What Is a Placement Ratio?

The golden ratio is an irrational number defined as (5-1) / 2. The levels used are quite broad, for example: mathematics, physics, architecture, art and even music. The unique nature of the golden ratio was first applied to dividing a line segment. If the total length of a line segment is the denominator of the golden ratio plus the unit length of the numerator, if we divide it into two halves, the long is the denominator unit length, and the short is the numerator unit length, then the ratio of the short line length to the long line length is Golden ratio.

Golden ratio

A line segment is divided 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. The ratio is an irrational number. The approximate value of the first three digits is 0.618. Because the shape designed in this proportion is very beautiful, it is called the golden ratio, also called the Chinese-foreign ratio. This is a very interesting number, we approximate it with 0.618, and through simple calculations we can find:

0.618 / 1 = 0.618

1 / (1 + 0.618) = 0.618

The effect of this value is not limited to

The golden ratio is a mathematical proportional relationship. The golden ratio is strictly proportional, artistic, and harmonious, and contains rich aesthetic values. It is generally taken as 0.618 when applied, just as the pi is taken as 3.14 when applied.

The ratio of length to width of the Golden Rectangle is the golden section ratio, in other words, the long side of the rectangle is 1.618 times the short side. The golden section ratio and the golden rectangle can bring beauty to the picture, which is pleasant. It can be found in nature. The Passion Temple in Athens, Greece is a good example.

The golden section is an ancient mathematical method.

For its various magical functions and magic powers, there is no clear explanation in mathematics, only to find that it has repeatedly played our unexpected role in practice.

Because the Pythagoras school of ancient Greece studied the mapping of regular pentagons and regular decagons in the 6th century BC, modern mathematicians inferred that the Pythagoras school had touched or even mastered the golden section at that time.

In the 4th century BC, the ancient Greek mathematician Odoxus first studied this problem systematically and established the theory of proportionality.

About 300 BC Euclid absorbed the research results of Odoxus when he wrote The Original Geometry, and further systematically discussed the golden section, becoming the earliest treatise on the golden section.

The golden section was introduced to Europe by the Arabs before and after the Renaissance and was welcomed by the Europeans. They called it the "golden method", a mathematician in Europe in the 17th century, and even called it "the most feasible algorithm of Valuable algorithm. " This algorithm is called "three-rate method" or "three-number rule" in India, which is what we often call proportional method.

After the Middle Ages, the golden section was put on a mysterious cloak. Several Italian Pacaccioli called the Central and Moroccan ratio a sacred proportion, and wrote a book specifically for this. German astronomer Kepler called the golden section a sacred section.

It was not until the 19th century that the name Golden Section became common. The golden section has many interesting properties, and humans have a wide range of practical applications. The best-known example is the golden section method or the 0.618 method in optimization, first proposed by the American mathematician Kiefer in 1953, and popularized in China in the 1970s.

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This value is usually expressed in Greek letters.

Golden Ratio Stock Market Field

Here, we will explain how to get the Golden Section and use them to guide the next operation of buying and selling stocks.

The golden section is divided into two types: a single-point golden section and a two-point golden section.

Here is the method: There are two factors for drawing a single point (one is the golden number, and the other is the highest or lowest point)

The first step in drawing the golden section is to remember several special numbers:

0.191 0.382 0.618 0.809

1.191 1.382 1.618 1.809

2.191 2.382 2.618 2.809

Among these numbers, 0.382, 0.618, 1.382, and 1.618 are the most important. The stock price is extremely likely to generate support and pressure at the golden section line generated by these 4 numbers.

The second step is to find a point. This point is the highest point at the end of the rising market and turning down, or the lowest point at the end of the falling market and turning up. Of course, we know that the highs and lows here refer to a certain range and are local. As long as we can confirm that a trend (whether it is rising or falling) has ended or temporarily ended, the turning point of this trend can be used as the point of golden section. Once this point is selected, we can draw the golden section line.

When the rising market started to turn down, we were extremely concerned about where this fall will be supported. The golden section provides the following price points. They are multiplied by the peak price of this time by several of the special numbers listed above. Assume that the peak of this rise is 10 yuan, then

8.09 = 10 × 0.809

6.18 = 10 × 0.618

3.82 = 10 × 0.382

1.91 = 10 × 0.191

These prices are likely to become support, with 6.18 and 3.82 most likely.

In the same way, when the declining market starts to turn around, we care about where we will rise to the pressure. The position provided by the golden section is the price of the bottom point of this decline multiplied by the special number above. Assume that the bottom price of this fall is 10 yuan, then

11.91 = 10 × 1.191 21.91 = 10 × 2.191

13.82 = 10 × 1.382 23.82 = 10 × 2.382

16.18 = 10 × 1.618 26.18 = 10 × 2.618

18.09 = 10 × 1.809 28.09 = 10 × 2.809

20 = 10 × 2

Will likely become a pressure point in the future. Among them, 13.82 and 16.18 and 20 yuan are most likely to become pressure lines, and those over 20 are rarely used.

