Plants are a big category in the biological world. Generally there is chlorophyll, no nerve, no feeling. There are algae, lichens, mosses, ferns and seed plants, which are divided into gymnosperms and angiosperms. There are more than 300,000 species.
origin
2.5 billion years ago (Proterozoic), the earliest plants in the history of the earth belonged to fungi and algae, and then algae once flourished. It was not until 438 million years ago (Silurian) that green algae got rid of the shackles of water environment, landed on the earth for the first time, evolved into ferns, and clothed the earth with green clothes for the first time. 360 million years ago (Carboniferous), pteridophytes were extinct, replaced by lycopodium, wedge-shaped, true ferns and seed ferns, forming a swamp forest. The main plants of Paleozoic were almost completely extinct 248 million years ago (Triassic), while gymnosperms began to rise and evolved pollen tubes, completely getting rid of the dependence on water and forming dense forests. Angiosperms (flowering plants) began to appear 1.45 million years ago (Cretaceous), and developed rapidly in the later period, replacing gymnosperms and forming the angiosperm era that continues to this day. Modern types of pine, cypress, and even Metasequoia, Sequoia and so on. , are produced in this period.
trait
Plants have the ability of photosynthesis-that is, they can use light energy and chlorophyll that animals don't have to produce food by using water, minerals and carbon dioxide. After releasing oxygen, glucose, an energy-rich substance, remains as a component of plant cells.
Plants have obvious cell walls and nuclei, and the cell walls are composed of glucose polymer-cellulose.
The ancestors of all plants are single-celled non-photosynthetic organisms. They devour photosynthetic bacteria and form a mutually beneficial relationship: photosynthetic bacteria live in plant cells (the so-called endogenous phenomenon). Finally, bacteria become chloroplasts, which are organelles that exist in all plants but cannot survive independently.
Plants are usually inactive because they don't need to look for food.
Most plants belong to angiosperms, which are flowering plants, including many kinds of trees.
The best plants
The longest plant on land.
In the tropical forests of Africa, there are towering trees, exotic flowers and plants, and "ghost ropes" that trip you. This is a white rattan wrapped around the tree for countless times.
White rattan, also called provincial rattan, is also produced in Yunnan, China. Rattan chair, rattan bed, rattan blue, rattan bookshelf, etc. , are made of rattan as raw material.
Rattan stems are usually very thin, as thick as a small handleless wine cup, and some are thinner. It has a cluster of pinnate leaves at the top, and there are thorns on the leaves. The upper part of the stem is long and strong until the tip of the stem, and it is covered with large, pointed downward-bending spines. Like a barbed whip, it swings with the wind. As soon as it touched the big tree, it clung to the trunk and soon grew a bunch of new leaves. Then it continued to climb along the trunk, while the leaves below gradually fell off. After climbing to the top of the tree, the white rattan kept growing, but there was nothing to climb, so its longer and longer stems hung down, and the tree was regarded as a pillar and wound around it into countless strange circles.
Rattan is 300 meters long from root to top, which is twice as long as the tallest eucalyptus in the world.
The tallest tree
If the World Tree Height Competition is held, only Australian almond eucalyptus will be eligible to win the championship.
Almond eucalyptus is generally as high as 100 m, and one tree is as high as 156 m. Its trunk soared into the sky, reaching 50 stories. This is the tallest tree that man has ever measured. Birds are singing at the top of the tree, which sounds like the buzzing of mosquitoes under the tree.
This kind of tree is 30 meters long around the base, with straight trunk, obviously tapering upward, and dense branches and leaves at the top. The leaves are strange. Generally, the surface of a leaf is facing the sky, but its side is facing the sky, like hanging on a branch, parallel to the projection direction of sunlight. This strange appearance is to adapt to the dry climate and strong sunshine, reduce direct sunlight and prevent excessive evaporation of water.
The tallest broad-leaved trees in China-Wangtian Tree and Qingtian Tree.
A giant tree was discovered in the tropical dense forest of Xishuangbanna, Yunnan Province, China in the 1970s. Its elegant posture and tall trunk stand upright on the tree, making it impossible to look up at its top, even the sensitive altimeter is of no help here. Therefore, people call it a tree looking up to heaven. The local Dai people call it an umbrella tree.
