Who invented the golden ratio? The golden ratio is also called

Since the Pythagoreans of ancient Greece in the 6th century BC studied the drawing of regular pentagons and regular decagons, modern mathematicians have deduced that the Pythagoreans had already touched and even mastered the division at that time.

In the 4th century B.C., the ancient Greek mathematician Eudoxus was the first to systematically study this problem and established the theory of proportions. Around 300 BC Euclidias.

Wrote "Geometric Originals".

He absorbed the research results of Eudoxus, and further systematically discussed the division of the world, which became the earliest treatise on the division of the world. After the Middle Ages, the division was covered with a mysterious cloak, and several Italian Pacioli called the middle and the end ratio the sacred proportion, and wrote a book specifically for it. German astronomer Kepler.

Call the ** division a sacred division. It was not until the 19th century that the name ** partition gradually became popular. Split numbers have many interesting properties, and humans have a wide range of practical applications for it.

The most famous example is the division method or method in the science of optimization, which was first proposed by the American mathematician Kiefer in 1953 in China in the 70s.

Needless to say, do it, Pythagoras.

Proportions are also known as splits. Proportion is a mathematical constant, generally expressed in Greek letters. This is also the origin of the first proportion.

**The scale is an irrational number, and the approximate value is: 20 decimal places) when applied: 1.

**The division has strict proportions, artistry, harmony, and contains rich aesthetic value, and the appearance of many animals and plants is presented in the group. Nowadays, many industrial products, electronic products, buildings or works of art are commonly used to show their functionality and aesthetics.

And a simple calculation of the proportion can reveal a very interesting phenomenon: 1 collapse argument.

Invented by the ancient Greek mathematician Eudoxus.

Divide a line segment into two parts, the ratio of the length of the shorter part to the length of the longer part is equal to the ratio of the length of the longer part to the overall length, and the ratio is an irrational number, and the approximation of the first three digits is . Because the shape designed according to this ratio is very beautiful, it is called ** ratio, also known as the ratio of the outside to the outside.

Ratio is an irrational number defined as (5-1) 2. It is used in a wide range of levels, such as: mathematics, physics, architecture, art and even **.

The unique properties of proportions are first applied to splitting a line segment. If the total length of a line segment is the unit length of the denominator plus the numerator of the proportion, if we divide it into two halves, the longer is the length of the numerator unit, and the shorter is the length of the denominator unit, then the ratio of the length of the long line to the length of the ** is the ratio.

More than 2,000 years ago, Eudoxus, the third largest arithmetic scientist of the Athenian school in ancient Greece, first proposed ** division. The so-called ** division refers to the division of the line segment with a length of l into two parts, so that the ratio of one part to the whole is equal to the ratio of the other part to the part. The easiest way to calculate the ** division is to calculate the Fibocian sequence 1, 1, 2, 3, 5, 8, 13, 21 ,..

The ratio of the last two numbers is 2 3, 3 5, 5 8, 8 13, 13 21 ,..approximate.

** Partition was introduced to Europe by the Arabs around the time of the Renaissance and was welcomed by the Europeans, as they called it"Golden Law", a mathematician in Europe in the 17th century, even called it"The most valuable of all algorithms"。This algorithm is called in India"Three-rate method"or"The rule of three numbers", which is what we often call the proportional method.

Actually, it's related"Segmentation", which is also recorded in our country. Although it is not as early as the ancient Greeks, it was independently created by ancient mathematicians in our country and later introduced to India. Verified

The proportional algorithm in Europe originated in China and was introduced to Europe from Arabia through India, not directly from ancient Greece.

(1) ** Partition Law This was discovered by the ancient Greek mathematician Pythagoras in the sixth century BC, and later the ancient Greek aesthete Plato called this ** division. This is actually a proportional relationship of a number, that is, a line is divided into two parts, and the ratio of the long segment to the short segment is exactly equal to the ratio of the whole line to the long segment, and its numerical ratio is: 1 or 1:, that is, the square of the long segment is equal to the product of the full length and the short segment. With strict proportion, artistry and harmony, it contains rich aesthetic value. Why do people instinctively feel the existence of beauty in such proportions?

In fact, this is closely related to the evolution of human beings and the normal development of the human body.

The mathematician Fabrens wrote a book in the 13th century about the combination of some singular numbers. The combination of these singular numbers is that any one number is the sum of the first two numbers, 5 3, and so on. Some say that these figures were derived from his research pyramids.

The pyramid is closely related to the singular numbers listed above. The geometry of the pyramid has five faces, eight sides, and a total of thirteen levels. When you look at it from either side, you can see three levels.

The length of the pyramid is 5,813 inches (5-8-13), and the percentage ratio of the high base and bottom is 0 618, which is any two consecutive ratios of the above mysterious numbers, such as 55 89 0 618, 89 144 0 618, 144 233 0 618.

In addition, the length of any side of a pyramidal pentagonal tower is equal to 0 618 of the diagonal diagonal. Also, the total number of the bottom four sides is 36524 22 inches, a number equal to a hundred times the light year!

It's an interesting set of numbers. The reciprocal of 0 618 is 1 618. For example, 144 1 168 and 0 618 0 5 168 equals 1.

Another person has studied sunflowers and found that sunflower flowers have 89 braids, 55 facing one side and 34 facing the other. Mysterious? Yes, this set of numbers is called mystery numbers.

And 0 618 and 1 618 are called golden sections.

** Segmentation with human beauty.

In the study, it was found that in the appearance structure of bodybuilders, many data are related to "** segmentation". The human body segmentation factors include 18 "** points", such as the umbilicus is the division point from the top of the head to the sole of the feet, the Adam's apple is the division point from the top of the head to the umbilicus, and the interglabellar point is the division point from the origin point to the chin. 15 "rectangles", such as torso contour, head contour, facial contour, lip contour, etc.; 6 "** indexes", such as the nasolabial index refers to the ratio of the width of the nasal wing to the length of the mouth cleft, the lip index refers to the ratio of the length of the mouth cleft to the distance between the two eyes, and the lip height index refers to the ratio of the height of the upper and lower lip redness on the midline of the face. 3 "** triangles", such as the triangle on the front of the outer nose, the triangle composed of the root point of the nose to the corner points of the mouth on both sides, etc.

In addition, in recent years, domestic scholars have successively found that the relevant "** segmentation" data, such as the ratio of length to width of the anterior teeth, the ratio of eyebrow spacing to the medial canthal spacing, etc., are close to the proportional relationship of "** segmentation".

Proportionality Proportion is an irrational number defined as (1+ 5) 2.

It is used in a wide range of fields: mathematics, physics, architecture, and fine arts. As well as the human body.

The unique properties of proportions are first applied to splitting a straight line. If the total length of a straight line is the denominator plus the unit length of the numerator in the proportion, if we divide it into two halves, the longer is the numerator unit length, and the short one is the mother-child unit length, then the ratio of the length of the long line to the length of the ** is the ratio.