Current location - Training Enrollment Network - Mathematics courses - Divine comedy mathematics
Divine comedy mathematics
Divine Comedy is a special epic because it describes the poet's own imaginary experience. The whole poem is divided into three parts: hell, purgatory and heaven. Each part consists of thirty-three songs. Together with the overture of the book, there are more than 100 songs, totaling more than 14 thousand lines.

This long poem, in the form of fantasy literature peculiar to the Middle Ages, describes Dante getting lost in a dark forest in the early morning of Friday before Easter in 1300. At dawn, he came to the foot of a sunny mountain. He was about to climb the mountain when he was stopped by three wild animals (leopard, lion and wolf, symbolizing lust, rape and greed). The situation is very critical. At this time, Virgil, the great poet of ancient Rome, appeared. He was entrusted by Bedric, the lover of Dante's youth, to rescue Dante and then take him to hell and purgatory as his guide.

Hell is divided into three parts: the first part is in Edith City, which is divided into five floors. There are some pagan souls, lecherous people, gluttons, greedy spenders and angry souls before death. These people have suffered all kinds of hardships here. The second part, in Diez, is also divided into three layers, which are full of evil souls. The third part is a huge deep well, divided into four layers, with an ice lake at the bottom, where all souls who have killed relatives or committed various betrayal crimes are frozen.

Those who can enter purgatory are souls whose sins can be punished and forgiven. The punishment here is not as cruel as in hell, and it has the nature of atonement, so the soul is more willing to accept it. The mountain of purgatory is divided into seven grades, which purify the seven original sins of human beings: arrogance, jealousy, anger, neglect, greed, gluttony and lust. When the soul washes away a sin, it rises to a higher level, so that it can gradually rise to the top of the mountain. The top of the mountain is a paradise on earth. Virgil brought Dante here and left, and then Dante was taken away by Bedric. After experiencing the ninth heaven, they finally came to God. At this time, Dante realized that his thoughts were consistent with those of God. The whole epic came to an abrupt end.

▲ Da Vinci (1452- 15 19) was an outstanding representative of the Renaissance, and his achievements and contributions were various. Leonardo da Vinci was born in the small town of Vinci near Florence. He is a genius. On the one hand, he is keen on artistic creation and theoretical research. He studies how to use lines and three-dimensional modeling to express various problems of the body. On the other hand, he also studies natural science. Leonardo da Vinci was the greatest and most famous master of the Italian Renaissance. He is not only a talented painter, but also a great mathematician, scientist, mechanic and engineer. He is a versatile and all-round man. He is versatile and has made many contributions to mankind. He can not only paint, carve and build houses, but also invent weapons and design the world's first plane. He is also a doctor, musician and dramatist, and has made great achievements in the research of physics, geography and botany. He has noble morality, Wen Ya demeanor, strong physique and extraordinary strength. It is said that he can easily break a horseshoe with one hand. He can write and draw with both hands. His handwriting with his left hand is the other way around, so people can only read it in the mirror.

"This is the most beautiful right hand in the history of world art; This pair of faces, once seen, will never be separated from our memory. " (Mona Lisa) "This is the best painting of mankind. The great success of this painting makes no one dare to set foot in this subject again." (The Last Supper) This is a self-portrait of the painter at the age of 62. A few strokes left a model in the history of sketch art for future generations. "(Leonardo da Vinci's self-portrait)

In the eyes of his contemporaries, Leonardo da Vinci was like a legendary magician with a reputation of omnipotent genius. In the eyes of modern people, it is remarkable that he established himself as the greatest painter with only twelve complete works.

It is generally believed that art is not science. But according to Da Vinci's definition, art, especially painting, is not only a science, but even "after all, it is a science".

Leonardo da Vinci not only found the fascinating beauty on the surface of things, but also lost the perspective of physicists and anatomists. He has both the observation of scientists and the expressive power of artists, and is the first artist in the history of art to systematically study the ratio of human body to animals. He studied anatomy for 40 years and personally dissected more than 30 bodies of all ages. He is not only familiar with the proportion outside the human body, but also understands the structure inside the human body, so the proportion, structure and dynamics of the characters in his works are very accurate and impeccable. This famous sketch of human anatomy contains a perfect figure of a circle and a square, which is considered as the most successful idea.

