Why does swimming need to be represented by three dimensional coordinates, and is there a four dimen

One-dimensional refers to straight lines, two-dimensional is planar, and three-dimensional is three-dimensional space.

The three-dimensional ones are represented in three dimensions, so there is no four-dimensional one, and the athlete's body will rise and fall on the water surface when swimming, so it is a change in spatial position, which is represented by three-dimensional coordinates.

Hehe, I'm the first, I'll continue to help you if you have any questions in the future.

Do you know what thinking is?

Personally, I think that in addition to the length and width of the plane area, there is also a very important aspect, that is, "high", that is, the water depth within the pool or any water area in the rivers and lakes.

In addition, [four-dimensional] should be a space-time concept, right? In simple terms, the four-dimensional space is not composed of x, y, and z axes, but also an infinitely extended time axis, in short, the universe ......

You can't swim forever in an infinite area of water, right?

Because the coordinates of the swimming pool in a general sense are to represent the position of each point in the swimming pool, but it does not mean that the four-dimensional coordinates cannot be used, as mentioned above, the fourth dimension is generally considered to be time. Therefore, swimming pools that only study the location of the spatial focus generally do not need to use four-dimensional coordinates. If the four-dimensional coordinate is used to represent the swimming pool, then this coordinate can not only represent the points of the swimming pool at one time, but also the points of the swimming pool at other times.

To put it simply, four-dimensional coordinates allow you to see the pool at 7 a.m., at 4 p.m., and at other times.

Hope it helps you o(o

If the landlord is not talking about four-dimensional space-time but four-dimensional space, then four-dimensional space is in addition to up and down, left and right, front and back, plus one dimensional other space. This extra dimension exists, but it's too small for us to detect. It's as if hair looks 1 dimensional, but it's actually 3 dimensional.

If the landlord is talking about four-dimensional space-time, then it is three-dimensional space plus one-dimensional time, because under special relativity, they write it in the form of ds 2=dx 2+dy 2+dz 2-(cdt) 2 and has invariance. That is to say, for events that have a causal relationship, space and time are not independent.

Length + Width + Height + Time.

Length, width and height are represented in the same coordinates, using the xyz axis.

Time is represented by another coordinate, with a t-axis.

Only below three dimensions can be described.

Four-dimensional and above are only mathematical theories and cannot be modeled.

First of all, I would like to tell you that if you still insist on time as the fourth dimension, then the fourth dimension will always be a complex superposition of three dimensions, and will not be mosaic into the fourth dimension, just like laying out a few pieces of paper like this, although it does take a certain amount of time, but the spelling out is always a flat figure. The real four-dimensional space can not be called three-dimensional space, because the three-dimensional space is a three-dimensional expression, and the four-dimensional space is developed in the direction of the W axis on the basis of the three-dimensional space. Due to our limited vision, we can only see a three-dimensional projection of a four-dimensional geometry.

And we can't go to the fourth dimension, because before we go in, we're destroyed. For example, if you draw a circle on a piece of paper and draw a dot inside the circle, the dot will never escape the circle's containment, but if we now superimpose countless pieces of paper on the paper and allow the circles and dots to enter the other papers freely, the problem arises, the dot can escape on any paper, but the circle can't guess which paper the dot will escape from, so it can't contain it. So in the same way, when we enter the four-dimensional space, our blood is trapped in the body, and it is restrained by the body, and there is no way to escape.

Trouble comes in an instant when we enter the four-dimensional space, blood can escape in an instant, and our body can't contain it. Can we live without blood?

The world we live in is four-dimensional.

There are 3 spatial dimensions and one time dimension.

More than four dimensions are unthinkable.

Because we grew up in a four-dimensional world.

It's like ants grow in a three-dimensional world.

There is no difference between high and low in the eyes of ants.

I can give you a way to imagine for yourself.

A straight line, if we look in the direction of the line.

It is a point.

A planeIf we look in the direction of the plane, it is a straight line.

A geometry we see from different sides is a different 2D shape.

So you can imagine what it's like to have more than four dimensions.

Four-dimensional space is generally considered to be three-dimensional space plus fourth-dimensional time. In this way, the four-dimensional space is a process, and each four-dimensional parameter is a state. What will it be like beyond the fourth dimension, I can't say. You can do what you want.

For more abstract, take a look at the introduction of the encyclopedia.

Copy-paste, trouble.

Two-dimensional coordinates, as you must know, are plane coordinates, x-axis and y-axis.

In this way, a point on the plane can be determined, and the three-dimensional coordinates are a z-axis on the ridge, and the z-axis is perpendicular to the axis, so that the three axes can be rotated to determine a point in space.

Four-dimensional is to add a concept of time to the three-dimensional basis, so that a certain point at a certain time can be determined.

There is an explanation that impresses me in a brief history of time, he said: In terms of appearance, the dimension of space is similar, just like when the plane flying in three-dimensional space is flying, its shadow is one-dimensional in the trajectory, and the four-dimensional space is more like a two-dimensional space from a certain point of view.

Upstairs, there is a letter for jujubes"c"What do you mean?

The fourth dimension is time, and philosophically you can't step into the same river twice, and that's what it means, because there's a difference in time.

The concept of dimension in the narrow sense:

Generally, three-dimensional refers to the three axes of x, y, and z, corresponding to length, width, and height.

A four-dimensional system, on the other hand, refers to the addition of a time dimension to the three dimensions.

The concept of dimension in a broad sense is more complex and abstract. These are generalized coordinates.