Looking up at the sky, trees can generally reach 60 meters. People have measured and analyzed a tree and found that it grows quite fast. A 70-year-old tree is 50 meters high. Individual even as high as 80 meters, DBH is generally around 130 cm, up to 300 cm. These rare giant trees in the world stand in the upper layer of the valley rainforest, which is generally more than 20 meters higher than the trees on the second floor. They really have the momentum to go straight into the sky!
Wangtianshu belongs to Dipterocarpaceae, Lu 'an. Liu An belongs to this family, 1 1 members, and most of them live in Southeast Asia. Wangtianshu only grows in Yunnan, China, and is a rare and special tree species unique to China. The tree is tall and straight, with alternate leaves, pinnate veins and yellow flowers arranged in panicles, emitting a fragrance. Its fruit is hard. Cephalotaxus chinensis generally grows in 700- 1000 meters of valley rain forest and mountain rain forest, forming an independent community type and displaying a unique natural landscape. Therefore, the academic community regards it as a symbolic tree species of tropical rain forest.
Wangtianshu has excellent material, fast growth and high productivity. The trunk volume of a tree can reach 10.5 cubic meter, and the average annual growth of a single tree is 0.085 cubic meter, which is 2-3 times that of other tree species in the same forest. Therefore, it is an excellent tree species worth popularizing. At the same time, its wood is rich in gum, its flowers contain perfume oil and many other unknown components, which need further analysis and utilization.
Cephalotaxus is listed as a national first-class protected plant because of its high scientific and economic value and extremely narrow distribution range.
Wang Tianshu also has a very close "twin brother" named Qing Tianshu. In fact, it is a variety of Cephalotaxus fortunei, which was also found in Guangxi in the 1970s. The shape of this giant tree is very similar to that of its brother, and it is also extremely tall, often reaching 60-65 meters, and the height under the bare branches is more than 30 meters. Its material is hard, corrosion-resistant, smooth and beautiful, which has high economic value and scientific research value. This giant tree is only found in Nong Gang Nature Reserve in Guangxi, so it is also strictly protected.
The shortest tree
Ordinary trees can grow to 20-30 meters high. Under the temperate forest, there is a small shrub called Ardisia japonica with green leaves and red fruits. People like it very much and often regard it as a bonsai. It is only 30 centimeters high, so everyone has given it a nickname, calling it "not old". In fact, "not old" is six times taller than the shortest tree in the world. This shortest tree is called dwarf willow, which grows on alpine tundra. Its stems crawl on the ground, pull out branches, and grow an inflorescence like a willow, only 5 cm high. If the height of eucalyptus and apricot trees is compared with that of dwarf willow trees, the difference between one height and one height is 15000 times. Dwarf trees are almost as tall as dwarf willows. Dwarf arctic birch, which grows in the mountains near the Arctic Circle, is said to be a mushroom taller than dwarf arctic birch.
Why don't alpine plants grow tall? Because there is extremely low temperature, thin air, strong wind and direct sunlight, only those short plants can adapt to this environment.
The thickest tree
There is an interesting legend in Europe: the king and queen of ancient Arabia once led 100 cavalry to visit Mount Etna in Sicily in the Mediterranean. Suddenly it rained heavily, and the 100 cavalry quickly hid under a big chestnut tree, and the shade just sheltered them from the wind and rain. Therefore, the king named this big chestnut tree "Hundred Riding Big Chestnut Tree".
According to 1972 foreign reports, there is indeed a big chestnut tree called "Hundred Horses Tree" near Mount Etna in Sicily. Its trunk is about 55 meters in circumference, and it needs more than 30 people to hold hands to surround it. There is a big hole under the tree. Chestnut pickers use it as a dormitory or warehouse. This is indeed the thickest tree in the world.
Chestnut, the fruit of chestnut tree, is a kind of favorite food. It is rich in starch, protein and sugar, and has high nutritional value. Suitable for raw food, frying, cooking and cooking. It is not only sweet and delicious, but also has the medical functions of invigorating spleen and liver and strengthening body.
The largest tree
Some plants on the earth are very small, while others are very big. Like the giant sequoia in California, USA, it is tall and fat, and it is the "giant" in the tree, so it is also called the world master.
This kind of tree is generally about 100 meters high, of which the tallest one is 142 meters, with a diameter of 12 meters and a trunk circumference of 37 meters. It takes twenty adults to hold it. Almost as thick as the top and bottom, it lived for more than 3500 years. People have opened a hole from the lower part of the trunk, so they can pass by car or let four riders walk side by side. Even after the tree was sawed down, people had to climb up the trunk with long ladders. If the trunk is hollowed out, people can walk in 60 meters and get out of the fork hole. Its stump is big enough to make a small stage.
