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Without adding additional dimensions, a closed 2D is still 2D, and a closed 3D is still 3D. Closed lines form circles, and closed three-dimensional bodies form cubes.
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It's going to be a ball, because three dimensions have length, width and height, and I think it's going to be like this, you can imagine.
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A ball. Because the two-dimensional space is enclosed as a circle, the three-dimensional space enclosed is a sphere.
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Who says that the enclosure of a two-dimensional space is a circle? Thousands of them did not point out the error of the question. The zero dimension is a point, the one dimension is a line, or a straight line, or a curve, and it is a ring when it is closed, including a circle.
A two-dimensional space is a plane, or a plane, or a curved surface. Enclosed is a closed surface, which includes spheres. Notice that we are talking about a sphere, not a sphere, which is still two-dimensional.
Three-dimensional space is three-dimensional, including spheres, they can no longer be closed, and when enclosed, they are still three-dimensional. If you have to close it, you can only consider it from two aspects: big and small. To put it mildly, three-dimensional energy is enclosed into mass matter by a certain mechanism; To put it more broadly, the whole three-dimensional void is enclosed into the whole static universe, which is the shape of the universe.
As for what the four-dimensional space can be enclosed, even the three-dimensional space cannot be closed, let alone the four-dimensional? To be honest, the so-called four-dimensional space does not exist, Einstein and Minkowski regarded time as a one-dimensional special space, and believed that the universe was a four-dimensional space-time. The so-called four-dimensional or high-dimensional space is an abstract expectation of people's high-dimensional universe, which in fact does not exist at all.
Some people say that the four-dimensional space is closed as a supersphere, and this supersphere only exists mathematically, and does not exist in the real universe. Some people say that the Klein bottle is the topology of the four-dimensional space, and some people say that all the three-dimensional objects that our universe is called are the projections of the objects in the four-dimensional space, which is all nonsense. In fact, not only does there not exist a four-dimensional space, but there is also no so-called zero-dimensional, one-dimensional and two-dimensional space, because the points, lines and surfaces are all abstract, otherwise no matter how thin the line is, it is also three-dimensional and large.
No matter how thin the surface is, it is three-dimensional and thick. There is no such thing as a surface without any thickness or a line without thickness, this only exists in mathematics.
In short, the material world of this universe is only a three-dimensional space, a four-dimensional space-time, and there will be no other dimensions, nor will it be closed, even if it is closed, it is a three-dimensional three-dimensional.
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First of all, I personally think that the so-called fourth dimension of the four-slip trapped positive dimensional space is time, which is wrong, because the first three dimensions are the spatial dimension, and the fourth dimension should also be the spatial dimension, which is formed by various distortions, deformations and entanglements in the three-dimensional space we live in, such as the spatial distortion around the black hole. According to the theory of relativity, velocity and mass should affect the spatial changes around the object and thus time. In other words, the measure of temporal repentance cannot be said separately from space.
Even if you add a timeline to a 3D object, it still can't jump out of 3D space.
As for the closure of the four-dimensional space, it should be a state after the distortion of the three-dimensional space, and it is impossible to describe or imagine what it looks like, after all, we are all three-dimensional creatures, and we cannot imagine and describe the situation in a higher dimension. It can only be said that four-dimensional beings are beings that can jump out of the three-dimensional space of our existence.
Personal point of view, disagree please spray lightly.
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I always see people say that one dimension is a line and two dimensions is a surface. There are also examples of ants being two-dimensional creatures.
But what I want to say is that everything that is knowable in three-dimensional space is three-dimensional. Why? Because even nanometers are three-dimensional when magnified. Ants will also climb up in the corners.
Our so-called imaginary space, two-dimensional space, and their physical forms of existence are all just conjectures, no one has ever seen and cannot see them, but they exist theoretically. So one-dimensional, two-dimensional space is a paradox in itself. A line is a line, a two-dimensional plane is a surface, and a three-dimensional plane is called space.
It's like statistics, in other words, big data. The essence remains the same, but the expression is different.
The world is space, and other elements fill this space and make up this world. If you've ever seen a gossip diagram, you'll definitely be able to see what the world is. The elements of the world are like the eight trigrams, there is yin in yang, and yang in yin, and the eight hexagrams represent the laws of the world, like birth, old age, sickness and death, which together are the world.
That's why men will also have times of vulnerability, women will have times of strength, and tadpoles can only reproduce when they combine with eggs.
