Geometry, ultimate beauty

More than two thousand years ago, Plato said, "God will exist forever in the form of geometry."

It starts with a point and a line and ends with infinity.

Geometry may seem simple, but it can extend the most complex and changeable logic.

In nature, there are hexagonal honeycombs and snowflakes, and the golden ratio of nautiluses.

At the beginning of human civilization, there were the linear Great Wall, the triangular Pyramid of Khufu, and the rectangular Parthenon.

Geometry is an invisible rule that has a lifespan as long as the universe.

In the past, people worshiped and obsessed with geometry, but now people use and appreciate geometry.

From ignorance to exploration, it is the changing human beings and eternal geometry.

The relationship between people and geometry can be traced back thousands of years. Early human worldviews were often constructed through geometry.

Chinese people’s understanding of the world can be represented by squares and circles.

Song Yu wrote in "Dayan Fu", "The round sky is the cover, and the square earth is the cover." The circle represents wholeness and unity, and is obedient and inclusive; the square is the deduction and development of the circle, containing order and rules.

This concept can be traced back to the "Square Sky and Earth Map" derived from the Bagua Diagram. The hexagrams surrounding the outside represent the movement of heaven, while the hexagrams arranged in a square shape in the middle represent the movement of earth.

Celestial bodies such as the sun and moon are in perpetual motion, just like a closed circle without beginning or end; but the earth is quietly carrying us there, just like a square object at rest. Stable, there is the saying "the sky is round and the earth is round".

The Egyptians interpreted the world using circles and triangles. And this symbol has influenced the Western world to this day.

The Eye of Horus, composed of a triangle and a circle, is also known as the Eye of True Knowledge, which represents the distinction between good and evil, and the defense of health and happiness. The Egyptians usually used it to count, dividing it into geometric sequences of "2, 4, 8...64".

This string of numbers also coincides with the Bagua diagram.

The Egyptian Eye of Horus later gradually evolved into the Eye of God, which represents the eye of "God" that monitors human beings. The common form is an eye surrounded by a triangle and thousands of rays of light. It is best known for appearing on the U.S. national emblem and the back of the one-dollar bill.

This symbol was later used by organizations such as the Franciscan Society and the Vietnamese Cao Dai Church. On the one hand, its triangular part represents the supreme truth; on the other hand, the round, eye-like part also speaks of higher existences that humans cannot fathom and transcend.

In Islamic architecture, geometry is everywhere.

For example, the Imam Khomeini Mosque in Tehran has a sixteen-pointed star pattern as the center, extending outwards in an orderly manner into eight-pointed, four-pointed and other star patterns, and nested with other geometric patterns. , forming a larger geometric array.

In Islam, geometry also means philosophical and religious thought. The circle is the source and whole, symbolizing God, the Supreme Perfection, and the beginning of everything. The square evolved from the circle and represents the four directions, four seasons, four elements and other seemingly countless things, but in fact they are universal.

Whether it is a square or a circle, the Eye of Horus, or the geometric patterns of Islam, they are all shapes that the ancients relied on their own observations and experiences before the formation of science and technology, as well as their yearning for divinity. , the symbols and symbols formed.

The Japanese monk Sengai Yibo also once attributed the world to three forms: triangle, circle and square.

It can be seen that although different regions have different geometric beliefs, the final interpretation is surprisingly consistent.

Perhaps, this is some kind of unknowable mysterious truth.

The earliest people imagined through geometry, so geometry is often associated with religion, alchemy, blood sacrifice and holiness.

In 300 BC, Euclid wrote "Elements of Geometry", which was the earliest work to understand the world from a rational perspective. It was Leonardo da Vinci who really connected geometry. After him, geometry became a science.

One of Leonardo da Vinci's most famous masterpieces, "The Vitruvian Man", consists of a circle, a square and a naked man. The man's stretched posture also represents the "ten" shape and the five-pointed star.

Since modern times, this painting has been regarded as a symbol of occultism by various cultural works, but in fact, it can be said to be the earliest work to show the perfect proportions of the human body. It is the science of geometry. representative.

Leonardo da Vinci was obsessed with geometry, calling it the code to unlock the secrets of the universe.