Although almond eucalyptus is taller than giant sequoia, it is tall and thin, and its volume is not as big as giant sequoia, so giant sequoia is the largest tree in the world. There are no bigger plants on the earth.
Giant sequoia has great economic value and is a good material for sleepers, telephone poles and buildings. The wood of giant sequoia is not easy to catch fire and has the function of fire prevention.
The tree with the largest crown
As the saying goes, "it's good to enjoy the cool under a big tree." Do you know what tree has the most people enjoying the cool? This is a banyan tree in Bangladesh. Its crown can cover about 15 acre, which is as big as a football field.
Banyan trees in Bangladesh not only have dense branches and leaves, but also can take root from the branches. Some of these roots are suspended in mid-air and absorb water and nutrients from the air, which is called "air roots". Most air roots go straight into the ground and into the soil to absorb nutrients and support branches. The upright air roots are like tree trunks, and there are more than 4,000 banyan trees, which look like a forest from a distance. Therefore, the local people also call this banyan tree an "isolated forest". It is said that there was once an army of six or seven thousand people who enjoyed the cool under a big banyan tree. The locals also opened a lively market under an old banyan tree in Bangladesh. There is no bigger canopy in the world.
The tallest hedge
Around houses, vegetable gardens, orchards, etc. Plant a circle of trees, like a fence. This is called hedging, or hedging.
People often use hibiscus with beautiful flowers, prickly oranges, Ligustrum lucidum, and triangular maple with red leaves in autumn as hedges. Hibiscus and grapefruit are short shrubs. Although Ligustrum lucidum and Acer truncatum can grow tall, they are often pruned due to close planting, usually only 5-6 meters high. In England and Scotland, beech trees are used as hedges. After pruning, these trees are still 25 meters high, and some are as high as 30 meters. This is the highest hedge in the world.
The lightest tree.
Basha wood grows in the tropical forests of the United States, which is one of the fastest growing trees in the world and the lightest wood. This kind of tree is evergreen all year round and has a tall trunk. Leaves are like phoenix trees, five yellow and white petals are like hibiscus flowers, and the fruit splits like cotton. The southern part of Taiwan Province Province has been introduced for a long time. Since 1960, it has been widely cultivated in Guangdong, Fujian and other places and grows well.
The weight of balsa wood is only 0. 1 g per cubic centimeter, which is one tenth of the weight of the same volume of water. The poplar we used to make matchsticks is three and a half times heavier than it. Although its wood texture is light, but its structure is firm, it is a valuable material for special crafts such as aviation and navigation. Local residents have long used it as a raft to travel between islands. China uses it as a cork for thermos bottles.
A tree harder than steel.
You probably didn't expect a tree harder than steel, did you? This kind of tree is called white birch. The bullet hit this kind of wood, just like hitting a thick steel plate, and it did not move.
This precious tree is about 20 meters high, its trunk is about 70 centimeters in diameter and its life span is about 300-350 years. The bark is dark red or nearly black with white spots on it. The leaves are oval. Its origin is not wide, mainly distributed in southern Korea and the border area between South Korea and China, and there are also some along the southern coast of the Soviet Union.
The wood of birch is hard, three times harder than oak and twice as hard as ordinary steel. It is the hardest wood in the world, and people use it instead of metal. The Soviet Union used birch trees to make rolling balls and bearings for speedboats. Birch also has some wonderful characteristics. Because of its extremely dense texture, it sank as soon as it was put into the water. Even if it is soaked in water for a long time, its interior can still be kept dry.
The tree that is least afraid of fire
When you go to the big forest, you can see the "No Fireworks" sign in the distance. Because trees catch fire easily, a single spark can burn a large forest. However, in the South China Sea, there is a tree called sea pine. Its wood can be used to make pipelines, and even if it is smoked and burned for many years, it will not burn out. When you wrap a hair around the handle of a pipe and light it with a match, it will continue to burn. Because the heat dissipation capacity of sea pine is particularly strong, and its wood is hard and particularly resistant to high temperature, it is not afraid of fire.
