1, Introduction to Golden Section:
It is to divide a line segment into two parts, so that the proportion of one part to the total length is equal to that of the other part. [1] Its ratio is an irrational number, expressed as a fraction (√5- 1)/2, and the approximation of the first three digits is 0.6 18. Because the shape designed according to this ratio is very beautiful, it is called golden section, also called Chinese-foreign ratio. This demarcation point is called the golden section point, which is usually expressed by φ.
2, the golden section application:
It has strict proportion, artistic harmony and rich aesthetic value. The general application value is 0.6 18, and the announcer on the stage is not standing in the center of the stage, but standing on the side of the stage. The most perfect human body: the distance from navel to sole/the distance from top of head to sole = 0.618; The most beautiful face: the distance from eyebrow to neck/the distance from the top of head to neck =0.6 18.
Development history and geometric drawing method;
Development history:
In the 6th century BC, the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons, so modern mathematicians came to the conclusion that the Pythagorean school had touched and even mastered the golden section at that time. In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.
The golden section was introduced to Europe by Arabs around the Renaissance, and Euclid absorbed eudoxus's research results when he wrote The Elements of Geometry around 300 BC. After the Middle Ages, the name of golden section gradually became popular in19th century.
Geometric drawing method:
Make BD⊥AB pass through point B, so BD= AB/2. Connect AD and intercept DE=DB on DA. AB upper intercept AC=AE Then point C is the golden section of section AB. The golden section refers to the point where a line segment is divided into two parts, so that the ratio of the length of the original line segment to the longer part is the golden section.