In general, the set of parameters that determine the state of a system is the generalized coordinates of all the disintertransaction sets.

For example, in a multi-link system, where the length of each rod is determined, the angle between the rods is the set of parameters that confirm the linkage system. The set of angles of the connecting rod is called the generalized coordinates of the connecting rod system. For more information, please refer to the textbook related to theoretical mechanics.

We live in a three-dimensional space, a four-dimensional space-time. is the assumption of current physics. But inside the protons and neutrons, the so-called string vibrations reach 11 dimensions.

It is said that it is 11 dimensions, but in fact, it is all mathematical operations, and you will understand it when you learn linear algebra. Many problems of time and space are actually mathematically derived, and it is difficult to explain them with Si, so I recommend you to take a look at Hawking's universe.

And give you a link.

The time and space we live in are mindful.

Space-time space-time is composed of time and space.

Space is three-dimensional (the x-y-z axis in three-dimensional geometry), and the time axis is four-dimensional.

Of course, there is no definitive proof of the existence of higher latitudes in our space-time.

However, a female professor at Harvard said that she would prove the existence of the fifth dimension as early as 2011, and that what we think of as the soul is hidden in the fifth dimension.

If there were higher latitudes, then parallel space-time would not be difficult to imagine.

In the near future, it is even possible to discover time tunnels, travel through time and space, and more.

There is a lot to be said about the specifics of space-time, including Einstein's theory of relativity.

If the landlord is interested, you can go and have a look.

Space is three-dimensional.

If space, time, or something is involved, I don't know how many dimensions are involved.

Three-dimensional refers to the spatial system composed of a direction in the plane two-dimensional system, the so-called three-dimensional, according to popular theory, it is only three directions that are artificially prescribed perpendicular to each other, and with this three-dimensional coordinate, it seems that the position of any point in the whole world can be determined. It turns out that three-dimensional is to determine the position.

Three-dimensional is the three axes of the coordinate axis, namely the x-axis, the y-axis, and the z-axis, where x represents the left and right space, y represents the upper and lower space, and z represents the space before and after, so that the three-dimensional sense of human vision is formed, and the three-dimensional animation is the three-dimensional animation made by the three-dimensional production software, so as to realize the trend of redevelopment.

The so-called three-dimensional space refers to the space we are in, which can be understood as having a front and back -- up and down -- left and right, if you take time as a kind of material, then add time is a four-dimensional space, but it is not difficult to understand that you can go back and forth in time at will, go back to the past, but it should be understood as"Just now"with"Now"It's a different substance, but you can't go back"Just now"with"In the past"

Three-dimensional refers to length, width, and height.

Add time to form four dimensions.

According to Einstein's concept, our universe is made up of time and space. The relationship between time and space is that there is an additional time axis in the structure of space compared with the three axes of length, width and height of ordinary three-dimensional space, and this time axis is an imaginary value axis (i.e., four-dimensional space).

According to Einstein's theory of relativity, the three-dimensional space we face in our lives plus time constitutes the so-called four-dimensional space. Since the time we perceive on Earth is very slow, we will not obviously feel the existence of four-dimensional space, but once we board a spaceship or reach the universe, we can find the change in time when the speed of the reference frame in which we are located begins to speed up or begins to approach the speed of light.

If you sail in a spaceship that is close to the speed of light, you will live a lot longer than a person on Earth. Moreover, the slowing down of the bell in the flying rocket also confirms this with facts. There is a potential here where the energy of matter changes with speed.

Therefore, the change and contrast of time is based on the speed of matter. This is the reason why time is one of the elements of what is a four-dimensional space.

One dimension is a line, two dimensions is a surface, three dimensions is static space, and four dimensions is dynamic space (because of time), of course, this is just a statement, not that the fourth dimension is time.

The parameters that we have to change in physics to describe a changing event. This parameter is called a dimension. A few parameters are just a few dimensions.

For example, to describe the position of a "door" is only an angle, so it is one-dimensional, not two-dimensional, and to put it simply: zero-dimension is a point, and there is no length, width, or height. One dimension is a line made up of countless points, only length, no width or height.

A two-dimensional is a surface made up of countless lines, with length, width, and height. A three-dimensional body is a body composed of countless faces, with length, width and height. Dimension can be understood as direction.

Because the human eye can only see in two dimensions, it is difficult to interpret more than three dimensions. Just as a person with normal intelligence and a congenital absence of one eye and one ear (so that there is no binocular effect, binaural effect), it is difficult for him to understand distance, and he is likely to think that the world is two-dimensional.

For example, a water pipe, people generally think that it is a three-dimensional object, but if you look at it from a distance, there is only one line left (1 dimension) A simple statement: n dimension is the space formed by n straight lines perpendicular to two by two Because human beings can only understand 3 dimensions, the later dimensions can be constructed by mathematical theories, but it is difficult to understand carefully. In quantum mechanics, string theory, which is still being established, holds that the world is 11 dimensions.

After all, Einstein's theory of relativity is something that few people can understand, so if you want to really understand it, you have to look at it. As far as we know, it's just scratching the surface. It can only be understood literally.

At least in the subjective world, it's hard for me to imagine a 4-dimensional space. Do not exclude those with a well-developed brain.

<>Or use the following formula:

Not an answer, just a suggestion:

You can find any book on mathematical physics and take a look at the section "Orthogonal Surface Coordinate Systems", which contains the Rasley operator that elaborates on n-dimensional spaces.