"bleeding" tree
Generally, the sap of trees is colorless and transparent after being damaged. Some trees, such as rubber trees and milk tree, can shed white latex, but I'm afraid you don't know that some trees can shed "blood".
In China, Guangdong and Taiwan Province provinces, there is a perennial vine called Kylin Xueteng. It usually wraps around other trees like a snake. Its stem can be as long as 10 meter. If you cut or cut a hole, there will be resin like "blood" flowing out, which will condense into something like blood after drying. This is a very precious Chinese medicine, which is called "Dragon's Blood" or "Kirin Failure". Through analysis, Dragon's Blood contains tannin, reducing sugar and resin, which can treat pain in bones and muscles, and has the effects of promoting qi circulation, relieving pain, expelling wind, dredging channels and promoting blood circulation.
Caulis Sargentodoxae is a genus of lianas in Palmae. Its leaves are pinnately compound, and the leaflets are linear-lanceolate, with three longitudinal veins on them. The fruit is oval with bright yellow scales outside. In addition to the stem, the fruit can also shed the resin of blood sample.
Coincidentally. There is also a common tree growing in the tropical rain forest in Xishuangbanna, China, called Dracaena. When it is injured, it will also release a purple resin to dye the injured part red. This kind of dyed dead wood is also called "Dragon Blood" or "Kirin Exhaustion" in Chinese medicine, which is similar to the "Dragon Blood" produced by Kirin blood vine.
Dracaena is a tree of Liliaceae. Although it is not too high, about 10 meter, the trunk is particularly thick, often reaching about 1 meter. Its long white ribbon-shaped leaves, sharp at the tip, like a sharp sword, are inserted in the branches layer by layer.
Generally speaking, monocotyledons cannot continue to thicken after they grow to a certain extent. Although Dracaena Dracaena is a monocotyledonous plant, the parenchyma cells in its stem can divide constantly, making the stem thicker and lignified year by year, thus forming a tree. Dracaena is native to the Canary Islands in the Atlantic Ocean. There are 150 species in the world, and only 5 species in China, which grow in Yunnan, Hainan Island, Taiwan Province Province and other places. Dragon's blood tree is also a long-lived tree, the longest of which can reach more than 6 thousand years old.
As luck would have it, there is also a kind of tree called annatto in Yunnan and Guangdong. If its branches are broken or cut, it will also shed juice like "blood". Moreover, its seeds have bright red fleshy skins, which can be used as red dyes, so it is also called mahogany.
Mahogany belongs to the genus Mahogany. Small evergreen trees, usually 3-4 meters high, some can reach 10 meters. Its leaves are similar in size and shape to those of sunflower. Petiole is also very long, with reddish-brown spots on the back of leaves. Interestingly, there are many colors, including red, white and rose, which are very beautiful. Even the fruit of mahogany is red, with soft thorns outside and many dark red seeds hidden inside.
The red pulp around the seeds of redwood trees can be used as a red dye to dye candy, and can also be used to spin and dye textiles such as silk and cotton. Its seeds can also be used as medicine, which is a convergent antipyretic. Bark is tough and rich in fiber, which can be made into strong ropes. Strangely, if the wood rubs against each other, it is very easy to catch fire!
Longevity in the tree
As the saying goes, "seventy years old is rare", and people live to be 100 years old. But people's age is nothing compared with some long-lived trees.
Many trees have lived for more than a hundred years. Apricot and persimmon trees can live 100 years. Oranges, oranges and chestnuts can live to be 300 years old. Fir trees can live for a thousand years. A Six Dynasties pine in Nanjing has a history of 1,400 years, but it is not old. The cypress tree in Qufu is still an antique 2,400 years ago. Castanopsis kawakamii in Alishan, Taiwan Province Province, has a history of over 3,000 years. This is the longest-lived tree in China, but it is not the first in the world.
The longest-lived tree in the world is the dragon's blood tree on Canary Island in western Africa. More than 500 years ago, the Spanish determined that it was about 8 thousand to 10 thousand years old. This is the oldest tree in the world. Unfortunately, it was destroyed in a typhoon in 1868.
The shortest-lived seed plant
In nature, there are many kinds of plants that reproduce by seeds, some are long-lived and some are short-lived. Woody plants live much longer than herbs. The "longevity stars" in the plant kingdom are all found in woody plants. Ordinary herbs can generally live for several months to more than ten years.