But since it's speculation, the bolder it is, the more interesting it is. I've heard a saying before that can be used to guess. He said that countless points make up lines, countless lines make up planes, and countless surfaces make up space, so what about countless spaces?
It's still space. But this space is composed of countless three-dimensional spaces, so his enclosed space is an infinite number of balls.
So is it possible to understand that four-dimensional beings are actually different three-dimensional from us in the same four-dimensional? But three-dimensional beings can only move in their own three dimensions, while four-dimensional creatures can move in any one of these four dimensions. So what exactly is a four-dimensional being?
However, this guess is also incorrect, because this guess is actually a three-dimensional space thinking mode in the **one-dimensional, two-dimensional and four-dimensional space. So it's wrong.
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Presumably we all know that zero-dimensional space can be understood as a point, one-dimensional space is similar to a straight line, two-dimensional space is a plane, and three-dimensional space is similar to a spatial Cartesian coordinate system, so what is four-dimensional space?
Human beings are three-dimensional animals, and stupid people cannot perceive more than three-dimensional space, and four-dimensional space is beyond human perception. Just like ants are two-dimensional space creatures, they can only move on a horizontal plane, and they only have the ability to perceive the plane direction, and they don't know the concept of up and down. So the question is, what is the four-dimensional space like with the file?
How to understand it?
The author is also an ordinary human being, and the author can only talk about this issue. Four-dimensional space-time, that is, three-dimensional space plus a timeline. Three-dimensional space does not have the concept of time, and when the concept of time is added, it becomes a four-dimensional space, and human beings are three-dimensional animals, but human beings are not purely in three-dimensional space, because there is a concept of time.
To put it simply, in a three-dimensional space, if there is a change of day and night, the four seasons alternate, time is advancing, everything is developing, not static, this is the four-dimensional space, human beings will also have birth, old age, sickness and death, no one can escape such a law, because everything is advancing. Four-dimensional space is an abstract existence, invisible, and intangible. If you are only in three-dimensional space, then everything should be static.
The existence of multidimensional space has always been a relatively big mystery. Is it possible for humans to enter other spaces? The answer is yes.
Everyone must have heard of a lot of supernatural events or unsolved mysteries. That is, human beings disappeared in an instant, lost consciousness, and when they reappeared, decades had passed on the earth, and the person concerned only felt that a few minutes had passed, such cases do exist, and you can check them on the Internet by yourself. The author believes that when a stupid human is asleep, the human brainwave may briefly enter the space of other dimensions, because when you fall asleep, you will feel that time flies quickly, and it seems that there are only a few minutes in a night, which may reflect the differences in space in different dimensions.
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Judging from the situation in front of the scum hall, three-dimensional space is already the limit explored by mathematicians, and so far, four-dimensional space has not been proven. However, it is the nature of mathematicians to seek laws, and it is not difficult to imagine the closure of four-dimensional space from the closure of one dimension to three dimensions. In physics, "dimension" represents a parameter, the zero dimension is a point, the imaginary one-dimensional is a straight line, the two-dimensional is a surface, and the three-dimensional is a body.
To put it simply, the second dimension is equivalent to a circle, the third dimension is a sphere, and the fourth dimension is a "folded body".
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The four-dimensional is actually a collection of three-dimensional spheres, and the closed three-dimensional space is actually a collection of a series of three-dimensional spheres.
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Enclosing the three-dimensional is the hypersphere, that is, the surface of the four-dimensional hypersphere.
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The four-dimensional space is our world, we can imagine the earth or the universe we live in as a four-dimensional space, the thinking space is actually a concept of time and space, it is relatively abstract, Brother Zhaokai is also a concept that we are not often envious of in life.
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Indeed, in my opinion, this four-dimensional space is actually just a concept of time and space. In short, any space with a four-dimensional space can be called a four-dimensional space, however, most of the four-dimensional spaces mentioned in daily life refer to the concept of four-dimensional space-time mentioned by Einstein in his general and special theories of relativity, and according to the concept of the famous scientist Albert Einstein, our universe is made up of time and space.
The relationship between time and space is to add a timeline to the structure of space, rather than the length of ordinary three-dimensional space. Width and height, this timeline is a virtual numerical axis. According to Einstein's theory of relativity, the three-dimensional space we face in life and time constitutes the so-called four-dimensional space.
Since time is slow that we perceive on Earth, we will not visibly feel the existence of four-dimensional space, but once we board the spaceship or reach the universe.
When the speed of the reference system itself begins to become faster or close to the speed of light, we can find the change in time by comparison. If you travel at close to the speed of light in a spaceship, you will live much longer than you would on Earth. There is a potential place here where the energy of matter changes with speed.