Leonardo da vinci was fascinated by geometric proportions and composition. In addition to the eternal mysterious smile, Mona Lisa also creatively solved the composition problem of the bust. For more than three centuries, all outstanding busts in the west have been influenced by this painting. He also enriched and developed the pyramid-shaped composition of predecessors. In The Virgin of the Rock, the isosceles triangle formed by the group images with the head of the Virgin as the vertex is as stable and harmonious as a pyramid. The Last Supper, like other works, designs pictures based on geometric figures, which embodies the symmetrical beauty of mathematics. Some people commented that this painting is a marriage of science and art, and philosophy left a kiss on this perfect combination.

Leonardo da vinci's greatest artistic contribution is to use light and shade to make the plane picture show a sense of space and three-dimensionality. In the early Renaissance, painters generally used lines to express perspective, single-line flat painting and monotonous colors. Leonardo da vinci studied light and shadow, initiated the gradual change method of light and shade, and used the technique of light and shadow to depict people and scenery, so that it presented a realistic three-dimensional sense. Until the emergence of Impressionism for hundreds of years, no one could surpass the stereoscopic painting system established by Leonardo da Vinci. The method of light and shade initiated by him changed the painting in this period, which is generally regarded by art historians as a turning point in painting art, and his artistic achievements directly influenced later artists such as Michelangelo and Raphael. Starting from The Last Supper, western painting really entered the heyday of the Renaissance.

Portrait painted by Leonardo da Vinci

Leonardo da vinci further summarized and sorted out fragmentary technical knowledge such as anatomy, perspective, shading and composition, and examined it from a scientific perspective. In his manuscript On Painting, he initially wanted to record an objective description of the physical world, but soon turned to perspective, proportion, geometry and optics, followed by anatomy and mechanics, and finally explored the mechanical function of the universe itself. On Painting was compiled by later generations from 18 notes of Leonardo da Vinci. Some people call it the most precious document in the whole art history.

Although sometimes his interest in science is so strong that he doesn't want to start painting, painting is his initial career after all. Just like learning other knowledge, Leonardo da Vinci tried to regard painting as a kind of science and spent his whole life in unremitting exploration. In the eyes of his contemporaries, Leonardo da Vinci was like a legendary magician with a reputation of omnipotent genius. In the eyes of modern people, it is remarkable that he established himself as the greatest painter with only twelve complete works.

It is generally believed that art is not science. But according to Da Vinci's definition, art, especially painting, is not only a science, but even "after all, it is a science".

Leonardo da Vinci not only found the fascinating beauty on the surface of things, but also lost the perspective of physicists and anatomists. He has both the observation of scientists and the expressive power of artists, and is the first artist in the history of art to systematically study the ratio of human body to animals. He studied anatomy for 40 years and personally dissected more than 30 bodies of all ages. He is not only familiar with the proportion outside the human body, but also understands the structure inside the human body, so the proportion, structure and dynamics of the characters in his works are very accurate and impeccable. This famous sketch of human anatomy contains a perfect figure of a circle and a square, which is considered as the most successful idea.

Leonardo da vinci was fascinated by geometric proportions and composition. In addition to the eternal mysterious smile, Mona Lisa also creatively solved the composition problem of the bust. For more than three centuries, all outstanding busts in the west have been influenced by this painting. He also enriched and developed the pyramid-shaped composition of predecessors. In The Virgin of the Rock, the isosceles triangle formed by the group images with the head of the Virgin as the vertex is as stable and harmonious as a pyramid. The Last Supper, like other works, designs pictures based on geometric figures, which embodies the symmetrical beauty of mathematics. Some people commented that this painting is a marriage of science and art, and philosophy left a kiss on this perfect combination.