The life span of plants is closely related to their living environment. In order to survive in the harsh environment, some plants have developed the skills of rapid growth and rapid flowering and fruiting through long and arduous "exercise".
There is a plant called Luohe Belt, which grows in the cold Pamirs. The summer there is very short. When it was just a little warm in June, the Luohe belt sprouted and grew in a hurry. It took a month to grow two or three branches and vines, which soon blossomed and borne fruit, and completed its life process before the arrival of severe frost. Its life is so short, but it can still be counted in months.
The most short-lived is the short-lived chrysanthemum growing in the desert, which can only live for a few weeks. There is a long drought in the desert. With a little rain, the seeds of short-lived chrysanthemum will germinate, grow, blossom and bear fruit, and complete its life cycle in a hurry before the drought comes, otherwise it will be "extinct".
The fastest growing plants on high places.
Bougainvillea, which grows in China, Yunnan, Guangxi and Southeast Asia, can grow 3.5 meters a year. At the 7th World Forestry Congress, it was called "miracle tree". Light wood, which grows in Central and South America, grows faster than flowering trees. It can grow 5 meters high a year. But the absolute champion of the growth rate of woody plants is Phyllostachys pubescens. It takes only two months from the appearance of bamboo shoots to the growth of bamboo, and it is as high as 20 meters, about six or seven stories high. At the peak of growth, it can rise by 1 m one day and night. Therefore, there is a saying of "mushrooming".
The growth of bamboo is very special. It is elongated one by one. There are as many knots and thick bamboo shoots as there are knots and thick bamboo. Once bamboo grows, it won't grow tall. All trees grow at the tip of the bud, which gradually thickens and elongates. After decades to hundreds of years, it will gradually become thicker and taller.
The slowest growing tree
The growth rate of trees in nature is really different, some are surprisingly fast and some are surprisingly slow. For example, in kalahari desert of the Soviet Union, there is a tree named Erweizga, which is short and has a round crown. If viewed from the front, it looks like a small round table. Its rising speed is very slow, 100 is only 30 cm long. Compared with the growth rate of Phyllostachys pubescens, it is really an old cow chasing cars. Erweizga trees need 333 years to reach the height of bamboo growth in one day.
Why is the Ervizga tree growing so slowly? In addition to its nature, the lack of rain in the desert, dry weather and strong wind are also important reasons.
Warm-blooded plant
No matter what the external environment, the temperature of plant flowers is always constant. For example, the temperature of pueraria lobata is about 38 degrees, and when the outside temperature reaches 20 degrees, the temperature is still about 40 degrees. This ability is to treat one's own flowers as a miniature environment, thus attracting insects and improving the pollination probability.
Is the mysterious number of plants the harmonious beauty arranged by God?
The "plum blossom" on playing cards is not a plum blossom or even a flower, but a clover. Clover is a very symbolic plant in western history. It is said that the first leaf represents hope, the second leaf represents confidence and the third leaf represents love. If you find a four-leaf clover, you will get lucky and find happiness. Looking for four-leaf clover in the wild is a game for western children, but it is difficult to find it. It is estimated that there is one four-leaf mutant for every ten thousand clovers.
In China, plum blossom has a similar symbolic meaning. According to folklore, the five petals of plum blossom represent Five Blessingg. In the Republic of China, plum blossom was designated as the national flower, claiming that the five petals of plum blossom symbolize the harmony of five ethnic groups, which has the significance of strengthening the five ethics, emphasizing the five permanents and applying the five religions. However, it is not unique that plum blossom has five petals. In fact, the most common number of petals is five. For example, other species belonging to Rosaceae, such as peach, plum, cherry blossom, apricot, apple and pear, all have five petals. The common number of petals is: 3, iris and lily (it seems to be 6, but it is actually two sets of 3); 8 pieces, delphinium; 13, chrysanthemum morifolium; The petals of sunflower are 2 1, and some are 34. Daisies have 34, 55 or 89 petals. However, there are few flowers with other petals. Why are the number of petals not randomly distributed? 3, 5, 8,13, 21,34, 55, 89, ... What's so special about these numbers?
Yes, they are Fibonacci series. Fibonacci (1 170- 1240) was a medieval Italian mathematician. Instead of counting the number of petals, he worked out this series when solving a problem about rabbit reproduction. Suppose you have a pair of newborn rabbits, a male and a female. They began to mate when they were one month old. At the end of the second month, the mother rabbit gave birth to another pair of rabbits. A month later, they also began to breed, and so on. Every female rabbit will give birth to a pair of rabbits every month when she begins to breed. Assuming no rabbits die, how many pairs of rabbits will there be in a year?
