1. pace
A regular octagon has eight vertices and eight outer corners. Through calculation, it can be known that each external angle of a regular polygon is equal to 360 degrees divided by its number of sides. So the degree of each external angle of a regular octagon is 360 degrees /8=45 degrees.
2. The relationship between regular polygon and circle
A regular polygon is a polygon with equal inner and outer angles. Each regular polygon can be inscribed with a circle. When the number of sides of a regular polygon is increasing, the degree of its internal angle will approach 180 degrees, that is, the regular polygon will gradually approach the circle.
3. The attributes of polygons
Except for special examples, such as rectangles and squares, most polygons are irregular. Coincidentally, regular polygon is a very special polygon with many unique properties. For example, all its vertices are on the same circle, and each inner angle is 120 degrees. For a regular octagon, the external angle is 45 degrees, which is one of its own unique properties.
4. Application area
Geometry is an important part of human civilization, and regular polygon is an important concept in geometry. Regular polygon and its spiritual connotation are not only used in scientific research and computer graphics, but also widely used in architectural design, painting, art, cultural tradition and other fields. For example, in the traditional culture of China, there is a saying of "gossip". Bagua is a pattern composed of eight regular triangles, which is a special regular polygon.
5. Symmetry of regular octagon
A regular octagon is a symmetrical figure. Not only can you draw eight identical triangles with each vertex as the center, but you can also connect each adjacent vertex to get four symmetrical axes. These symmetrical properties provide convenience for solving some geometric problems.
6. The application of octagon in nature
Octagon is also widely used in nature. The octagon is arranged like a bee hive, so it is closely related to bees in biology. Bees' hives are composed of hexagons and octagons. In each octagon, bees store honey as food. In engineering and architecture, octagon is also used in robots, building materials, designing architectural styles and so on.
7. The historical significance of octagon
Regular polygon has always been of great significance in history, and it plays a key role in many fields. For example, the Greek mathematician Johannes used regular polygons to explain the phase changes between astronomy. The Chang 'e-5 probe launched by China in 2020 has a regular octagon design, which also highlights the application and position of regular octagon in modern scientific and technological research in China.
summary
The degree of each outer angle of a regular octagon is 45 degrees. As a basic concept in geometry, regular polygon has important applications in science, engineering, architecture, cultural tradition and so on. As a form of regular polygon, regular octagon has symmetry, wide application fields and historical significance, which not only expands our understanding of geometry, but also helps people to vigorously promote technical and scientific research.