What is the golden section? What is this for?

0.6 18 is an extremely fascinating and mysterious number, and it also has a very nice name-the golden ratio, which was discovered by Pythagoras, a famous ancient Greek philosopher and mathematician, more than 2,500 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 excellent works have verified this famous golden ratio. Whether it is the Parthenon in ancient Greece or the Terracotta Warriors in ancient China, the ratio of vertical line to horizontal line is exactly 1 to 0.6 18.

Perhaps, we have learned a lot about the performance of 0.6 18 in science and art, but have you ever heard that 0.6 18 has an indissoluble bond with the fierce and cruel battlefield of gunfire and bloodshed, and also shows its great and mysterious power in the military?

0.6 18 and weapons and equipment

In the era of cold weapons, although people don't know the concept of the golden ratio at all, when people make weapons such as swords, broadswords and spears, the law of the golden ratio has already been reflected everywhere, because weapons made according to this ratio will be more handy to use.

When the rifle for firing bullets was first manufactured, the ratio of the length of the handle to the length of the gun body was unscientific and unreasonable, which was very inconvenient for grasping and aiming. 19 18, a corporal named alvin york of the American Expeditionary Force reformed this rifle, and the ratio of the reformed gun body to the handle was exactly 0.6 18.

In fact, from the sharp edge radian to the apex of bullets, shells and ballistic missiles flying along the track; It is not difficult to find the golden ratio everywhere, from the best dropping height and angle of the plane entering the dive bombing state to the best bomb avoidance slope when designing the tank shell.

In artillery firing, if the maximum range of an indirect gun is 12 km and the minimum range is 4 km, its optimal firing distance is about 9 km, which is 2/3 of the maximum range and very close to 0.6 18. In battle deployment, if it is an offensive battle, the position of artillery position is generally 1/3 times of the maximum range from its own front, and if it is a defensive battle, the position of artillery position should be 2/3 times of the maximum range from its own front.

0.6 18 and tactical arrangement

Some wars that happened very early in the history of our country all followed the law of 0.6 18. During the Spring and Autumn Period and the Warring States Period, Jin Ligong led an army to attack Zheng and fought a decisive battle with the Chu army supporting Zheng in Yanling. Gong Li took the advice of Miao Benhuang, a traitor of Chu, and took the right-wing army of Chu as the main attack point, so he attacked Zuo Jun, a part of China's army. Attack the Chu army with another department, and gather the soldiers of the upper army, the lower army, the new army and the public to attack the Chu right army. The choice of its main attack point is just at the golden section.

A series of wars commanded by Genghis Khan should be the first military action to show the golden ratio in the war. For hundreds of years, people have been puzzled why Genghis Khan's Mongolian cavalry swept across Eurasia like a hurricane, because only the nomadic people were brave, cruel, cunning, good at riding and shooting, and the cavalry was mobile, which was not enough to make a completely convincing explanation. Maybe there are other more important reasons? After careful study, we found the great role of the golden ratio. The combat formation of Mongolian cavalry is very different from the traditional western phalanx. In its five-row formation, the ratio of heavy cavalry wearing helmets and vests to quick and agile light cavalry is 2: 3, which is another golden section! You can't help but admire the genius of the horseback strategist. Strangely, the army led by such a talented commander is not invincible in all directions.

Christians in Europe are very talented in applying the golden ratio to religious art, but it seems that it is very late to realize whether this rule is useful in other aspects. Until the black powder period, muskets gradually replaced spears, and the Dutch general Morris, who took the lead in mixing musketeers and spearmen to transform the traditional phalanx, still failed to realize this. It was only after King Gustav of Sweden adjusted this formation that the Swedish army became the most effective army in Europe at that time. What he did was to add 96 musketeers to Morris' original squadron of 265,438+06 spearmen+65,438+098 musketeers. This change immediately highlighted the role of firearms and made it a watershed in the formation of the army in the era of cold weapons and hot weapons. It goes without saying that the ratio of 198+96 musketeers to 2 16 spearmen shows us the golden ratio again.

