Gold Segmentation--the designer's design tool

Designers in the design time, always encountered such a problem, and the people PK constantly, modify constantly. How big is the interface area? How big is the icon? How much is the color range? Why is it so defined? What is universal beauty? Many uier say, 50% by design, 50% by communication, then how to persuade others in the communication? Ads positioning, user groups, user environment, research can be used as a reference, here again to introduce us around the existence of the Golden Division, hope as a design tool, or create or PK.

I. Plants

"Golden angle" biologists have found a wide variety of plants, leaf form is different, but the arrangement of leaves on the stem has a special rule. We look down from the top of a plant and we find that the angle between the two adjacent leaves is about 137.50, and if each layer leaves only one piece to indicate, The angle between the first and second layers is about 137.50, then two to three, three to four, and four to five .... Between the two leaves into this angle, this angle is the most advantageous to the ventilation and daylighting of the leaves. What is the connection between the 137.50 horns of this leaf and the golden number? We know that a week is 3600,137.50: =137.50:222.50≈0.618. In other words, the growth laws of various plant leaves naturally hide the number of gold.

Sunflower flowers have 89 flower braid, 55 towards one side, 34 towards the other

Maple

Sneeze Wheat

1.1.2.3.5.8.13.21.34.55.89.144 ...

The number in the back is divided by the tree in front, and the more backward it tends to the gold ratio. Used in the design, such as a gear icon, the number of teeth can refer to this series of numbers. PK Word: This is the law of nature.

Two. Animal

The Fibonacci curve is drawn from this set of numbers, and Netherfield retracement the sequence when it comes to solving the problem of rabbit breeding. Suppose you have a male and female pair of newborn rabbits that start mating at the size of one months, and at the end of the second month, the female rabbit produces another pair of rabbits, and after one months they start reproducing, and so on. Each female rabbit in the beginning of breeding each month to produce a pair of rabbits, assuming that no rabbit died, in a year after the total number of rabbits? • At the end of January, the first pair of rabbits mated, but only 1 pairs of rabbits; at the end of February, the female rabbit produced a pair of rabbits, a total of 2 pairs of rabbits; at the end of March, the oldest female rabbit produced the second rabbit, a total of 3 pairs of rabbits, at the end of April, the oldest female rabbit produced the third Rabbit, two months before the female rabbit produced a pair of rabbits, There are 5 pairs of rabbits; And so on, the rabbit logarithm is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... See the pattern? • Starting from the 3rd number, each number is the sum of the previous two numbers.

Here is a brief introduction to the Fibonacci, understand that the next perimeter can always bluff.

Italian mathematician, 12, 13th century European mathematical Community representative figure. Born in Pisa, he followed his business father to Bougeuil in North Africa (now http://www.aliyun.com/zixun/aggregation/34099.html "> The small port in eastern Algeria Bejaia), where he was educated." Later in Egypt, Syria, Greece, Sicily, France and other places to visit, familiar with the different countries in the business of the arithmetic system, he thought that the use of Indian-Arabic digital is the most convenient.  1200 years or so back to Pisa, with great concentration of writing. A total of 5 of his books are preserved. The most important is the Abacus book (completed in 1202, 1228 revision), the Abacus does not refer to the Roman Abacus or sand table, actually refers to the general calculation. A total of 15 chapters, 1~7 Chapter system introduced India's digital and accounting system, as well as Integer, scores of various methods of calculation, the result of the nine method to check. Several tables, such as multiplication table, prime number table and factor table are also listed. The 8~11 chapter is a commercial computing problem, such as price, profit, interest, currency conversion, etc., reflecting the extensive business dealings of the medieval Mediterranean region.

