratio). Euclid’s explanation of this ratio is as follows:

“A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”

(If a line segment is cut on the “limit to mean ratio”, the ratio of the length of the line segment to the length of the longer segment is equal to the ratio of the length of the longer segment to the shorter segment.)

The line segment of the golden ratio: a + b: a = a: b. Picture/wikipedia

The gold aspect ratio 1.618 that everyone often talks about is calculated from the ratio in the picture above. As long as the shorter line segment b is defined as 1 unit, the longer line segment a is defined as the x unit, and a little bit of the one-dimensional quadratic equation that has been used in the mathematics of the middle school, the solution can be calculated as 1.6180339887… or 0.6180339887… these two All irrational numbers that are not at the end can be regarded as the value of the golden ratio. Just like another famous irrational number-Pi, which is based on “Pi“To indicate that the golden ratio also has its own symbol called “φ”. “Φ” is usually pronounced as “fai”, followed by “Pi“Rhymes the same, but defenders of orthodox Greek pronouncing may insist on pronouncing it as “fee.”

At the beginning, Euclid only said so much, purely to explain the meaning of mathematics and geometry. But what he couldn’t think of was that this “limit-to-average ratio” would become a spokesperson of beauty, bringing unlimited space for future mankind’s imagination.

Convergence of mathematics and humanities, the “sacred proportions” of the Renaissance

The term “golden ratio”, which is familiar to modern people, was not widely circulated until around the 1830s. Prior to this, its status had been elevated to a more noble and sacred position. During the Renaissance, the mathematician and Franciscan monk known as the “Father of Accounting”-Luca. Luca Pacioli, published a book called Divina scalee. He discussed the properties of regular polyhedrons and semi-regular polyhedrons starting from the “limit to mean ratio” defined by Euclid.

“Sacred Proportions” published by Luca Pacioli in 1509. The illustrations in the book were drawn by Leonardo. Picture/wikimedia

Pacioli was inspired by the study of “the ratio of limit to mean” and began to connect with the theology he was familiar with. He found that the three line segments (full length, long side, short side) mentioned in this ratio all describe the same line, which resembles the Christian theology, that the Father, Son, and Holy Spirit are in a trinity. And the irrational number of the solution of this ratio has the inexhaustible nature, just like mortals cannot understand the almighty and infinite God. The ratio of the two line segments is equal (full: long = long: short), which represents the eternal inexhaustibility of God. Transgender and ubiquitous attributes.

Pacioli, who saw the theological explanation from mathematics, renamed the “limit-to-mean ratio” as the “sacred ratio.” In his work, he further analyzed the ratio of ancient Greek and Roman architecture to the human body structure with the “sacred ratio”. In his view, the torso ratio of human beings created by God also implies the “sacred ratio.” These contents further strengthen the connection between “sacred proportion” and “beauty”.

Since then, “sacred proportions” have become inseparable from “religion” and “beauty.” Pacioli’s breakthrough in the interpretation of pure mathematical theory in religious philosophy successfully made this magical ratio out of the comfort zone of mathematics and became a common topic among mathematicians, theologians, and artists. Later, it was gradually discussed. Evolved into the “golden ratio” that is popular in later generations. Pacioli can be said to be an indispensable hero behind opening up the popularity of the “golden ratio”.

Has the universe existed since its birth? The password hidden in nature is actually a “golden sequence”

Although the mathematics and art circles are still arguing whether the Pyramids of Giza and the Parthenon are built according to the golden ratio, there is no need for human design. Nature itself contains the beauty of the golden ratio. The Fibonacci number, which is famous for describing the problem of “rabbit giving birth to rabbit”, can be said to be the twin brothers of the golden ratio. The zeroth term of the Fibonacci sequence is 0, the first term is 1, and the value after the second term is the sum of the first two terms, so the order will be:

1、1、2、3、5、8、13、21、34、55、89、144、233……

A square with the Fibonacci number as the side can be pieced together to produce an approximate golden rectangle (1: 1.618)! Picture/wikimedia

In the late Renaissance, the famous astronomer Johannes Kepler discovered that dividing the last term of the Fibonacci sequence by the value of the previous term would be 1/1 = 1, 2/1 = 2, 3 / 2 = 1.5, 5/3 = 1.67, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.615… After calculating here, have you also noticed the mystery? As the number sequence continues to divide, this value will approach the golden ratio more and more! Therefore, the alias of the Fibonacci sequence is called the “golden sequence.”

The plants in nature are actually mathematics masters who are well versed in the mystery of creation. Try to count the number of petals of the daisy, and you will find that they all happen to be Fibonacci numbers of 13, 21, or 34. How can the leaves be placed between the leaves so that they will not block each other from absorbing sunlight? How to arrange the petals of a rose to look beautiful and symmetrical? How do the seeds on the pine cones grow so that the limited space can be effectively used? The answers to these questions are all: The ratio of rotation angles (with 360° as the denominator) must conform to the golden ratio!

For a symmetrical rose, the angle that determines the position of its petals follows the golden ratio. Picture/Pixabay

It is not just the plant world, whether it is the growth of nautilus shells, the flight trajectory of eagles approaching their prey, or the appearance of tropical cyclones on satellite images, even the spiral arms of spiral galaxies in the universe show spirals that follow the golden ratio. From small to single-handed shells to large galaxies light years away, there are hidden figures of the golden ratio. Nature’s love for this wonderful ratio has fascinated scientists.

The equiangular spiral hidden in the golden rectangle. Picture/wikimedia

Living animals and plants and inanimate cyclones or galaxies are invariably subject to a magical ratio, showing a beauty that seems to have existed since the birth of the world, unshakable, consistent and regular. Human beings who belong to nature are constantly searching in all kinds of buildings or works of art, eager to prove the correlation between the golden ratio and beauty. However, even the masterpiece of David in the eyes of the world, there is no way to get close to the golden ratio 100%. After all, the error can never be completely eliminated, let alone the finite we can not exhaust the infinite φ. It is precisely because the golden ratio is a kind of beauty that human beings cannot fully grasp, it forces us to keep working hard on the road of pursuing beauty, and then move forward.


The “golden ratio” that even nature favors is almost synonymous with “beauty.” And what is around us that uses the golden ratio?

That’s right! This is this Creator Z16 notebook computer.

The Creator Z16, which uses a 16:10 screen, has 11% more visual space than the commercially available 16:9 screen, making creation more free and spacious. In addition, 16:10 (1.6) is also very close to the golden ratio (1.618), allowing you to feel the “beauty” that contains the mystery of all things and that mathematicians have been quenching for more than two thousand years when creating.

Based on the human-oriented design concept, the touch panel of Creator Z16 allows people to operate more intuitively and give inspiration at any time. The 90 Whr large-capacity battery with fast charging function and a 2.2 kg body made of 15.9 mm thin metal can perfectly match the pace of modern people’s mobility and work anytime and anywhere. The QHD+ ultra-high-quality panel built with True Pixel display technology, coupled with the exclusive True Color technology for color correction before leaving the factory, can accurately present brilliant images.

Want to stick to your aesthetics of life, but don’t want to give up the pursuit of pragmatism? Children only make choices, you can take it all! Let the Creator Z16, which combines the golden ratio and strong strength, become your muse!

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