Man and the Golden
in the human body contains a variety of \point margin of glabella point made under the chin point to the split point, etc.) is almost adjacent to each part of the body into gold than with human nature (animals, plants, the universe, human beings) the growing awareness of depth man on the \The product was 23.175 ℃, the temperature in this environment, the body's metabolism, and physiological function of biological rhythms are at their best.
, it was found the magic ratio in nature is everywhere. Plants and animals from low to high human, from mathematics to astronomical phenomena, almost all imply that the proportion of the structure.
plants and Golden
it was found that the leaves of plants, different styles, full of vitality, to the beauty of nature and the beautiful green world. Although the leaf shape varies with the species, but it's in the order in the stem (known as phyllotaxis) is very regular, not chaotic. Stems from the top of your plants look down upon careful observation, found in the adjacent upper and lower leaf between the two about as 137.5 ° angle. If you only draw one on each leaf to represent the first and second floors of the adjacent angle difference between the two leaves is about 137.5 °, after two to three, three to four, four to five ... ... 2 into the angle between the leaves are. Botanist has been calculated that: the point of view leaves lighting, ventilation is the best. Arrangement of leaves, how ingenious!
137.5 ° angle between the leaves in the possession of any \We know that a week is 360 °,
360 ° -137.5 ° = 222.5 °
137.5 °: 222.5 ° ≈ 0.618.
Look, this is the \Leaves the arrangement of delicate and magical, and yet hidden 0.618, consistent with mathematical accuracy in the \
pear too, its leaves arranged along the logarithmic spiral, which also ensures no overlap between the leaves, leaves just below the top leaves from sunlight leaked through the gap between where it is largest lighting arrangement. Can be seen along the logarithmic spiral of the golden circle by circle is born, is the best choice leaves arranged.
also in the midst of the leaves have golden section does exist. The main vein and petiole and main vein of the length and the ratio of about 0.618; sunflower chrysanthemum and pine cones in the spiral, the distribution of plant stem on the bud, seed development and animal horns forming the growth of fixed-style, follows the Golden Ratio.
Building and Golden
the geometry of the pyramid has five surfaces, eight sides, a total of 13 levels. Entry by any
watching to all three levels can be seen. Length is 5813 pyramid inches (5-8-13). Whether the ancient Greek Parthenon, or the ancient Chinese terracotta warriors and horses, their vertical and horizontal line between the surprise, the proportion of 1 to 0.618. Notre Dame de Paris, France, the positive ratio of the height and width is 8:5, its every window aspect ratio too. Huangpu River east bank of the Oriental Pearl TV Tower, the tower up to 468 meters. New York, United Nations building in the use of architectural design in the Golden Ratio.
Golden
universe and we know that solar system has eight planets were found in the present. But as early as the mid-18th century, German natural scientists Titius discovered that if the 0,3,6,12,24,48,96 series of each number plus 4, and Deshu except with 10 to its The result is:
(0 +4) ÷ 10 = 0.4 (Mercury 0.387 AU from the sun actually)
(3 +4) ÷ 10 = 0.7 (actual 0.723 Venus astronomical units from the sun)
(6 +4) ÷ 10 = 1.0 (Earth actual 1.000 astronomical units from the Sun)
(12 +4) ÷ 10 = 1.6 (Mars actual 1.524 astronomical units from the sun)
(24 +4) ÷ 10 = 2.8 ( asteroid belt)
(48 +4) ÷ 10 = 5.2 (actual 5.203 Jupiter astronomical units from the sun)
(96 +4) ÷ 10 = 10 (Saturn 9.56 AU from the sun actually)
by Comparison of these figures we can see Titius calculated values with the actual distance of the planet to the sun is indeed very similar. 1766, Titius in the \But the book was published and is not cause for widespread concern. 1772, Berlin Observatory,
uggs outlet store, was taken note of this long wave - strange rules, and it is prepared to \But the need to explain is: Why is 0,
cheap ugg boots,3,6,12,24,48 this series plus another 10 to 4, rather than anything else except a few? Titius and Bode did not make any explanation. Which contains any secret? They both also did not say.
recent years, the golden section method was used to calculate the distance of planets from the sun, the result is also amazing!