Leonardo da vinci's greatest artistic contribution is to use light and shade to make the plane picture show a sense of space and three-dimensionality. In the early Renaissance, painters generally used lines to express perspective, single-line flat painting and monotonous colors. Leonardo da vinci studied light and shadow, initiated the gradual change method of light and shade, and used light and shadow to depict people and landscapes, making them present a realistic three-dimensional sense. Until the emergence of Impressionism for hundreds of years, no one could surpass the stereoscopic painting system established by Leonardo da Vinci. The method of light and shade initiated by him changed the painting in this period, which is generally regarded by art historians as a turning point in painting art, and his artistic achievements directly influenced later artists such as Michelangelo and Raphael. Starting from The Last Supper, western painting really entered the heyday of the Renaissance.

Leonardo da vinci further summarized and sorted out fragmentary technical knowledge such as anatomy, perspective, shading and composition, and examined it from a scientific perspective. In his manuscript On Painting, he initially wanted to record an objective description of the physical world, but soon turned to perspective, proportion, geometry and optics, followed by anatomy and mechanics, and finally explored the mechanical function of the universe itself. On Painting was compiled by later generations from 18 notes of Leonardo da Vinci. Some people call it the most precious document in the whole art history.

Although sometimes his interest in science is so strong that he doesn't want to start painting, painting is his initial career after all. Just like learning other knowledge, Leonardo da Vinci tried to regard painting as a kind of science and spent his whole life in unremitting exploration.

Second, "I would rather fail in the exploration"

Rock Madonna

He once painted a giant mural comparable to The Last Supper, but it was destroyed at the last minute because of a low-level mistake.

He looked forward to flapping his wings like a bird, but his dream of flying was dashed in an instant. He wanted to carve the world's largest bronze horse statue with flying forepaws, but two years later he had to change it to a walking posture because of the difficulty in casting.

Leonardo da vinci, who was called "the giant among giants" by Engels during the Renaissance, made remarkable achievements in many fields of human knowledge. At the same time, with him, there are little-known bitterness, suffering and failure. However, he would rather fail in the exploration than live a happy life without any intention. He has been practicing this philosophy of life all his life.

When painting the giant mural Battle of Angalli, which can be compared with The Last Supper, he personally developed a new pigment and coated it with oil. Murals have stood on the wall with great momentum and vividness, but the paint on the wall has not dried thoroughly. He couldn't wait to test the outer coating he made, so he asked his assistant to move two large braziers and bake them under the murals, and the oil was baked. He ruined eight months' hard work with two braziers.

Shortly after the mural turned into a colorful stream, he started the test flight with indifference. 5 1 year-old Leonardo da Vinci moved his homemade giant bird to the top of the mountain like a fanatical teenager. The little apprentice grabbed the wooden frame of the giant bird and flew down the mountain, and soon fell down. This kind of aircraft is driven by the muscles of arms and legs, but it ignores the weight problem that the human body can't overcome: the muscles used by birds to fly account for half of the whole body weight, while humans only have one fifth. But if the failure of his flight exploration is too demanding, it is tantamount to blaming Franklin, who used kites to attract lightning, for not inventing the electric light. At that time, church thought dominated all the ideas in the world. For example, almost everyone believes that the earth is flat, and the ocean near the equator must be as hot as boiling water.

He was appointed as a court architect and carved the world's largest bronze statue of a knight, in which the horse's front hoof was thought to jump in the air. He used wax models to test countless times, and stumps with a thickness of more than ten centimeters piled up on the shed floor. The most difficult thing is that 10 ton metal solution must be injected into the mold quickly, and the problem of uneven cooling should be considered. The technical conditions at that time obviously could not support this idea. When the two-year deadline came, he couldn't get the horse to stand up, so he had to walk. After his death 100, the Spanish continued to try this technique, and then built a monument for the knight on horseback.

The inspiration of whimsy can make him catch what others can't, but he often gives up halfway. Perhaps he had to stop his work from time to time in pursuit of the idea of flying forever. At that time, the wool textile industry in Italy was very developed, and knitting needles were the most easily worn in the textile workshop. He drew various machines for grinding needles in his notebook. After repeated comparisons, he finally chose the most ideal one. But he immediately had the idea of a loom, and then he was immersed in the invention and design of looms and ball bearing machines. Unfortunately, these design drawings were just lying on the draft paper, and eventually they did not become machines. He turned to other research.

