Start with a little bit and end with infinity.
Geometry seems simple, but it can extend the most complex and changeable logic.
There are hexagonal hives and snowflakes in nature, as well as nautilus in golden proportion.
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 law, and it is as alive as the universe.
People used to worship and be obsessed with geometry, but now people use and appreciate it.
From ignorance to seeking, it is a constantly changing human being, an eternal geometry.
The relationship between man and geometry can be traced back to thousands of years ago. The early world outlook of mankind is often constructed by geometry.
China people's understanding of the world can be expressed by squares and circles.
Song Yu wrote in Da Yan Fu that "the round sky is the cover, and the square is the ground". The circle represents the whole and unity, smooth and inclusive; Square is the deduction and development of circle, which contains order and rules.
This concept can be traced back to the "Tianyuan Local Map" performed by gossip. Among them, the hexagrams around the periphery represent the operation law of the sky, and the hexagrams arranged in the middle square represent the operation law of the earth.
The sun, the moon and other celestial bodies move endlessly, like a closed circle without starting point and ending point; But the earth is quietly carrying us there, just like a square object is static and stable, so there is the saying that "the sky is round"
The Egyptians used circles and triangles to explain the world. This symbol has always influenced the western world to this day.
The eye of Horus, which is composed of triangle and circle, is also called the eye of true knowledge, which represents distinguishing good from evil and defending health and happiness. Egyptians usually use it to count and divide it into "2, 4, 8" ... 64 "geometric series.
This string of numbers also coincides with gossip.
The eye of Horus in Egypt gradually evolved into the eye of God, representing "God" to supervise human eyes. The common form is the eye surrounded by triangle and radiant light, which is widely known for appearing on the back of the American national emblem and one-dollar bill.
This symbol was later used by organizations such as * * * Economic Association and Vietnamese Gao Tai Association. On the one hand, its triangular part represents the supreme truth, on the other hand, its circular eye-shaped part also tells the higher and greater existence that human beings can't perceive and surpass.
In Islamic architecture, geometry is everywhere.
For example, the Imam Khomeini Mosque in Tehran, centered on the star pattern of 16, extends outward into star patterns such as octagon and four corners in turn, and is nested with other geometric patterns to form a more grand geometric pattern array.
In Islam, geometry also means philosophy and religious thought. The circle is the source and the whole, symbolizing the supreme and perfect God and the beginning of all things. The square evolved from a circle, representing seemingly endless things such as four seasons and four elements, but in fact everything is connected.
Fiona Fang, the eye of Horus, or the geometric patterns of Islam are all symbols and symbols formed by the ancients with their own observation and experience and their yearning for divinity before the formation of science and technology.
Fan Yi, a Buddhist monk in Japan, 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 explanation is surprisingly consistent.
Perhaps, this is some unknown mysterious truth.
The earliest people imagined it through geometry, so geometry is often associated with religion, alchemy, blood sacrifice and sacredness.
In 300 BC, Euclid wrote The Elements of Geometry, which was the first book to understand the world from a rational perspective. It is leonardo da vinci who really connects geometry with philosophy. 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 stretching posture also represents the "cross" and the five-pointed star.
Since modern times, this painting has been regarded as a symbol of mysticism by various cultural works, but it can actually be said to be the earliest work showing the perfect proportion of the human body and the representative of geometric science.
Leonardo da vinci was obsessed with geometry and called it the code to unlock the secrets of the universe.
He not only made full use of geometric composition in his paintings, but also used it to solve the design of central dome buildings and the planning of ideal cities. Before Magellan sailed around the world, he calculated that the diameter of the earth was more than 7000 miles, and skillfully used geometric structure to design concept maps such as submarines and airplanes.
No wonder some people call Leonardo da Vinci a whisper or a future traveler.
Another person who uses geometry to interpret the universe is Kepler.
He once wrote a book defending Copernicus' theory, The Mystery of the Universe. It shows the periodic meeting of Saturn and Jupiter in the zodiac, and connects the inscribed circle and the circumscribed circle on the polyhedron according to a certain proportion, saying that this may be the geometric basis of the universe.
In fact, since the establishment of pyramid of khufu, people have been explaining it from a scientific perspective.
For example, the side length of the square at the bottom of the pyramid *2÷ The height of the pyramid is exactly equal to 3. 14, which is π.
The length of pyramid of khufu base is 230.36m, which is 36 1.3 1 kubit (Egyptian unit of measurement), which is about 1 year.
......
These measurements, observations and summaries represent the transition from ignorance of geometry to scientific treatment of geometry.
Maybe they are not rigorous in modern times, but they are mysterious and romantic.
Humans who began to look at geometry from a scientific perspective are also human beings who have stepped out of childhood and stepped into youth.
In the 20th century, mankind set off an aesthetic revolution from painting to design to architecture, which subverted the aesthetic concept for more than ten years. And the protagonist of this change is geometry.
In 19 15, the Russian artist Malevich exhibited a work with only black squares.
He called his work "supremacism" and said so in the declaration of the same name.
"Art no longer serves the country or religion. It no longer describes the truth in history, but wants to part ways with objective physical attributes. It believes that it can exist without things and art for art's sake. "
Although this passage has the extreme personal color of Malevic, it does convey the characteristics of aesthetic changes in that period: more traceability and more pursuit of functionality.
Under these two principles, various new styles and schools emerged one after another during World War I and World War II. What they have in common is that they are all fascinated by geometry.
The most avant-garde designers and artists of that era often challenged traditional aesthetics with simple geometric figures and bright colors.
For example, Ritfeld, regarded as the representative of de stijl in the Netherlands, challenged and rewritten the design trend at that time with "red and blue chairs" and "Z" chairs. Danish designer Pan Dong wrote a new chapter in home design with pure geometric figures, such as cubes, spheres or cylinders.
Nowadays, geometry has become an important part of modern aesthetics. Geometry, used to the extreme, has become its own way of expression, and has also become a weather vane of the times and a master in the field.
Make good use of Yayoi Kusama, geometry is an outlet of her emotions; Issey Miyake, who juggles between three-dimensional and plane, regards geometric figures as brand symbols.
The one closest to us, and the one that maximizes the application of geometry, belongs to the architect I.M. Pei. All his works-from commercial skyscrapers to art museums-represent a careful balance between avant-garde and conservatism.
The Louvre pyramid, once criticized by French celebrities, became another architectural myth in Paris after its completion.
Suzhou Museum, adjacent to Humble Administrator's Garden and Lion Forest, seamlessly connects ancient and modern customs with geometric ink architecture.
I.M. Pei showed the highest form of contemporary geometric beauty. With the growth of human civilization, we have lost our blind worship of geometry and intuitive presentation. Geometry has become an aesthetic way, representing people's pursuit of the ultimate and admiration for nature.
Today, geometry is no longer primitive worship and instinctive belief. It is endowed with more significance and value by people with rational and creative thinking.
Why are we obsessed with geometry?
Maybe the movie "200 1 A Space Odyssey" can give the answer.
In the film, there is a non-human protagonist, the black stone tablet, which cannot be ignored. Every time it appears, it is a guiding plot.
One interpretation is that the black stone tablet symbolizes the invisible God and is the ultimate of the universe.
This ultimate shape is a black cuboid.
Simple geometry, including complex Vientiane.
The world is infinite, human beings are short, and geometry is eternal.
Editors' banquet
-References-
Round and square
Start with functionalism
Geometrical Aesthetics in Architecture