0.732 × 0.618 = 0.446 (0.387 Mercury actual astronomical units from the sun)
1.000 × 0.618 = 0.618 (Venus actual 0.723 astronomical units from the sun)
1.52 × 0.618 = 0.939 (1.000 Earth actual astronomical units from the sun )
2.80 × 0.618 = 1.73 (1.52 Mars actual astronomical units from the sun)
5.20 × 0.618 = 3.213 (the actual asteroid belt 2.8 astronomical units from the sun)
9.54 × 0.618 = 5.89 (Jupiter from the sun actually 5.2 astronomical units)
19.2 × 0.618 = 11.86 (Saturn 9.54 AU from the sun actually)
30.1 × 0.618 = 18.601 (Uranus 19.2 AU from the sun actually)
: 1 astronomical unit is equal to 150 000 000 1000 m
these figures we can see that, in addition to the actual distance from Saturn to the Sun slightly larger error,
kids ugg boots, the other planets to the sun's distance values are still very close. If we take into account the gravitational interaction between planets and the eccentricity of the problem, numerical calculations may be more to be precise number. If the attractiveness of the sun than Saturn, but also by the enormous gravity of Jupiter, so it's actually less than the calculated distance is not difficult to understand. Of course, with the golden section method to calculate the distance between the planet to the sun, with the Titius - Bode set is the same as in the calculation of Neptune and Pluto has been challenged on its analysis of the reasons yet to be continued.
We know that the Milky Way is a huge celestial system, which accounted for 90% of stars, gas and dust accounted for 10%, while most of these substances gathered in the vicinity of the central plane running around the galactic center. From the side view of our Milky Way, it is flat like a discus, the diameter of 25 to 30 between 1000 seconds 1000 seconds gap, and our planet and solar system for human habitation, from the galactic center at 8.5 to 1000 seconds gap place. Recent years, it was found: the location of our solar system, the Milky Way is precisely the radius of the golden belt. That is: 27.5 ÷ 2 × 0.618 = 8.4975 (1000 seconds between)
wonderful \The point line is divided into two parts,
uggs for cheap, one long, one short, and long segment and short segment with more than just equal to the entire paragraph than long, the point is this line of golden point. This ratio: 1:0.618 ... and 0.618 ... the number was called \
interesting things, this number can be seen everywhere in daily life: people's navel is the golden section point of the body length; some plant stem and leaf adjacent the angle between the two is exactly the circle into 1:0.618 ... the angle between two radii. According to the researchers found that the angle of the plant ventilation and natural lighting is best.
architects of the number 0.618 ... special preference, whether the ancient Egyptian pyramids, or Notre Dame or the Eiffel Tower in modern times, are ultimately the number 0.618 .... It was also found that some paintings, sculpture, photography, mostly in the main screen of 0.618 ... Department. Musicians who think that the piano on the strings of 0.618 Ma ... Department will be more soft, sweet sound of the piano.
number 0.618 ... also makes optimization possible. Optimization is an optimization problem seeking. If the steel needed to join a chemical element to increase the strength of steel, assuming that is known to be added per ton of steel in a quantity of chemical elements between the 10,002,000 grams. To obtain the most appropriate dosage, is usually taken to test the mid-point range, and then the experimental results, respectively 1000 g and 2000 g when compared to experimental results, selects the two points higher strength as a new range then take the midpoint of the new range to experiment until the best results obtained so far. However, the efficiency of this method is not high, if the test points were taken at intervals of 0.618, will greatly enhance the efficiency of this method is called \16 tests, we can do 2500 to the former method the test results!
\Perhaps, in its body, there is more mystery, waiting for us to explore, so that it can better serve us,
uggs sale, for us to solve more problems.
military and Golden
0.618, a very charming and mysterious figure, and it has a very nice name Golden Section, which is the ancient Greek philosopher, Mathematics Home Pythagoras discovered 2,500 years ago. Throughout the ages, this figure has been regarded as a scientific and aesthetic descendants golden rule. In art history, almost all of the outstanding works have similarly proved that the famous golden section, both the ancient Greek Parthenon, or the ancient Chinese terracotta warriors and horses, they went so far between the vertical lines and horizontal fully consistent with the proportion of 1 to 0.618.
0.618
with weapons and equipment in the cold weapons, although it still does not know the concept of the golden section rate, but people in the manufacture of swords, knives, spears and other weapons, the golden ratio have long been the rule reflected everywhere out, because according to the proportion of manufactured such weapons will be more handy to use them.
when firing rifle bullets just created when it's shot put, and Barrel's length ratio is very scientific and rational, very easy to grip and aim. To 1918, a man named Alvin? York, U.S. Expeditionary Force corporal, this rifle was modified, improved gun-type frame and the proportion of guns to precisely meet the 0.618 ratio.