Most of leonardo da vinci's works and manuscripts were not published until many years after his death. Dampier, a historian of science, commented: "If he publishes his works, science will jump to the situation a hundred years later."

Da Vinci, an outstanding genius, left a wealth full of wisdom to future generations. His predictive ability and insatiable spirit of exploration are still amazing after centuries.

Third, "what hinders me is the lack of time"

Portrait painted by Leonardo da Vinci

He has endless dreams like a god, but only mortal life and strength; He conceived thousands of plans, but only completed a few; His greatest ambition is to discover everything, study everything and create everything, but only the art of lines and colors brings him eternal praise.

Leonardo da vinci's life is an endless road, which is full of chapters and pages of unfinished works. He said: "I have never been hindered by greed or laziness. What hinders me is the lack of time. " He wants to be an engineer, strategist, musician, mathematician, philosopher and architect, but the world thinks he is just a painter who paints an eternal smile.

Leonardo da Vinci worked for the Duke of Milan for seventeen years, as a military engineer, architect, painter, sculptor and musician. He was the most popular court emcee at that time, responsible for organizing court festivals and celebrations, and independently played a variety of roles equivalent to the general director, host, screenwriter, composer, costume designer, choreographer and so on of CCTV Spring Festival Evening.

From the 12 paintings and more than 7,000 pages of manuscripts and design drawings left to future generations, it can be seen that Leonardo da Vinci was much more interested in science than painting. His achievements in scientific research are no less than his artistic achievements.

In astronomy, he observed celestial bodies and came to the conclusion that "the sun does not move". Before Copernicus, he denied the geocentric theory and fantasized about how to use solar energy. He thinks that the moon itself does not shine, but only reflects the brightness of the sun.

In physics, he discovered the liquid pressure, put forward the concept of connecting device, developed the lever principle, and deduced the relationship between the acting force and the arm length. His description of the inertia of objects was later confirmed by Galileo's experiments. He also denied the possibility of creating perpetual motion machines.

Leonardo da Vinci was fascinated by anatomy and physiology. At first, he studied anatomy to make artistic modeling more accurate, but later it developed into an independent scientific research field. His greatest contribution to anatomy is to create a set of charts, which are still widely used today. He was the first person to show the internal structure of the human brain with wax, and the first person to imagine making hearts and eyes with glass and ceramics. He even drew a picture of the baby developing inside the mother. Leonardo da Vinci studied the heart and blood circulation system, found that the heart has four chambers, and drew the heart valve, which is the first anatomical map of arteriosclerosis in history.

Leonardo da Vinci's research and inventions also involve military and mechanical fields. He designed aircraft, helicopters, parachutes, machine guns, tanks, submarines, double-hull warships, cranes, spinning wheels, machine tools, punching machines, bicycles and so on. He also made great contributions in the fields of mathematics and hydraulic engineering.

Leonardo da Vinci was also an outstanding thinker. He firmly believes in science and often shows suspicion and boredom with religion. He once wrote: There is only one truth, and it is not in religion, but in science. He proposed to take nature as a teacher and encourage people to learn from nature. He believes that knowledge comes from practice and its acquisition depends on direct observation and experience. His experimental working method was developed by Galileo in practice, and then summarized by British philosopher Bacon in theory, which became the most basic research method of modern natural science. It paved the way for the inventions of Galileo, Kepler, Newton and others.

Art historians have commented that there is only one Leonardo da Vinci ahead of the times. He is an all-encompassing and exquisite genius and an insatiable lonely explorer. The tentacles of his thinking are far beyond his time, and some of them can actually meet our time.

Later generations' practice of Da Vinci's research thought

It is said that it is a practice of Leonardo da Vinci's "research ideas" because in his time, Leonardo da Vinci's research can only stay in the "ideas" stage and there is no way to advance to the "results" stage. But some of his ideas have been successfully realized by modern people.

First, Leonardo da Vinci "designed" a parachute, and one person successfully copied it.