Gold segmentation algorithm: 1. If the segment AB is divided into segments AC and BC by Dot C, and, then the segment AB is divided by the point C Gold, and the point C is called the Gold division of the segment AB, and the ratio of AC to AB is called the gold ratio. The gold ratio is calculated by calculation. 2. Golden Rectangle: A rectangle is called a golden rectangle if it has a gold ratio on both sides. It is made up of a square and another small golden rectangle. In fact, as in figure (4), if the two sides of the large golden rectangle are set to A and B, then after a square is divided, the sides of the remaining small rectangles are (b) and a, and their ratios are (b): A. This indicates that the small rectangle is also a golden rectangle.

3. How do I get the golden point of segment C? Here's how to do this: first draw a reference Y axis (vertical axis), as shown in the figure. The point A is located on the Y axis, horizontally drawing a ab line, arbitrarily long. With a as the center, AB is the radius, draw a circle, get the x point that intersects the Y axis. namely Ax=ab. Take the AX's center point Z, which is az=zx. Connect the ZB, and take Z as the center, ZB a circle for the radius, and get the Y (intersection point below). namely Zb=zy. Finally, taking a as the center point, AY a circle for the radius, and obtains the C point which intersects with AB, at this time Ac=ay. The C point is the golden point of separation.

The curve Golden section of the Nautilus is also reflected in the composition of the Web page, such as Titter's ipad version.

Three. People

1. Facial proportions. The person who looks sorry to the audience is different, but the beautiful people have many similarities. Hepburn has this standard three flat five eyes, as the public beauty, we look at his face with those golden section.

Another example of an ordinary sister Fengjie, compared to see, in the cartoon image can be exaggerated facial parts of the golden ratio.

2. Body proportions

Navel: head-foot of the division point, (2) Throat: Head-navel of the dividing point; (3), (4) Knee joint: navel-plantar dividing point, (5), (6) Elbow joint: shoulder joint to middle Finger point, (7), (8) Nipple: This dividing point on the longitudinal axis of trunk nipple; (9) Eyebrow point: Hairline to the bottom of the chin spacing between 1/3 and the lower 2/3 of the division point; (10) The lower nasal point: hairline to the bottom of the jaw between 1/3 and above 2/3 of the split point, (11) Lip bead point: nasal bottom to the bottom of the jaw between 1/3 and Lower 2/3 of the division point; 3 and the upper 2/3 of the division Point, (13) left angle: The opening line of the horizontal left 1/3 and right 2/3 of the division Point, (14) Right angle: mouth crack horizontal line 1/3 and left 2/3 of the split point. (15) In the human body two-thirds is water, in 22.5 ℃ environment, the body's metabolism is in the best state, and 22.5 ℃ is the body's normal body temperature 36.5 ℃ 0.618 Times Times, (16) The Heart Center is located at the golden point of the chest cavity, (17) The whole spine 0.618 is the chest and waist demarcation, namely the 12th thoracic vertebrae, from the shoulder to the middle finger The tip of 0.618 is the elbow joint, from the elbow joint to the middle finger fingertip 0.618 for the wrist, from the knee to the tip of 0.618 is the ankle. (18) Graceful, slender fashion models and dancing dancers, their legs and stature are similar to the ratio of 0.618.

Thinking: If Xiao Ming's height is 1.75 meters, if the navel in the position of 0.97 meters, raised pad with more high-energy to reach the human body's golden point of division? The answer is published at the bottom.

3. In addition, and the human body related to the Golden Division also: 12 months a year, 12 of 0.618 is 7.4, the 7 August human blood lymphocytes most, it can participate in the fight against bacteria, so at this time is the most powerful human resistance period. The lowest temperature in a day is 2 o'clock in the morning the temperature is the highest in the 14 o'clock, the golden point between them is 9.4, morning 9, 10 o'clock temperature is the most appropriate day, when the person's mind clearest, the highest efficiency. Three main fitness points of Chinese medicine JuJube Hundred, springs and the position of the palace is also consistent with this Division law: hundred will be located in the front of the hair to the end of the 0.618, the spring is located in the palm of the foot of the 0.618, the Labor Palace in the palm of the 0.618 place.

