What is the golden section? Where is the golden section of Mona Lisa?

1. golden section refers to dividing a line segment into two parts, so that the ratio of the length of the original line seg

What is the golden section? Where is the golden section of Mona Lisa?

1. golden section refers to dividing a line segment into two parts, so that the ratio of the length of the original line segment to the longer part is the golden section. There are two such positions on the line segment.

2. Using two golden points on the line segment, you can make a regular pentagram and a regular pentagram.

3. The golden section is approximately equal to 0.6 18: 1.

4. More than 2000 years ago, Odox Sass, the third largest mathematician of Athens School in ancient Greece, first proposed the golden section. The so-called golden section refers to dividing a line segment with length L into two parts, so that the ratio of one part to the whole is equal to the ratio of the other part. The simplest way to calculate the golden section is to calculate the ratio of the last two numbers of Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 2 1, ... 2/3, 3/5, 4/8, 8/655.

Before and after the Renaissance, the golden section was introduced to Europe by Arabs and was welcomed by Europeans. They called it the golden method,17th century European mathematicians, and even called it the most valuable algorithm among all kinds of algorithms. This algorithm is called the three-rate method or the rule of three numbers in India, which is what we often say now.

6. Where is the golden section of Mona Lisa? To understand the golden section, let's start with a painting, the Mona Lisa.

Mona Lisa and Leonardo da Vinci's Mona Lisa are the works of famous Italian scientists and artists during the Renaissance. All visitors to Paris will definitely go to the Louvre Museum to enjoy the Mona Lisa's smile? .

Leonardo da Vinci is not only a painter, but also one of the best geniuses in human history, and has made outstanding achievements in astronomy, physics, engineering, cryptography, anatomy, architecture, archaeology and other fields. For example, he is regarded as a great master of modern anatomy, and has drawn many anatomical drawings.

He is also obsessed with machinery, and often involves some machinery that is beyond the times, such as sketches of helicopters and submarines.

But he was afraid that someone would use his invention to do bad things, so many manuscripts were filled with passwords, and the movie The Da Vinci Code began with this story.

As a scientist, the shadow of science is naturally hidden in his paintings. For example, the Mona Lisa has many golden sections and golden rectangles. So, what are the golden section and the golden rectangle?

From Fibonacci to golden ratio. I talked about Fibonacci sequence before. This series is 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144? The feature is that the first two items add up to the last item. We can use the latter item to compare a number, such as 1? 1= 1, 1? 2=0.5? The list is as follows:

We will find that Fibonacci series is getting bigger and bigger, but the ratio of two adjacent terms always seems to be close to a number of 0.438+08? . In fact, it can be proved mathematically that the ratio of two adjacent numbers in Fibonacci sequence is indeed a fixed value after infinite terms, and it is an irrational number, close to 0.6 1809895? . This number is the golden section.

The golden section was put forward much earlier than Fibonacci series. According to legend, Pythagoras, an ancient Greek mathematician, once heard the blacksmith strike the iron in the street. His voice is very regular and beautiful. After going home, I carefully studied and found the golden ratio.

The general definition of the golden section is as follows: there is a line segment, find a point on the line segment and divide the line segment into two parts, A and B. The ratio of the length of the shorter part (A) to the length of the longer part (B) is equal to the ratio of the longer part (B) to the total length (A+B), then this point is called the golden section point, and this ratio is called the golden section.

It is not difficult to solve this ratio. Let us assume that the total length of the line segment is 1, the length of B is X, and the length of A is 1-x, so that this relationship can be written as follows:

We can change this formula into the following equation.

According to the root formula, x is

This figure is the golden ratio, which is about 0.6 18.

The application of golden section in aesthetics for a long time, people have always thought that the golden section ratio is the most beautiful. In painting, sculpture, architecture and other fields, people use the golden section without exception.

For example, Venus with a broken arm and Mona Lisa are both treasures of the Louvre City Hall? Sculpture, 2.02 meters tall, her navel is exactly the golden section, and the ratio of the part above the navel to the part below the navel is close to 0.6 18.

In fact, normal people don't have such a good proportion, so the little girl who loves beauty can improve her leg length through high heels and make her figure more attractive. One of the reasons why ballerinas stand on tiptoe when dancing is that their body proportions are closer to the golden section and their visual beauty is stronger.

In architectural design, people will also involuntarily use the golden section. Such as the Great Pyramid of Khufu in Egypt. The length of the base of the side triangle is 2b=230.37, the height h = 146.59m and the height a =186.5m.. By comparing the half of the length b of the base with the height a of the side triangle, the golden ratio of 0.6 18 is exactly obtained.

In modern architecture, people also use the golden section to pursue visual beauty. For example, the Eiffel Tower, a landmark building in France, has a total height of 300 meters (antenna 24 meters). The three observation platforms are located at 57.6m,115.7m and 276. 1 m respectively. The height of the second observation platform is about the golden section of the whole tower: the ratio of the lower height to the upper height is about 0.6 18.

Another example is the Oriental Pearl in Shanghai, whose tower is 468 meters high. At its golden section, the designer arranged an upper sphere to make the whole building look harmonious and beautiful.

In addition to painting and architecture, there are so-called nine squares in photography? Statement. In fact, it is to find two golden section points on the floor and width and make a straight line. Four straight lines intersect and there are four intersections. These four points are people's interests? . Put the scenery we want to highlight on the golden section line or interest point, and the whole picture will look natural and beautiful.

At the same time, if the aspect ratio of the photo is the golden ratio, the photo will also look beautiful in size. A rectangle of this size is called a golden rectangle. The golden rectangle has one feature: if you keep dividing squares in the golden rectangle, the rest is still a golden rectangle.

Moreover, if we connect the diagonals of these squares with smooth curves, we will form a spiral, which is called the golden spiral? . The golden spiral is everywhere in nature. For example, the curve of Nautilus is a golden spiral.

When people design stairs, it will give people a sense of beauty to let the stairs approach the golden spiral from a certain angle.

The Golden Section in the Mona Lisa Now we can go back to the Mona Lisa. Mona Lisa's face is close to a golden rectangle, and the ratio of head width to shoulder width is close to the golden ratio. If we draw a golden spiral, this golden spiral can pass through the important parts of the Mona Lisa, such as nostrils, chin, head and hands. These designs, I don't know if Leonardo da Vinci deliberately did it, or is it a coincidence?

I think maybe art and science are interlinked. The earliest development in the Renaissance was art, with artists such as Leonardo da Vinci, Michelangelo and Raphael, then science, and great scientists such as Galileo and Copernicus.

Art pursues beauty and science pursues truth. Truth is the most beautiful.