Golden ratio military applications

Perhaps, we have learned a lot about the performance of 0.618 in science and art, but have you heard that 0.618 is also inextricably linked to the fierce and brutal battlefield of gunfire, smoke, and the brutal battlefield? Military also shows its huge and mysterious power?

Weaponry

In the cold weapon era, although people did not know the concept of golden ratio at all, when people were manufacturing weapons such as swords, broadswords, and spears, the rules of golden ratio had been reflected everywhere, because they were manufactured in such proportions. Weapons will be more handy to use.

When the rifle that fired the bullet was just manufactured, the ratio of the length of its handle to the body was unscientific and reasonable, and it was very inconvenient to grasp and aim. By 1918, a corporal named American Expeditionary Force named Alvin York had modified this rifle, and the ratio of the improved gun body to the handle exactly matched the ratio of 0.618.

In fact, from the radian of a sharp saber blade to the apex of bullets, cannonballs, and ballistic missiles flying along the trajectory; from the optimal bombing height and angle of the aircraft into the dive bombing state, to the optimal bomb shelter slope when the tank shell is designed We can also easily find that the golden ratio is everywhere.

In the artillery firing, if the maximum range of a certain range sighting gun is 12 kilometers and the minimum range is 4 kilometers, its optimal shooting range is about 9 kilometers, which is 2/3 of the maximum range, which is very close to 0.618. In combat deployment, if it is an offensive battle, the position of the artillery position is generally 1/3 times the maximum range from the front of the enemy. If it is a defensive battle, the position of the artillery position shall be 2/3 times the maximum range from the front of the enemy.

Tactical formation

In some wars that took place very early in the history of our country, they all followed the law of 0.618. During the Spring and Autumn Period and Warring States Period, Jin Ligong led the army to defeat Zheng and defeated the army of Zheng Chu at Fuling. Li Gong obeyed the advice of Miao Yihuang, the betrayer of Chu, and took the right army of Chu as the main attack point. Therefore, he attacked the left army of the Chu army with one of the Chinese army; the other army attacked the Chu army with the other army. The pawns of the army, the new army, and the clan attacked the right army of Chu. The choice of its main attack point is exactly on the golden section.

The military action that best embodies the Golden Section in the war should also be a series of battles under the command of Genghis Khan. For centuries, people have wondered why Genghis Khan's Mongolian cavalry swept through Eurasia like a hurricane, because only the bravery and nobility of the nomadic people, the cruel and treacherous, the cavalry and the mobility of cavalry The reasons are not enough to give a fully convincing explanation. Perhaps there are other more important reasons? After careful study, she really discovered the great function of the golden section law. The combat formation of the Mongolian cavalry is very different from the traditional square formation in the West. In its 5-row formation, the ratio of heavy cavalry and fast light cavalry in human helmets and vests is 2: 3, which is another golden section. !! You can't help but admire the genius of the horseback military strategist. The army commanded by such a genius commander is not all over the world, and it is strange.

The battle between Macedonia and Abela in Persia is a successful example of Europeans using 0.618 in warfare. In this battle, Alexander the Great of Macedonia chose his army's point of attack at the left and central junction of King Persian Darius' army. Coincidentally, this part also happens to be the "golden point" of the entire front, so although the Persian army has dozens of times more troops than Alexander, with its strategic wisdom, Alexander defeated the Persian army. The profound impact of this war is still clearly visible. In the Gulf War, the multinational force defeated the Iraqi army by using a similar array.

If the two forces are at war, if one of them loses more than one-third of their strength and weapons, it will be difficult to continue fighting with each other. Because of this, in modern high-tech wars, military powers with high-tech weapons and equipment have adopted long-term air strikes, completely destroying more than one-third of the strength and weapons of the other party, and then launching ground attacks. Let us take the Gulf War as an example. Before the war, military experts estimated that if the equipment and personnel of the Republican Guards lost or exceeded 30% by aerial bombardment, they would lose their combat effectiveness. In order to bring the Iraqi army's wear and tear to this critical point, the US-British coalition repeatedly extended the bombing time for 38 days, until it destroyed 38% of Iraq's 428 tanks in the theater, 32% of 2,280 armored vehicles, and 3100 artillery 47%. At this time, the strength of the Iraqi army dropped to about 60%, which was the critical point at which the army lost its combat effectiveness. That is, after weakening Iraq s military strength to the golden section, the US-British coalition forces pulled out a desert saber and slashed it to Saddam. It took only 100 hours for ground operations to achieve the purpose of war. In this war known as the "Desert Storm", General Schwarzkopf, who created a miracle that killed only a hundred people, is not a master figure, but his luck is almost equal to all Military art masters are just as good. In fact, what really matters is not luck, but the commander who led a modern army. In the planning of the war, he intentionally or unintentionally involved 0.618. In other words, he entrusted the blessing of the Golden Rule more or less.

In addition, in modern warfare, the military of many countries often carry out sub-echelons when carrying out specific offensive tasks. The first echelon accounts for about two-thirds of the total strength and the second echelon accounts for about one-third. In the first echelon, the force invested in the main attack direction is usually 2/3 of the total strength of the first echelon, and the assist direction is 1/3. In defensive battles, the strength of the first line of defense is usually 2/3 of the total, and the weapons of the second line of defense are usually 1/3 of the total.