4.DNA ratio. Most of all, the DNA molecule in the human life process also contains the "golden ratio". Each of its double helical structures is made up of 34-aye and 21-io ratios, of course 34 and 21 are numbers in the Fibonacci series, with a ratio of 1.6190476, very close to the Golden section of 1.6180339. Does this mean that the golden rule is more fundamental than the genetic code in DNA? Because the structure that carries the DNA--the double helix--also follows the Golden Division law.

Four. Architectural sculpture

The Eiffel Tower is a monumental building, in honor of the 100 anniversary of the French Revolution, Paris decided to hold an international exposition in 1889, and to build a permanent memorial building. When it was first built in 1889, the Eiffel Tower reached 300 metres, the tallest building in the world until 1930, and was still the tallest (a radio antenna was added to the top of the Eiffel Tower in 1959 to increase the tower to 320 meters). The Eiffel Tower is located 57 meters, 115 meters and 276 meters from the ground, each has a platform, the calculation shows: (300-115) 300=0.617. The ratio is very little compared with gold, which shows that the position of the second floor of the Eiffel Tower is very close to the golden point of the tower height, and that the second platform is the turning point for the four legs of the Eiffel Tower to begin to fold. The high and bottom sides of the Egyptian pyramid are golden proportions.

The sculpture Venus Body parts also meet the gold ratio.

Five. Painting photography

Mona Lisa's Smile

Leonardo da Vinci's "beautiful password" altogether has six big "the rule", the width of the face must be 4 times times that of the nose, and the width of the forehead, the length of the nose, and the length of the mandible must be equal; The researchers were surprised to find that 5 of the "six laws" were miraculously consistent with modern aesthetic standards, with only one The law of the nose-mouth ratio "has a slight discrepancy with modern times." The small mouth type is the Renaissance esthetic standard, the mouth width is the nasal width 1.5 times times is considered the most perfect. In contrast, the study found that modern people generally believe that the ratio of mouth width to nasal width is 1.6 more beautiful. Leonardo's "beautiful code" was so demanding that most ordinary people could not fully meet their standards. The researchers also said: "Although the findings show that the size, combination and location of facial organs can have an impact on personal attractiveness." But a person's beauty is a complex combination, which also involves many other factors. ”

Nine composition method of photography

Nine composition implies, the screen on average nine equal, and four points on the side of the intersection is the golden point, when shooting, place the body at any point in the four intersections of the diagram, rather than at the center or near the center of the picture. and four points, it is generally believed that the top right point is the ideal position.

Six. Other

1. The golden section of the American play

* Blooming petals hidden in the wings of dragonflies, the heart is a horse spiral composition, and the spiral arrangement and the Golden Section and Fibonacci sequence related.

• Behind the Frog is the Greek 21st letter Phi (Φ), which is used to represent the golden segment, 1.6180339887.

• The shape of the angle is the Fibonacci helix, and careful observation can see the number on the corner, that is, the Golden segment value phi-φ--1.6180

• The body shape of the hippocampus is the Fibonacci spiral Fibonacci Helix, and the line contained in the Helix represents the proportion of the golden segment. The tail of the hippocampus is Fibonacci spiral, and some pictures include a structural map of L-histidine histidine and L-proline proline.

2. Mobile interface

iphone Sudoku Interface, each icon is 57*57, the icon width and the top of the icon to the next row of the height of the icon is the proportion of the gold ratio.

• The traditional nine-sudoku form of the mobile phone, the screen also carried out a visual gold segmentation.

wm6.5 of the honeycomb system, hexagonal on the one hand the most provincial space, on the other hand also close to the gold ratio of the 5-side type.

The summary of the Golden section is over, some examples can be flexibly applied to the design, hope to see this article of the students, whether the design or PK are helpful.

Welcome to the discussion, thank you:

PS: Xiaoming's answer 1.75*0.618-0.97=0.11 Rice

(This article originates from Tencent WSD Blog, please indicate the source when reprint)