1859, Hamilton got a regular dodecahedron model. As we know, a regular dodecahedron has 12 faces, 20 vertices and 30 sides, and each face is the same regular pentagon.
He invented a mathematical game: if these 20 vertices are regarded as 20 big cities, such as Paris, new york, London and Peking … and these 30 edges are regarded as roads connecting these big cities.
If there is a person, he starts from a big city, and every big city walks through it only once, and finally returns to the starting city. Can this method be realized?
This is the famous "problem of traveling around the world".
If we know the legend of the Seven Bridges, we will realize that this is a problem within the scope of topological research.
This method is very important to solve this problem. This requires very special geometric thinking. This kind of problem can't be tried with the dotted line of dodecahedron.
Imagine if this dodecahedron is made of rubber film, then we can press this dodecahedron into a plane. Assuming that the method proposed by Hamilton can be realized, then these 20 vertices must be a closed 20-corner world.
According to this idea, we entered the most preliminary field of topology. The final answer is that Hamilton's idea can be realized.
Hamilton was the first person to put forward quaternion. This achievement is still engraved in the place where his genius generate sparked.
Complex numbers can be used to represent plane vectors and are widely used in physics. People will naturally think: can we find a "three-dimensional complex number" to represent the space by imitating the complex number set?
From 65438 to 0828, Hamilton began to study quaternions carefully. Quaternion is a part of linear algebra and a kind of hypercomplex number. But before Hamilton, no one put forward quaternion, and Hamilton was also studied to solve the problem of expressing space quantity.
After studying for more than ten years, Hamilton made no progress. He is a genius in mathematics and has few problems. He's really in trouble this time. By 1843, Hamilton had studied 15 years.
One afternoon, the sunset is infinite, the autumn colors are bright and beautiful, and the scenery is pleasant. Hamilton's wife saw her husband immersed in research, hardly knowing whether it was cold or hot, and wanted him to go out to relax and adjust his body.
She said, "honey, the nature outside is not as interesting as your math, but it is not inferior." Go out and have a look. What a beautiful autumn! "
Hamilton, persuaded by his wife, put down the problem at hand and walked out of the study.
The husband and wife walked and unconsciously came to the moat. The autumn wind is soft and cool and the river is sparkling. The fresh air with the aroma of ripe fruits and natural soil makes people feel refreshed and clear-headed.
They are intoxicated with nature, and when the twilight is boundless, the evening scenery is pleasant. They came to Bolohan Bridge, facing the fresh water vapor and looking at the lights. Hamilton's mind is thinking without something, which seems far and near, and what seems clear and vague lingers in his mind for a long time. I can't take it out. I can't take it out. All of a sudden, these impression-like feelings turned into bright spots, all the fog of the past disappeared, and the lightning of thinking flashed across the sky of the soul. Hamilton's eyes lit up, and those clear dots appeared one by one.
Hamilton quickly took out his notebook and recorded the ecstatic results. In the past 15 years, a whole 15 years, I finally found a solution here!
Taking this opportunity, Hamilton strode home and plunged into the study, forgetting to eat and sleep. For several days, I was almost motionless, concentrating on writing and calculating from time to time. In a few inches of manuscript paper, Hamilton sorted out an epoch-making paper.
1843, 1 1 In June, 2006, the field of mathematics was a sensation, and Hamilton and the Irish Academy of Sciences announced "quaternions" to the world.
Hamilton proved that it is impossible to establish a three-dimensional complex number based on real numbers and make it have various operational properties of real numbers and complex numbers.
1853, Hamilton wrote a lecture on quaternions, which was published in 1857. In the second year after his death, that is, 1866, the quaternion principle was published.
Hamilton keenly felt the physical meaning of quaternion. Unfortunately, he left this world without witnessing the transformation of quaternion.
It is on the basis of Hamiltonian quaternion theory that the great Maxwell got out of the puzzle by using the tool of vector analysis and got the world-famous electromagnetic theory.
The study of quaternion promotes the development of vector algebra. /kloc-in the 9th century, mathematicians proved the hypercomplex system, and human thinking reached an unprecedented broad field.
Until now, a stone tablet still stands at Bolohan Bridge in Dublin, Ireland, where Hamilton stopped. The inscription reads: "1843 65438+ 10/6, William? When Hamilton crossed the bridge, he flashed the multiplication of quaternions, which was significantly different from real numbers and complex numbers. "
Who knows, how many people who stop to recall can know that behind the "inspiration flash" of scientific exploration, there are years of hardships?