South African newspapers reported on 28th that a British man used a parachute made according to the design sketch of Leonardo da Vinci in the 5th century to descend 2120m in the air, which proved that this pyramid-shaped landing device worked well. The parachute descended slowly in the air until it reached an altitude of 900 meters. He cut off the connection with the parachute and completed the landing action with a modern parachute. He said that although the landing device designed by the inventor in the15th century could be used for safe landing, he could not operate it to accurately select the landing site.

Leonardo da Vinci had never made a draft parachute before 1485, because experts doubted its feasibility. The parachute consists of tarpaulins, ropes and six wooden sticks 1 m long, weighing 180 kg.

Secondly, Norway built a bridge designed by Leonardo da Vinci.

101October 3 1 day, the Queen of Norway and more than 500 guests from all walks of life cut the ribbon for a unique bridge in the cold wind and drizzle in northern Europe. Helicopters hover over people's heads, cranes slowly lift 48,000 square feet of white cloth, and a wooden bridge with a length of 100 meters and a height of 8 meters is displayed in front of everyone. Three light-colored wooden arches, like three hard bows pulled back by the shooter, firmly support the bridge. Incredibly, the designer of this bridge was Leonardo da Vinci 500 years ago. For this reason, the bridge was named "Mona Lisa".

1502, Leonardo da Vinci drew a wonderful sketch of arch bridge design for Istanbul, Turkey, which spans two continents. The bridge is 346 meters long and spans the Bosphorus. If it can be built, it will be the longest bridge in the world at that time. But the Sultan of Turkey refused to build the bridge. He thought it was too difficult and expensive. Therefore, the bridge stayed on the drawing for 500 years.

1995, Norwegian artist Vebjoern Sander came across this design sketch. He recalled: "The first time I saw her, I was conquered by her exquisite appearance. She is the perfect combination of function and aesthetics. " Through various efforts, Sander finally persuaded the Norwegian Highway Administration that the principle of Leonardo da Vinci's design of the bridge was completely established and the bridge could be built. After investigation, the location of the bridge is determined to be Australia, more than 30 kilometers south of Oslo, Norway, just adjacent to the European highway 18 from Stockholm to Oslo.

At present, the cost of the completed footbridge is $65,438+0,360,000. Except for the stainless steel handrails, it is completely made of wood. In fact, Leonardo da Vinci's design was made of stone, but the Norwegians thought that stone was too expensive, so they changed the material for building the bridge to wood.

It is reported that this is the first time that leonardo da vinci's architectural design has been put into practice, and this design is a classic example of aesthetics and design. Thornton proudly said, "Five centuries ago, people thought it was impossible to build this bridge, but we built it. We have successfully proved that the principle of Da Vinci's design of this bridge is feasible. " Sander said that he still has a dream, "We want to promote this kind of bridge all over the world so that every continent can build the Mona Lisa Bridge".

William shakespeare (1564— 16 16) was the most important writer in Britain and Europe during the Renaissance. He was born into a merchant family in Stratford, central England. When I was a teenager, I received basic education in the local grammar school, studied Latin, philosophy and history, and got in touch with the works of ancient Roman playwrights. Later, he dropped out of school to make a living because of his family's decline. When Shakespeare was young, famous troupes often toured the countryside, which cultivated his interest in drama. 1585 or so, he left his hometown and went to London. First he worked as a handyman in the theater, then he became an actor, and then he changed to writing plays. Shakespeare not only participated in performances and screenwriters, but also had extensive contacts with society, and often went to court or went to the countryside with the troupe. These experiences broadened his horizons and laid the foundation for his creation.

1590 to 1600 is the early period of Shakespeare's creation, also known as the historical drama and comedy period. During this period, Shakespeare's humanistic thought and artistic style gradually formed. At that time, Britain was in the heyday of Queen Elizabeth's rule, with stable and unified kingship and prosperous economy. Shakespeare is full of confidence in realizing humanistic ideals in the real society, and his works are full of optimism and clarity. During this period, he wrote nine historical plays, including Richard III (1592), Henry IV (parts I and II) (1597- 1598) and Henry V (10). The basic theme of the script is to support the central kingship, condemn the feudal tyrant and praise the enlightened monarch. For example, "Henry IV" shows the picture of the turbulent domestic situation. The nobles United against the king, but the rebellion was finally quelled; The prince lived a dissolute life earlier, but later he made a mistake and made great contributions to quelling civil strife. In the play, historical facts and artistic fiction are highly unified. Falstaff is one of the most vivid characters. He is selfish, lazy and timid, but he is alert, intelligent and optimistic, which makes people laugh.