The Battle of Abela between Macedon and Persia is a successful example of Europeans using 0.6 18 in the war. In this battle, Alexander the Great of Macedonia chose the attack point of his army at the left-middle junction of the army of King Darius of Persia. Coincidentally, this part is also the "golden point" of the whole front, so although the Persian army is dozens of times more than Alexander's military forces, Alexander defeated the Persian army with his own strategic wisdom. The far-reaching impact of this war is still clearly visible today. In the Gulf War, the multinational forces used similar disposal methods to defeat the Iraqi army.

When two armies are at war, if one of them loses more troops and weapons than 1/3, it will be difficult to fight with the other. Because of this, in modern high-tech wars, military powers with high-tech weapons and equipment take a long-term air strike, first completely destroying the other side's troops and weapons above 1/3, and then launching a ground attack. Let's take the Gulf War as an example. Before the war, according to military experts' estimation, if the equipment and personnel of * * * and the National Guard were lost by air strikes by 30% or more, they would basically lose their combat effectiveness. In order to make the Iraqi army's losses reach this critical point, the American-British coalition forces repeatedly extended the bombing time by 38 days, until they destroyed 38% of 428 tanks, 32% of 2,280 armored vehicles and 47% of 3 100 guns in the theater. At this time, the Iraqi army's strength dropped to about 60%, which was the critical point for the army to lose its combat effectiveness. That is, after Iraq's military strength was weakened to the golden section, American talents pulled out the "desert saber" and cut it at Saddam. It only took 100 hours of ground combat to achieve the purpose of the war. In this war known as "Desert Storm", General schwarzkopf, who created a miracle that only 100 people were killed in a great war, was not a master, but his luck was almost as good as that of all military art masters. In fact, what really matters is not luck, but the commander-in-chief who leads a modern army intentionally or unintentionally involves 0.6 18 in the planning of the war, which means that he is more or less blessed by the golden ratio.

In addition, in modern wars, multinational armies often carry out specific offensive tasks by echelon. The strength of the first echelon accounts for about 2/3 of the total strength, and that of the second echelon accounts for about 1/3. In the first echelon, the troops invested in the main attack direction are usually 2/3 of the total strength of the first echelon, and the auxiliary direction.

It is 1/3. In defensive operations, the strength of the first line of defense is usually 2/3 of the total, and the strength and weapons of the second line of defense are usually 1/3 of the total.

0.6 18 and strategic campaign

0.6 18 is not only reflected in the weapons and battlefield layout at a time and place, but also fully displayed in the macro-war with a vast territory and a long time span.

Napoleon the Great, a lean man, never thought that his fate would be closely linked with 0. 18. June, 18 12, is the coolest and pleasant summer in Moscow. After the battle of Borokino, which failed to destroy the Russian army, Napoleon led the army into Moscow at this time. At this time, he is full of ambition and arrogance. He didn't realize that genius and luck were disappearing from him at this time, and the peak and turning point of his career came at the same time. Later, the French army withdrew from Moscow in frustration in the heavy snow and howling cold wind. Three months of triumph, two months of climax and decline, from the time axis, when the French emperor overlooked Moscow through the flame, his foot just stepped on the golden section.

194 1 On June 22nd, Nazi Germany launched the "Barbarossa" plan against the Soviet Union and carried out the blitzkrieg. In a very short period of time, it quickly occupied the vast territory of the Soviet Union, and constantly pushed forward into the territory. For more than two years, the Germans kept the momentum of attack, until the "Barbarossa" operation ended in August 1943, and the Germans turned to the defensive, and they were no longer able to launch an attack that could be called a battle against the Soviets. The Battle of Stalingrad, recognized by all war historians as the turning point of the Soviet Patriotic War, took place in1July after the war broke out, which was the golden point of the 26-month timeline of the rise and fall of the German army.

These examples scattered in the dust of history are really incredible. In isolation, they are too like one accident after another. But creation never does anything for no reason. If too many accidents show the same phenomenon, can you continue to treat them calmly as accidents? No, at this time, you must admit that this is the law.