Golden section, how to apply it perfectly in architectural design?

The golden ratio is the result of final compromise in life, trading, design and other occasions, and it is also the most effective. Equity distribution, benefit distribution and visual effect are all accepted by everyone.

In design, the golden ratio is the most compromise, which makes most people accept the mathematical ratio. 0.6 18 What a beautiful number!

The geometric branch of mathematics is widely used in architecture, just like the Mobius ring mentioned above, which has long been a bad street in architecture. These buildings can be classified by geometry. The picture came from the network and has been deleted.

Golden section of classical geometry

The golden section is considered as the most perfect proportion in geometry and has been widely used in architecture since ancient times.

The picture shows the Parthenon in ancient Greece. Its ratio of height (red line) to bottom (blue line) is 0.6 18 (because of perspective, the bottom is shorter). Such an ancient building will be more magnificent.

The picture shows the Oriental Pearl Tower. In fact, the geometric composition of this building is very monotonous, and the complete circle or sphere is often avoided because it is too eye-catching in the picture. However, the designer used the golden ratio in many parts of the building to make it harmonious and beautiful. As shown in the figure, the ratio of the height of the upper sphere (red line) to the total height (blue line).

Polyhedron of classical geometry

Polyhedron has many branches, and regular polyhedron has its own rigorous mathematical logic. For example, a simple polyhedron whose surface can be transformed into a sphere through continuous deformation has a famous Euler formula in its vertex number V, edge number E and face number F, and V-E+F=2.

However, the application of a single polyhedron with complete rules in architecture is indeed limited. After all, buildings can only adapt to the environment if they are rich and changeable. Therefore, polyhedral clusters combined according to mathematical laws have become the main force of this kind of buildings.

A large apartment project proposed by TammoPrinz, the capital of Peru, a South American country.

Computational geometry in emerging geometry

When it comes to the beauty of mathematics in architecture, we can't help talking about the snake gallery in toyo ito, which is so famous.

This is a collaboration between architect toyo ito and mathematician Belmond.

It looks like a very complicated random pattern from the outside, but it is actually a rotating cube algorithm. The intersecting lines form infinite repetitive motion, with different triangular, trapezoidal, transparent and translucent feelings. Although the building has only existed for three months, visitors are surprised by the relaxation and movement that a box space can create.

These complex, well-documented and extensible algorithms, models and matrices enable Ito and Belmond to re-recognize the space in the process of mutual inspiration and influence, and finally achieve the increasingly humanized architectural space they are looking for.

. . . . . . . . . . . . . I'm so tired that I don't want any more.

I'd better have more.

Graphic density of classical geometry

Several or dozens of plane graphics with the same shape and size are spliced together and paved without gap or overlap, which is the dense paving of plane graphics. -Baidu Encyclopedia

This application field is mainly floor tiles and some fabrics in the Middle East, which is actually a variant of complex polygons. In order to realize the dense paving of graphics, it is necessary to conform to a set of geometric algorithms, and interested friends can learn online.

Splicing of plane graphics

Splicing of three plane figures

But that's not what I want to say, because it seems a little far from the building. What I want to talk about is the higher-order form, that is, surface subdivision. Since the beginning of Ford Motor Company, we have entered the big industrial era of quantitative production. Quantitative production can reduce costs, but customized products are always expensive. Some modern architects like to build curved buildings. In order to reduce the cost, the usual practice is to turn a curved building into a straight one and assemble the skin with a limited number of polygons. This is an extremely complex algorithm, which is usually the core secret of major surface design institutes. One criterion to judge whether the algorithm is good or not is the smoothness of the skin.

For example, the Guangzhou Opera House designed by Zaha

Minimum surface of emerging geometry

In mathematics, minimal surface refers to a surface with zero average curvature. For example, a surface with a minimum area that satisfies certain constraints. In physics, an example of the smallest curved surface obtained by minimizing the area can be soap bubbles blown out after soaking in soap liquid. The extremely thin surface film of soap bubbles is called soap liquid film, which is the surface with the smallest surface area to meet the surrounding air conditions and the shape of soap bubble blower.

For example, 1972 is the home of Munich Olympic Games.

Of course there are many others.

I think there are two main reasons why designers use math tools. One is to find yourself a reason to do complex modeling; The second point is beneficial to design and construction. Since it can be described by mathematics, it is more convenient to express than something really irregular.

As for such a struggle, I don't know the meaning of consciousness. . . . It just reminds me of the video of Chai Jing interviewing Ding Zhongli, quoting the comments of Zhiyiou @ Sun.

Academician Ding was not very good at handling interviews, and went back repeatedly from the beginning, paving the way for the gunpowder smell of the whole interview. He neglected some scientific problems, which were simple to him, but not to others.

Such as the difference between numerical simulation science and experimental science. As a paleoclimatologist, a disciple of Academician Liu Dongsheng pays attention to obtaining the first-hand information of paleoclimate from strata/ice cores/marine sediments. Naturally, he doesn't like IPCC climatologists who sit in front of computers and calculate simulation curves, and denounces them as "fortune tellers' crystal balls". It's interesting to joke about this in the industry, but it's not suitable for popular science. As Rutherford said, science is divided into physics and stamp collecting.

The factors affecting climate change are extremely complex, and it is impossible to accurately simulate all variables with the existing scientific level. There are some artificial factors in the operation of various weights, but this simulation has at least its inherent logical and scientific significance. The simulation curve of IPCC is obtained by averaging different 14 fitting curves, and it is found that it has a good correspondence with reality. However, this "democratic" simulation completely ignores its inherent scientific logic, and it is reasonable to be repeatedly suspected.

You mean the facade. The overall shape is ok, but it is a waste of space. Now what Party A requires is space, so your idea is not easy to realize.