In fact, from the sharp edge of the arc saber, to bullets, artillery shells, the flight trajectory of ballistic missiles along the apex; dive bombing from the air into the state's best bomb height and angle, to the best design of tank shell bullet slope, we can easily find golden ratio is everywhere.
in artillery fire, if aiming a gun between the maximum range of 12 km, the minimum range of 4 kilometers, its best shooting distance of 9 km, the maximum range of 2 / 3, and 0.618 are very close to . Deployed during the fighting, if fighting is offensive, artillery positions, locations and general distance side front 1 / 3 times the maximum range of office, if a defensive battle, the artillery positions should be configured from the front side 2 / 3 times the maximum range of office.
0.618 and tactical manoeuvering
occurred early in our history some of the war, they are all followed the laws of 0.618. Spring and Autumn Period, Jin Cheng Li company cutting his troops, with the assistance Chu Cheng, a decisive battle in Yanling. Li Chu Pan Chen Miao public listen to Ben Wong's proposal to Chu Youjun as the main attack points, and therefore of a military offensive in the Chu Zhi Zuo Jun; to another military offensive into Chu, set on the military, under the Army, New Army and the Death SHAANXI attack Chu Youjun. The main point of attack options, just in golden point.
the golden law embodied in the war's most outstanding military action, should devaluation Genghis Khan commanded a series of war. For centuries, people Genghis Khan's Mongol cavalry, why can a camel as the hurricane swept across the Eurasian continent swept quite difficult to understand, because only the sturdy nomads brave, cruel, treacherous, good at riding and shooting, and the mobility of these reasons cavalry are not enough to have to make a completely convincing explanation. Perhaps there are other more important reason? Closer inspection, turned it and found the great role of golden section. Mongolian cavalry fighting formation of the square and the Western tradition very different in its formation, 5-row system, vests, helmets were heavy cavalry and light cavalry Smart quick ratio of 2:3, which in turn is a golden split! You can not help but admire the genius strategist who horseback Intuition, is such a genius commander in chief command of the army, not a Thief, invincible, that pigs fly.
Macedonia and Persia Abela war, the Europeans will be 0.618 for the war in a more successful example. In this battle, Macedonia's Alexander the Great to his troops attack points, selected in the Persian army of King Darius the left wing and the central junction. Coincidentally, this is just the front part of the \The profound impact of the war are still visible even today, in the Gulf War, the multinational force is similar to the composition method used to defeat the Iraqi army.
two forces at war, if one of the troops, weapons lost 1 / 3, it is difficult to go again at war with each other. That is why, in modern high-tech war, with high-technology weapons and equipment have taken a long time military power means air strikes, first destroy the other 1 / 3 of troops, weapons, after which a ground offensive. Let us take the Gulf War as an example. Before the war, according to military experts estimated that if the Republican Guard of equipment and personnel losses by aerial bombing reached or exceeded 30%, it will basically lose their combat effectiveness. In order to achieve this the loss of Iraqi critical point, the US-British coalition bombed again and again to extend the time for 38 days continuously, until the destruction of the Iraqi tanks in the war in the region 428 38% 2280 32% of armored vehicles in, guns in 3100 47%, then dropped to 60% of Iraqi military power around, this is the critical point hors de combat troops. Also is to weaken Iraq's military forces to the golden point, the US-British coalition was taking the \In this known as \artists as well. What's really important is not luck, but he led a modern army commander during the war strategizing, the consciously or unconsciously involved in the 0.618, that is, he more or less asked the Law of the Divine blessing.
In addition, in modern war, many of the nation's military attacks in the implementation of specific tasks, often carried out sub-echelon, first echelon of troops total strength of about 2 / 3 of the second echelon of about 1 / 3. In the first echelon, the main direction of the input is usually the first echelon of troops total strength of the 2 / 3 assists direction was 1 / 3. Defensive battle, the first line of defense is usually the strength of the total number of 2 / 3, the second line of defense forces and weapons are usually the total number of 1 / 3.
0.618 and strategic battle
0.618, not only in arms and 1:01 in the lineup on the battlefield embodied, but also in the vast region, the time span of the macro war, also without exception, been fully demonstrated.
coastal bases of the Emperor Napoleon could not think of how his fate will be closely linked with 0.618. June 1812, the year is Moscow, the most cool and pleasant summer climate in the Russian military failed to destroy the effective strength of the Battle of Borodino, Napoleon at this time, led his army into Moscow. At this time, but puffed up with pride he, insufferably arrogant. He did not realize that talent and luck this time are also a little bit from him and disappeared, the peak of his career and a turning point in his life is also coming. Later, the French will in the snow Fen Yang, wind whistling in the dingy to leave Moscow. The victory three months plus two months into the boom-bust, from the Timeline view, overlooking the French emperor, flames raging through the city of Moscow, the foot of the golden section line just to tread.