Therefore, the change and contrast of time takes the velocity of matter as a reference system.
That's why time is one of the elements of four-dimensional space, and I also have a newer idea that all dimensions are made up of time. Without time, there is no space, including the most basic one-dimensional space, which should actually be easy to understand, because without time, the existence of space itself has no meaning, because space-time itself is an indivisible whole, then, why can time form different dimensional spaces, here, we can think of time as a variable that can be decomposed, time can be decomposed, which may be a bit difficult to understand.
As for the question of what kind of four-dimensional space is the closure of two-dimensional space, three-dimensional space is a circle, and three-dimensional is a sphere, I will explain it here today.
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Four-dimensional space includes the concept of time. At present, no one can present a four-dimensional space in front of people. But I think it could be a closed period of time in an area.
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Indeed, if I think that this four-dimensional space is actually the concept of time and space. In a nutshell, any space with a four-dimensional space can be called a four-dimensional space. However, the four-dimensional space mentioned in daily life mainly refers to the four-dimensional space-time mentioned by Einstein in the general theory of relativity and the special theory of relativity.
Concept, according to the famous scientist Albert Einstein, our universe is made up of time and space.
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This four-dimensional space is actually just a concept of time and space. In a nutshell, any space with a four-dimensional space can be called a four-dimensional space.
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The fourth dimension is a cube that overlaps and overlaps. We all know that human beings have made many breakthroughs in scientific exploration, but many miraculous phenomena in nature cannot be fully explained by our scientific theories. The universe in which human beings live is only a three-dimensional space;
For us, the existence of higher levels cannot be understood by normal logic for the time being. It's like a creature living on a two-dimensional plane that can never imagine what the three-dimensional world is like.
In Newton's vision of absolute space-time, space and time are eternal, unabated, so he does not need to consider the connection between "higher dimensional" and "multiverse"; It was not until Einstein proposed the general theory of relativity that mankind first realized the form in which space and time existed;
Gravity, on the other hand, distorts space-time into a geometry. From the perspective of the entire observable universe, the three-dimensional world should be a sphere with a "bounded infinity" surface; However, when human beings have crossed into the four-dimensional world, what kind of state is the four-dimensional world in our eyes?
According to the model proposed by the great physicist of this century, Mr. Stephen Hawking, in his book "A Brief History of Time", in the four-dimensional world, objects with three-dimensional structures exist only in a linear way; Time and space are intertwined with each other in an overlapping relationship;
Within the four-dimensional world, human beings can participate in the long river of time through consciousness, and even re-engage in history from the past and the future. And the only way to reach the four-dimensional space is through the "wormhole", which is a tunnel connecting dimensions and dimensions.
Moreover, in the four-dimensional space, there is more than just one universe within the hail. In addition to having a positive universe that is parallel to the current human race, there is also an "anti-universe" that is opposed to the current universe by any physical law, and together they make the four-dimensional space function normally.
In the theory of superstring Sun Dou, the four-dimensional space is not the end of the dimension, and the highest level of the universe is the eleven-dimensional world.
The high-dimensional space or low-dimensional space we are talking about is theoretically possible or exists in mathematical formulas. At present, there is no sign of the existence of other dimensional spaces, and of course it is difficult for humans to detect them. >>>More
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The conventional solution is the current analysis method, assuming that the current of size i is connected and sent out at two points of the Japanese diagonal respectively, then the electric potential at infinity can be set to the electric potential of 0, and the electric potential of the access and outlet points is assumed to be +u and -u by symmetry, and the current can be considered to flow from the access point to infinity, and then flow back to the contact point from infinity. In the previous process, the current flows symmetrically, so that the first section of the z-shaped path from the inflow point to the reserve point has the current of i 4, the second section has i 12 (i.e. i 4 is divided into 3 parts), and the third section is still above i 12 (a careful analysis of the diagram shows that this node is two flows in and two out); A similar analysis is performed in the latter process (except that the current is in opposite directions). In this way, the superimposed currents on the three paths are i 3 (i.e. i 4 + i 12), i 6, i 3, and the potential drops to ir 3 + ir 6 + ir 3 = 5ir 6, and this should be equal to the total voltage drop of 2u (i.e. 2u = 5ir 6), so the equivalent resistance r'=2u/i=5r/6 >>>More
One-dimensional arrays hold the same values, but in the case of matrices, determinants. >>>More
Here's a version to dynamically create a 2D array and then look for it: >>>More