Dating back to ancient civilizations, the octagon has emerged as a mysterious and sacred symbol in cultural heritages around the world. From religious buildings to royal palaces to folk crafts, its presence is everywhere. This geometric figure not only represents the harmony and unity of all things in the universe, but also carries the beautiful vision of the ancients for the future world.

In ancient Greek philosophy, the Pythagorean school believed that numbers are the basic components of nature, and the octagon, because of its symmetry and stability, can reflect the sense of order between heaven and earth. In traditional Chinese culture, "Bagua", as one of the important concepts of Taoism, further strengthens people's understanding and belief in this shape. We can deeply appreciate the powerful spiritual power conveyed by the octagon by visiting famous historical and cultural sites such as the Hall of Supreme Harmony in the Forbidden City in Beijing and the murals of Mogao Grottoes in Dunhuang.

why the octagon is the closest to a circle without losing the existence of angular characteristics? this is due to the visual balance brought by the eight equal angles and parallel side lengths precisely divided inside it. The angle between each vertex and its adjacent sides is 135 degrees (external angle), and the whole polygon shows almost perfect rotation symmetry. In addition, when we pass a diameter through the center of the circle, we can get two straight line segments perpendicular to each other and of the same length, which is called "orthogonal axis", so that any direction will give the impression of uniformity.

Through the study of multiple practical cases, it is shown that the octagon is easier to achieve physical structural stability than other types of polygons, and it also has a wide range of applications in engineering mechanics. For example, in the field of bridge design, we can often see examples of towers or piers constructed in this form, and in architectural design, many high-rise residential buildings will choose to adopt similar layout schemes to increase the indoor lighting area while reducing the impact of wind load and other factors.

With the development and changes of the times, traditional elements are gradually given new vitality and become an important part of the current popular trend. Today, in the fashion industry, home decoration and even technology products can see a large number of innovative works based on the octagon. These designs not only inherit the ancient wisdom crystallization, but also integrate modern aesthetic concepts and technical means, showing an unprecedented style.

For example, in the luxury industry, Chanel launched a series of high-end jewelry series called "Mademoiselle Privé", which uses a large number of eight-pointed star patterns as the core theme, in order to pay tribute to the founder of the brand. At the same time, Apple has cleverly added a small groove made of metal cutting around the LOGO on the back of the iPhone to form an octagonal-like effect, which not only improves the overall texture but also enhances the recognition. There are also highlights in cross-border cooperation: well-known architect Frank Gehry and Swiss luxury watch manufacturer Patek Philippe have jointly created an art museum on the banks of Lake Geneva. Its appearance is like a huge crystal ball floating on the water. The museum body adopts a huge octahedral frame support structure made of glass curtain walls, which has become a major local landmark landscape.

Craftsmanship often brings unexpected surprises. Many exquisite octagonal objects come from the dexterous hands of craftsmen, and each process takes a lot of time and energy to polish and perfect. Here are some traditional handicraft workshops that have been handed down for many years, such as the exquisite inlay process on wood carving furniture or the delicate and smooth hand-painted patterns on the surface of ceramic utensils. Through the close-up photos taken in front of the camera, the audience felt as if they were on the scene and felt the dedicated and persistent work attitude.

In the depths of Beijing's old hutong, there is a time-honored cloth shop called "Rui Chi Xiang". The traditional Chinese clothing buttons sold in the shop are typical octagonal shapes. The manufacturing process is extremely complicated and meticulous. First, high-quality natural materials such as ivory, cow bone and even jade can be selected for many times before the initial forming can be completed after carving and trimming. Then, special dyes are used to soak, color and dry to make the color brighter, lasting and not easy to fade. Finally, high-temperature sintering and curing should be adopted to ensure that the finished product is firm and durable and will not be easily damaged and deformed. In addition to clothing accessories, there are many unique folk artworks handed down from many regions, such as paper-cut window grilles, embroidered tapestries, etc., which are also inseparable from the figure of the octagonal element to add a bit of elegance.

Walking in the streets of the city, you will inadvertently meet places or items with octagonal signs. The elegant stretching posture at the top of the bus platform, the simple and charming design on the backrest of the park bench... These are all small but unique in daily life. This part of the content aims to guide everyone to pay attention to the artistic atmosphere hidden in the surrounding environment, and encourage more people to try to add such characteristic elements in their living space, and jointly build a more colorful picture of life.

there are many European-style old villa communities along hengshan road in Shanghai. most of them were built around the 1930 s and 1940 s. clear water brick walls are commonly used for exterior wall facades with reddish-brown glass tube tile roofs. exquisite and small octagonal stone carving decorative components can often be seen around door and window openings. When the sun goes down and strolls here, the golden sun shines on the gaps in the mottled walls, mapping out a picture as beautiful as oil paintings. The pine and cypress trees that grew up in the cold and dry weather conditions in the north have also been trimmed into regular and neat cones and stand in the center of the courtyard to act as green bonsai, adding a little vitality to the winter.