1941 年 6 22, Nazi Germany against the Soviet Union launched \depth. In more than two years time, the Germans have maintained the momentum of attack, until August 1943, \Battle of action for the attack. War historians are all recognized as the turning point of the Great Patriotic War the Soviet Union Battle of Stalingrad, the war broke out in the first 17 months, it is the Germans the rise and fall of 26 months time axis of golden point.
golden ratio in the human world (the environment, whether biological or social environment) is almost ubiquitous. The best means is that human life processes in DNA molecules, also included the \Each of its double helix structure in Egypt by 34 long and 21 wide ratio of composition of Egypt, of course, 34 and 21 is a Fibonacci series of numbers, their ratio of 1.6190476, very close to the Golden Section 1.6180339. Does this mean that law is the golden ratio of DNA in the genetic code more basic things? Because the structure of DNA bearing the double helix structure follows the Golden Section. Golden Section in our universe may be DNA in the genetic code?
mathematical papers on the 0.618
do steamed bread, steamed bread base will put less acid, alkali put more bread will turn yellow, green and with a base flavor. How much would be appropriate alkali put it? This is an optimization problem; to enhance the strength of steel, to add carbon in the steel, adding too much too little is bad. How to join the number of carbon steel to the highest intensity? This is also a selection problem. In daily life and production, we often encounter optimized.
However, the amount of alkali and bread good or bad the relationship between the carbon number and the relationship between the strength of steel, if not simply a mathematical formula that out, then, should do? We might look to learn to cook bread in the process: put much of this base, next time put a little less the next base up a little, and then the next came alive again in a little more, and so on. Test results every time, ultimately adding the appropriate amount of alkali to make good bread. Splendid! Cook gave us inspiration: The test solution to!
answer a selection problem is often required to do if the tests. Arrange these test method, must choose, pay attention to science. For example, how much carbon steel preferred to add the issue, have been estimated assuming a dosage of 1,000 grams per tonne to 2,000 grams. If the equalization method to be tested and used, they should select 1001 g, 1002 g ... for the test points, requiring a total of 1000 tests done. If calculated by the day to do an experiment, you need to spend nearly three years to complete. Too time-consuming it! Time is life today, of this method is clearly undesirable. More scientific arrangement of way? Can reduce the number of trials, quickly find the best spots?
end, mathematicians have designed a mathematical theory to be tested scientific method, which is also known as \Mathematics Master Hua (1910 ─ ─ 1985 years) since 1964, traveled from north to south 20 provinces (municipalities) to promote the optimization. He single-factor optimization problems, the most used method is 0.618.
0.618 golden section method is based on principles of design, therefore, also known as the golden section method.
Now, we use 0.618 to arrange the preferred method of adding the amount of carbon test.
0.618 Determination of the first test is the test range of 0.618. This addition amount calculated by the following formula:
(large - small) × 0.618 + small = the first point. ①
The first addition is:
(2000-1000) × O.618 +1000 = 1618 (g).
again in the first point of symmetry points for a second trial, this point can be the following formula to calculate the quantity (since the dosage of the trial points are calculated by the following):
large - in + Small = second point. ②
Secondly, the quantity is:
2000-1618 +1000 = 1382 (g).
compare the two test results, if the second better than the first, then remove the part of more than 1618 g; better if the first point, then remove the 1382 g following section. The second point assumes that better test results, then remove the part of more than 1618 grams, the left to find the second part of the symmetry point to do the third test.
third point, the quantity is:
1618-382 +1000 = 1236 (g).
then the third test results compared with the second point, if the second point is still better, then get rid of 1236 g the following section, if the third is good, then remove the 1236 g following section, in the left part of the identified The second point of the symmetry points for a fourth time trial.
fourth addition is:
1618-1382 +1236 = 1472 (g).
after the fourth test,
MBT Shoes Cheap, then compared with the second point, and choice. In the left part of the same method to continue testing until the best point found so far.
repeated experiments, comparison and choice time and time again. Starting from the second test, each test can remove the appropriate scope of 382/1000, gradually narrow the scope of the study, the best point of becoming closer. Thus, 0.618 methods with less number of tests can quickly find the best spots.
many factories in the ratio formula, process operating conditions, and method used to solve the optimization problem 0.618, resulting in improved quality, increased production,
ugg boots australia, reduced consumption and achieved good economic results. For example, food processing through the optimization of processing technology to increase rice yield generally 1 to 3%. If the whole population by the total number of grain processing, one year is equivalent to hundreds of millions of kilograms of grain yield. You might find a life or production optimization problem, with the 0.618 method to try to see to solve it? I believe you can enjoy the joy of success!
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