Three formulas of golden section

The three formulas of golden section are: line segment division formula: the longer line segment is the median of the ratio of the shorter line segment to the original line segment. Formula of golden section: the longer line segment is 0.6 18 times of the original line segment, and the shorter line segment is 0.382 times of the original line segment. Golden section ratio formula: the ratio of longer line segment to shorter line segment is about 1.6 18, the ratio of longer line segment to original line segment is about 0.6 18, and the ratio of shorter line segment to original line segment is about 0.382.

The golden section law refers to the classical proportional standard in painting, sculpture and architecture. It is based on the ratio of two unequal parts in a whole, that is, the ratio of a small part to a large part is equal to the ratio of a large part to the whole. When applied to portrait schema, the golden section law stipulates that the length of a person from foot to knee is equal to half the length of this leg. Similarly, the length of one leg is half the height of the whole body.

The so-called ideal proportion of a rectangle is also determined by the golden section law. In a rectangle conforming to the golden section law, the diagonal length of the square formed by the long side and the short side is equal. The ratio calculated by this ratio is about 0.6 18, which is about 5 to 8.

So according to the golden section law, the short side of a rectangle is about 0.6 18 of the length of the long side. According to Euclid's geometric principle, Vitruwe calculated this ratio in BC 1 century and wrote it into his book Ten Books on Architecture. In this book, he established the standard architectural proportions of columns, spaces and the whole house. Of course, he also mentioned that corresponding changes should be allowed according to the actual situation.

origin

The golden ratio of 0.6 18033988 ... is an irrational number full of infinite magic. It not only plays a magical role in mathematics, but also can be found in architecture, aesthetics, art, military, music and even speculation.

Four thousand years ago, the ancient Egyptians used the golden section method when building the Great Pyramid. Two thousand three hundred years ago, the ancient Greek mathematician Ogilvy first gave the calculation of the golden ratio by geometric method. Michelangelo and Leonardo da Vinci integrated the golden section into their paintings and sculptures, and the perfect harmony of the golden section flowed in the music of Beethoven, Mozart and Bach.