Not only did he make full use of geometric composition in his paintings, he also used it to solve the design of central dome buildings and the planning of ideal cities. He calculated the earth before Magellan sailed around the world. Its diameter is more than 7,000 miles, and it cleverly uses geometric structures to design concept drawings of submarines, aircraft, etc.

It’s no wonder that some people call Leonardo da Vinci an extraterrestrial visitor or a traveler from the future.

Another person who used geometry to decipher the universe was Kepler.

He once wrote a work "The Mystery of the Universe" in defense of Copernicus' theory. It shows the regular encounters of Saturn and Jupiter in the zodiac chart, and connects the inscribed and circumscribed circles at a certain ratio on a polyhedron. It is said that this may be the geometric basis of the universe.

In fact, since the establishment of the Pyramid of Khufu, some people have been explaining it from a scientific perspective.

For example, the side length of the square at the base of the pyramid * 2 ÷ the height of the pyramid is exactly equal to 3.14, which is π.

The base of the Pyramid of Khufu is 230.36 meters long, which is 361.31 cubits (Egyptian unit of measurement), which is approximately the number of days in a year.

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These measurements, observations and summaries represent the transition from the period of ignorant geometry to the scientific treatment of geometry.

Perhaps they are not rigorous enough in modern times, but they have a different kind of mystery and romance.

Human beings who begin to look at geometry from a scientific perspective are also human beings who have stepped out of childhood and entered youth.

In the 20th century, mankind launched an aesthetic revolution from painting to design to architecture, subverting the aesthetic concepts of more than ten centuries. The protagonist of this revolution is geometry.

In the 1915 exhibition titled "Exhibition 0.10 (0.10 Exhibition)", the Russian artist Malevich exhibited a work painted only with black squares.

He called his work "Suprematism" and said in his manifesto of the same name,

"Art no longer serves country or religion. It no longer depicts the events in history. It wants to part ways with the objective nature. It believes that it can exist apart from things and make art for the sake of art.”

Although this passage contains Malevich’s extremely personal color, it is indeed true. It conveys the characteristics of the aesthetic changes of that period: tracing back to the origin more and pursuing functionality more.

Under these two principles, various new styles emerged in endlessly during World War I and World War II. The only thing they have in common is that they all have a fanatical obsession with geometry.

The most avant-garde designers and artists of that era often used simple geometry and bright colors to challenge traditional aesthetics.

For example, Rietfeld, who is regarded as a representative figure of the Dutch De Stijl, challenged and rewritten the design trends of the time with his "Red and Blue Chair" and "Z" shaped chair. Danish designer Pan Dong simply used pure geometry, such as cubes, spheres or cylinders, to write a new chapter in home design.

Today, geometry has become an important part of modern aesthetics. Geometry, used to the extreme, has become not only its own expression, but also the vane of the times and a master in the field.

For Yayoi Kusama, who makes good use of dots, geometry is an outlet for her emotions; Issey Miyake, who plays with three-dimensional and flat surfaces, has turned geometry into a brand symbol.

The one closest to us, who also maximized the application of geometry, is the architect Ieoh Ming Pei. All of his works—from commercial skyscrapers to art museums—represent a careful balance between the avant-garde and the conservative.

The Louvre Pyramid, which was once criticized by French celebrities, became another architectural myth in Paris after its completion.

Adjacent to the Humble Administrator’s Garden and the Lion Grove, the Suzhou Museum uses geometric ink architecture to seamlessly connect ancient and modern styles.

I.M. Pei demonstrates the highest form of contemporary geometric beauty. With the growth of human civilization, today we have lost our blind worship of geometry and its intuitive presentation. Geometry has become an aesthetic method, representing people's pursuit of perfection and respect for nature.

Today, geometry is no longer a primitive worship and instinctive belief. It has been given more meaning and value by people's rational and creative thinking.

Why are we obsessed with geometry?

Maybe the movie "2001: A Space Odyssey" can give the answer.

In the film, there is a non-human protagonist Black Monument that cannot be ignored. Every time it appears, it guides the plot.

One interpretation is that the black stone tablet symbolizes the invisible God, the ultimate in the universe.

And this ultimate form is a black cuboid.

Simple geometry encompasses all complexities.

The universe is endless, human beings are short-lived, and geometry is eternal.

Editor丨The Last Banquet

-Reference Materials-

"The Circle and the Square"

"Starting from Functionalism"

"Geometric Aesthetics in Architecture"