1 At the end of the month, the first pair of rabbits mated, but only 1 pair of rabbits; At the end of February, the mother rabbit gave birth to two pairs of rabbits. At the end of March, the oldest female rabbit gave birth to a second pair of rabbits, a total of three pairs of rabbits. At the end of April, the oldest female rabbit gave birth to a third pair of rabbits, and the female rabbit born two months ago gave birth to a pair of rabbits. There are five pairs of rabbits. ... class =' class1' > If calculated in this way, the logarithms of rabbits are: 1, 1, 2,3,5,8,1,34,55,89, 144, ... Starting from the third number, each number is the sum of the first two numbers.
Plants seem to be fascinated by Fibonacci. Fibonacci number exists not only in flowers, but also in morphological characteristics such as leaves, branches, fruits and seeds. Leaf order refers to the arrangement of leaves on the stem, and the most common one is alternating leaf order, that is, only 1 leaf is born on each node, which is interactive. Starting from any leaf, connect the falling point of each leaf with an upward line. It can be found that this is a spiral, circling upwards until the falling point of another leaf above coincides with the falling point of the initial leaf, which is the end point. The number of spirals around the stem from the first leaf to the last leaf is called leaf order. The leaf order of different plants may be different and the number of leaves may be different. For example, the leaf order of elm is 1 (that is, 1 around the stem) and there are 2 leaves; Mulberry with leaf order 1 and 3 leaves; Peach, leaf order is 2 leaves and 5 leaves; Pear, the leaf order is 3 leaves and 8 leaves; Apricot, leaf order 5, with 13 leaves; The leaf order of pine is 8, with 2 1 leaf ... expressed by the formula (the number of leaves around the stem is the numerator and the number of leaves is the denominator), which are 1/2, 1/3, 2/5, 3/8, 5/ 13, respectively.
If you look at the sunflower disk, you will find that its seed arrangement constitutes two sets of embedded spirals, one is clockwise and the other is counterclockwise. Counting the number of these spirals, although different varieties of sunflower will be different, the number of these two groups of spirals is generally 34 and 55, 55 and 89 or 89 and 144, in which the former group of numbers is clockwise and the latter group is counterclockwise, and each group of numbers is two adjacent numbers in Fibonacci series. Look at the arrangement of scales on pineapples and pinecones. Although it is not as complicated as a sunflower disk, there are two groups of similar spirals, the number is usually 8 and 13. Sometimes this spiral is not so obvious and needs careful observation, such as cauliflower. If you study a cauliflower carefully, you will find that the arrangement of small flowers on the cauliflower also forms two sets of spirals. If you count the number of spirals, are they also two adjacent Fibonacci numbers, such as 5 clockwise and 8 counterclockwise? Fold a small flower and observe it carefully. It is actually composed of smaller flowers arranged in two spirals, and its number is also the number of two adjacent Fibonacci numbers.
Why do plants prefer Fibonacci numbers so much? This is related to another "mysterious" number, which was noticed and even worshipped by people as early as ancient Greece. Suppose there is a number φ, which has the following interesting mathematical relationship:
φ^2 - φ^ 1 -φ^0 =0
Namely: φ 2-φ- 1 = 0.
This equation has two solutions:
( 1 + √5) / 2 = 1.6 180339887 ...
( 1 - √5) / 2 = - 0.6 180339887 ...
Note that the decimal parts of these two numbers are exactly the same. The positive solution (1.6180333865 ...) is called golden number or golden ratio, which is usually expressed by φ. This is an irrational number (decimals are infinitely cyclic and cannot be expressed by fractions), which is the most unreasonable irrational number. It is also an irrational number. π π can be accurately approximated by 22/7, natural constant e can be accurately approximated by 19/7, √ 2 can be accurately approximated by 7/5, and φ can't be accurately approximated by fractions with single denominator.