The comedies created in this period include poetic A Midsummer Night's Dream (1596), The Merchant of Venice (1597), The Merry Wives of Windsor (1598), and Much ado about nothing (/) The basic themes of these plays are love, marriage and friendship, which are full of lyrical colors and show Shakespeare's ideal of humanistic life. At the same time, he also wrote three tragedies such as Romeo and Juliet (1595). Although the work has a sad side, the basic spirit is the same as comedy. Shakespeare also wrote the long poems Venus and adonis (1592- 1593), The Shame of Lucretius (1593- 1594) and 154 sonnets.

/kloc-At the beginning of the 7th century, the regime of Queen Elizabeth and James I changed, the social contradictions in Britain intensified, and social evils became increasingly exposed. During this period, Shakespeare's thought and art became mature, and the humanistic ideal collided fiercely with social reality. He felt that his ideal was difficult to realize, and his creation turned from praising humanistic ideals in the early days to exposing and criticizing social darkness. The second period of Shakespeare's creation (1601-1607) is also called the tragic period. He has written Hamlet (160 1), Othello (1604), King Lear (1606), Macbeth (1606) and Ty of Athens. In Othello, Desdemona, who was born in a noble family, married Othello the Moor privately despite the opposition of her father and society, showing the theme of opposing racial prejudice. The reason for their tragedy is not only Othello's jealousy, but also the powerful evil forces represented by Iago. Othello's sobriety before his death contains the victory of human reason. King Lear shows a broken society. King Lear paid the price of his life because of his stubbornness, and also brought great disaster to the country and people. The protagonist has changed from a feudal monarch with absolute authority to a homeless old man with nothing, and the fate and character of the characters have undergone tremendous changes, which is the most distinctive in Shakespeare's works. In Macbeth, a hero became a personal careerist and tyrant because of his inner ambition and external instigation. Its tragic significance lies in that personal ambition and egoism can destroy a person who is not evil. Generally speaking, these tragedies profoundly exposed the decay of feudal nobles, appalling egoism, the evil of money relations and the suffering of working people; Stylistically, it reduces the atmosphere of romance and joy, increases the mood of melancholy and indignation, and makes the image fuller and the language more proficient.

After 1608, Shakespeare entered the last period of his creation. At this time, Shakespeare saw that the ideal of humanism could not be realized in the real society, so he turned from writing tragedies to writing legendary dramas, from exposing and criticizing the darkness of the real society to writing dream worlds. Therefore, this period is also called Shakespeare's legendary drama period. During this period, his works often solved the contradiction between ideal and reality through myth and fantasy and supernatural power; The works are permeated with the spirit of forgiveness and reconciliation. There is no joy in the early stage and no gloom in the middle stage. But full of beautiful life fantasies and rich romantic feelings. The Tempest (16 1 1) best represents the style of this period and is called "a will written in poetry". In addition, he also wrote three legendary dramas, such as cymbeline and The Story of Winter, and the historical drama Henry VIII.

Shakespeare's works, starting from the truth of life, profoundly reflect the characteristics of the times and social essence. In his view, drama "seems to give nature a mirror: show its face to virtue, show its posture to absurdity, and show its image and imprint to the times and society". Marx and Engels praised Shakespeare as a classic writer of realism, and proposed that drama creation should be more "Shakespearean". This is a creative principle put forward in view of the disadvantages of "turning the individual into a simple mouthpiece of the spirit of the times" in drama creation. The so-called "Shakespearization" means that the writer, like Shakespeare, is good at starting from the truth of life, showing a broad social background and providing a typical environment with the characteristics of the times for the characters and events in his works; The plot of the work should be vivid and rich, and the characters should have distinctive personality and typical significance; The realistic depiction and romantic atmosphere in the works should be skillfully combined; Language should be rich and expressive; The writer's tendency should be hidden and naturally revealed in the plot and character description.