What kind of sphere?

If you look at your environment, it may seem like you live in a flat flight. After all, that’s why you wander about a new city using a map: a piece of glossy paper that symbolizes all places around you. This is probably why some people in the past believed that the earth would be flat. But many people now know that that is far away from the truth.

He lives in the face of a large space, such as the beach ball size of the world with fewer bumps. The surface of the sphere and the plane is two 2D spaces, meaning you can travel in two ways: north of south or east and west.

What other spaces can you live in? That is, what other spaces are surrounding 2D? For example, the largest donut is another 2D area.

For the Geometric Topology, mathematics such studies study all posts that can occur in all measurements. Even if you try to design safe networks of sensor, mining data or used Origami to include satellites, a basic language may be toopology.

Shape of space

If you look at the universe you live in, it looks like a 3D space, just as the surface looks like a 2D space. However, like the earth, if you’ve been looking at the universe, it can be a more complex space, such as a large 3D version of a 2d beach area or something more extraordinary.

While you do not need toopology to decide that you are living in something like big beach ball, you know all 2D potential posts can be helpful. For more than 100 years ago, Mathematic discovered all 2D posts that can occur and many of them.

In the last few decades, statistics have learned much about all 3D gaps. While we do not have a full understanding of us in making 2D spaces, we know more. With this information, scientists and astronomers can try to find out where 3D people are actually living.

While the answer is completely unknown, there are many wonderful and more wonderful opportunities. Options become more complex if you look at time as a measure.

To see how this can work, be careful that define something in space – Say a comet – you need four numbers: three to describe the position of it and one to describe the time at that time. These four numbers are the ones that make up 4D space.

Now, you can look at what spaces of 4D can also occur in those vacancies.

Toopology with high size

During this time, it may seem that there is no reason to look at the gaps of greater size, because that is the highest undesirable size. But the Physics branch is called the war shows that the universe is more sizes than four.

There is also effective use of the higher higher spaces, such as the Robot Motion Structure. Suppose you are trying to understand the three-foot movements on a factory. You can place the grid down and describe each robot position per x and y they link to the grid. As each of the three robots need two links, you will need six numbers to describe all robot positions. You can translate potentially possible robots as a 6D place.

As the number of robots increases, the size of the space increase. To adjust additional information, such as issues of obstacles, makes space more complex. To read this problem, you need to study the spaces of great size.

There are many scientific problems where high science problems arise, from the model of planets and spacecraft to understand “the formation” of large details.

Tied with knots

Another type of problems for studying the topologists is one way that can live within one another.

For example, if you catch the knotted loop of the rope, then we have 1D space (loop of the rope) within 3D space (your room). Such loops are called mathematics.

Studying knots first grow without physics but it has become a place between topology. They are important how many scientists understand 3D and 4D spaces and have a happy and tendency for researchers who are trying to understand.

In addition, knots have many requests, from string theory in physics to physics to DNA repetition of Biology in chemistry.

What do you live?

GOOMETRIC TOPOLOGY is a good and complicated story, and there are still exciting questions to respond.

For example, Smooth 4D Poincaré is a blockor of the 4d “simple” space, as well as the Slice-Ribbon Colocture aims to understand how Knots relate to 4D spaces.

Topology is currently useful in science and engineering. Displaying a lot of mysteries of spaces in all measurements will best understand the world’s environmental problems.

John Etnyre, Professor of Mathematics, Georgia Institute of Technology

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