Strategic battle

0.618 is not only reflected in the weapons and the battlefield layout of the moment and place, but also in the macro war with a wide area and a long time span.

A mighty Napoleon Emperor would never have imagined that his fate would be closely linked to 0.618. In June 1812, it was Moscow's coolest and pleasant summer of the year. After failing to eliminate the Bolokino battle of the Russian forces, Napoleon led his army into Moscow at this time. At this time, he was full of ambition and could not live forever. He didn't realize that genius and luck were disappearing from him at this moment, and the peak and turning point of his life career were coming at the same time. Later, the French army evacuated Moscow in the heavy snow and cold wind. Three months of victory and two months of prosperity and decline, from the time axis, when the Emperor France overlooked Moscow through the blazing flames, his foot was just stepping on the golden section.

On June 22, 1941, Nazi Germany launched the "Barbarossa" program against the Soviet Union and carried out a blitz. In a very short time, it quickly occupied the vast territory of the Soviet Union and continued to advance deeper into the country. For more than two years, the Germans had maintained the momentum of the offensive. Until August 1943, the "Barbarossa" operation ended, and the Germans have since turned into defensive positions. They are no longer capable of launching the Soviet army once. Offense for campaign action. The Battle of Stalingrad, widely recognized by all historians of war as the turning point of the Soviet Patriotic War, took place in the 17th month after the outbreak of the war. It was the golden section of the 26-month timeline of the German army's rise and fall.

We often hear the term "golden section". Of course, "gold section" does not refer to how to divide gold. This is a metaphorical statement, that is, the proportion of the division is as precious as gold. So what is this ratio? It's 0.618. People call this ratio the golden cut point and 0.618 the golden number. And people think that if it meets this ratio, it will look more beautiful, better, and more coordinated.

0.618 and war: Napoleon the Great defeated by the golden section?

0.618, an extremely fascinating and mysterious number, and it also has a very pleasant name-the Golden Rule, which was discovered by the ancient Greek philosopher and mathematician Pythagoras over 2500 years ago. Throughout the ages, this number has been regarded as the golden rule of science and aesthetics by future generations. In the history of art, almost all outstanding works coincide with this famous golden section. Whether it is the ancient Greek Parthenon or the ancient Chinese terracotta warriors, their vertical and horizontal lines are so unexpected. Fully in line with the ratio of 1 to 0.618.

Golden Ratio Math Application

The number 0.618 ... is more concerned by mathematicians. Its appearance not only solves many mathematical problems (such as: decile, quintile circle; find the sine and cosine values of 18 and 36 degrees), but also makes An optimization method is possible. The optimization method is a method for solving optimization problems. If a certain chemical element needs to be added during steelmaking to increase the strength of the steel, it is assumed that the amount of a certain chemical element needs to be added between 1,000 and 2000 grams per ton of steel. In order to obtain the most appropriate addition amount, Tests were performed in the 1000 g and 2000 g intervals. Usually the midpoint of the interval (ie 1500 grams) is used for the test. Then compare the test results with the experimental results at 1000 grams and 2000 grams, and select the two points with higher strength as the new interval, then take the midpoint of the new interval for the test, compare the endpoints, and continue until you get The best result. This experimental method is called the halving method. However, this method is not the fastest experimental method. If the experimental point is taken at 0.618, the number of experiments will be greatly reduced. This method of taking 0.618 intervals as the test point is the one-dimensional optimization method, also known as the 0.618 method. Practice has proved that for a factor problem, using the "0.618 method" for 16 tests can complete the "half method" for 2500 tests. So the great painter Da Vinci called 0.618 ... the golden number.

Golden Ratio Life Application

In life, there are many applications of the "golden section".

The 16:10 display is the embodiment of the golden ratio in industrial design. ^[1] Businessmen have always claimed that the 16: 9 display is a golden ratio, the 16: 9 display length to height ratio is 1.78, and the 16:10 display length to height ratio is 1.6. Obviously, the 16:10 display is closer to the golden ratio. It is a true golden ratio screen. ^[1]

Golden ratio human aesthetics

Interestingly, this number can be seen everywhere in nature and in people's lives: people's navel is the golden section of the human body's total length, and human's knee is the golden section of the navel to the heel.

Art creation

Most doors and windows also have a width-to-length ratio of 0.618 ... On some plant stems, the angle between two adjacent petioles is 137 degrees 28 ', which is exactly the angle between two circles that divide the circumference into 1: 0.618 ... According to research, this angle has the best effect on plant ventilation and lighting.

Architects have a particular preference for the number 0.618 ..., whether it is the pyramids of ancient Egypt, the Notre Dame of Paris, or the Eiffel Tower of France in the recent century, there are data related to 0.618 ... It has also been found that the themes of some famous paintings, sculptures, and photographs are mostly 0.618 ... in the picture. The artists believe that the strings of the stringed instrument at 0.618 ... make the sound softer and sweeter.