The golden number has some wonderful mathematical characteristics. Its reciprocal is exactly equal to its fractional part, namely 1/φ = φ- 1. Sometimes this reciprocal is also called the golden number and the golden ratio. If a straight line AB is divided by point C and AB/AC= AC/CB, then this ratio is equal to the golden section number, and point C is called the golden section point. If the top angle of an isosceles triangle is 36 degrees, then the ratio of its height to the bottom line is equal to the golden number. Such a triangle is called the Golden Triangle. If the aspect ratio of a rectangle is the golden number, then a square with its width is cut from the rectangle, and the aspect ratio of the remaining small rectangles is still the golden number. Such a rectangle is called a golden rectangle, which can be cut infinitely by the above method to get smaller and smaller golden rectangles, and if the diagonal corners of these golden rectangles are connected by arcs, a logarithmic curve is formed. Common newspapers, magazines, books, paper, ID cards and credit cards are all close to the golden rectangle, which is said to make people look comfortable. Indeed, in our life, golden numbers are everywhere, and buildings, works of art and daily necessities all like to use them in design, because it makes us feel beautiful and harmonious.
So what is the relationship between the golden number and Fibonacci number? According to the above equation:
φ^2 -φ - 1 =0,
Available:
φ = 1 + 1/φ
= 1 + 1/ ( 1 + 1/φ)
= ...
= 1 + 1/( 1 + 1/( 1 + 1/( 1 +...)))
According to the above formula, you can use a calculator to calculate φ: enter 1, take the reciprocal, add 1, take the reciprocal, add 1, take the reciprocal, ... and you will find that the sum is getting closer and closer to φ. Let's use fractions and decimals to represent the above approximate steps:
φ ≈ 1
φ ≈ 1 + 1/ 1 = 2/ 1 = 2
φ ≈ 1 + 1/( 1+ 1/ 1) = 3/2 = 1.5
φ ≈ 1 + 1/( 1+ 1/( 1+ 1)) = 5/3 = 1.666667
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+ 1))) = 8/5 = 1.6
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+( 1+ 1)))) = 13/8 = 1.625
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+( 1+( 1+ 1))))) = 2 1/ 13 = 1.6 15385
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+( 1+( 1+( 1+ 1)))))) = 34/2 1 = 1.6 19048
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+( 1+( 1+( 1+( 1+ 1))))))) = 55/34 = 1.6 17647
φ ≈ 1 + 1/( 1+ 1/( 1+( 1+( 1+( 1+( 1+( 1+( 1+ 1)))))))) = 89/55 = 1.6 18 182 ...
Did you find it? The numerator and denominator of the above scores are adjacent Fibonacci numbers. It turns out that the ratio of two adjacent Fibonacci numbers is about equal to φ. The bigger the number, the closer it is. When it is infinite, the ratio is equal to φ. Fibonacci number is closely related to gold number. Plants like Fibonacci numbers, but in fact they like golden numbers. Why is this? Is there some arrangement that God wants to make the world full of beauty and harmony?
The branches, leaves and petals of plants are homologous, and they all germinate and differentiate from the meristem of stem tip in turn. The new bud grows in a different direction from the previous bud and rotates at a fixed angle. If we want to make full use of the growth space, the growth direction of new buds should be as far away from the old buds as possible. So what is the best angle? We can write this angle as 360× n, where 0 < n < 1. Because the left and right angles are the same (only the rotation directions are different), such as n=0.4 and n=0.6, the results are actually the same, so we only need to consider the case of 0.5 ≤ n < 1. If the new bud wants to be as far away from the previous old bud as possible, it should grow in the opposite direction, that is, n = 0.5 = 1/2, but in this case, the second new bud is in the same direction as the old bud, and the third new bud is in the same direction as 1 new bud ..., that is, it only overlaps around 1 week. If There will be overlap after three rounds, and there are only five directions in total. In fact, if n is a true fraction p/q, it means that there is overlap around p, and * * * has q growth directions.
Obviously, if n is an irrational number that cannot be expressed by a fraction, it is much more "reasonable". What kind of irrational numbers do you choose? Pi, natural constant e and √2 are not good choices, because their fractional parts are very close to 1/7, 5/7 and 2/5 respectively, that is, they overlap around 1, 5 and 2 weeks respectively, with only 7, 7 and 5 directions in total. So the conclusion is that the more irrational the irrational number, the better and more "rational". As mentioned earlier, the most unreasonable irrational number is the golden number φ ≈ 1.438+08. That is, the optimal value of n is ≈0.6 18, that is, the optimal rotation angle of new shoots is about 360× 0.6 18 ≈ 222.5 or 137.5.