What is a wire harness orthogonal to a parallel harness in non Euclidean geometry?

What is non-Euclidean geometry?

First of all, we must understand Euclidean geometry, the plane geometry we learned in junior high school is actually Euclidean geometry, and those who have read junior high school believe that they understand the relevant knowledge of parallelism, congruence, similarity, etc., as well as the sum of the internal angles of a triangle is equal to 180°.

But in non-Euclidean geometry, some of our previous common sense no longer applies. For example, if there is a triangle on the sphere, what is the sum of its internal angles? (This was discovered by Harriot as early as 1603).

In the figure, the sphere is divided into 3 great circles (the great circle on the ball is a straight line, which will be described in detail later), and the sphere is divided into 8 triangles, each of which is congruent with the triangle of the opposite diameter, and the area is the same. The area of the sphere is 4 r 2, and in the figure t, t1, t2, t3 is the area of the corresponding triangle, , is the angle of the corresponding angle, so it can be derived:

In addition, it can be seen that t and t1 can form a contract, and the area is 2 of the entire sphere. Can get:

Again, it is also possible to get:

2), (3), (4) and the following formulas:

Then subtract equation (1) and we have:

As you can see, t is definitely not 0, so, and t is definitely positive, so there must be.

And it can also be seen from equation (6) that the value of t is related to the sum of , , so on the sphere, the larger the area of the triangle, the greater the sum of its internal angles, that is, there are no similar triangles on the sphere.

See, these situations seem to be completely different from what we have learned and understood before, but these are often encountered in real life.

To deepen the impression, you can do a small experiment on the difference between Euclidean geometry and non-Euclidean geometry, and you can understand Euclidean geometry and non-Euclidean geometry more perceptually

a) Take a flat piece of paper, such as A4 paper or workbook paper, and be sure to have no elastic paper.

b) Take a curved object, such as an apple, a basketball, a rugby, a bowl, etc.

c) Paste the flat paper to the object with curvature to ensure that the flat surface can be in full contact with the curved surface.

You will find that if you want to paste it, the flat paper will definitely have wrinkles, and if there are wrinkles, it means that there is still a part of the surface that is not attached to the curved surface. The geometric relations on flat paper are what we usually learn about Euclidean geometry, and the geometric relations of surfaces such as apples, basketballs, and football are the ones that non-Euclidean geometry focuses on.

Another example that comes across more often is a map, like drawing a straight line on a map (except for the vertical line in the middle of the map), and if you follow this line, you will go a long way.

Will go to the map here, you can lead to what is a straight line, read the above should have a certain understanding of non-Euclidean geometry, the following interested take a look.

What is a straight line? (Skip knowing).

The most basic definition of a straight line is the line with the shortest distance between two points. In the plane (Euclidean geometry) we can easily find that the ruler can be pulled as soon as it is pulled, and there is no ruler in non-Euclidean geometry. In both Euclidean and non-Euclidean geometry, there is a very simple way to find straight lines.

Polygon naming in mathematical geometry is strictly marked clockwise or counterclockwise, so....What is this diagram for you? And why only give a 5 ......?

Geometry is a discipline that studies the structure and properties of space. It is one of the most basic studies in mathematics, and it is the same as analysis, algebraic back, and so on.

The answer is very important, and it is extremely close. The word geometry first comes from the Greek word " by " ?

The words (land) and "surveying" are a combination of the words to refer to the measurement of land, i.e., geodesy. Later it was Latinized as "geometria".

The word "geometry" in Chinese was first coined by Xu Guangqi when Matteo Ricci and Xu Guangqi co-translated the Geometric Originals in the Ming Dynasty. At that time, no basis was given, but later generations believed that on the one hand, geometry may be a transliteration of the Latinized Greek word geo, and on the other hand, because the Geometry Originals also uses geometry to explain the content of number theory, and it may also be a paraphrase of magnitude (how much), so it is generally believed that geometry is a phonetic translation of geometria.

Theoretically, you do, but it doesn't matter if you don't, just look at the spatial structure.

Not only linear algebra and mathematical analysis are basic courses, but there are many other branches in the future, such as probability theory and mathematical statistics, combinatorics, graph theory, abstract algebra, complex variable functions, real variable functions, ordinary differential equations, etc.

What about graphics? Is it giving you graphics or what?

Geometry is divided into planar geometry, solid geometry and analytic geometry, the first two of which require high imagination, drawing and observation skills. Analytic geometry, on the other hand, requires high computational requirements, but sometimes it is necessary to apply knowledge of plane geometry in order to make the calculation simple. In short, learning geometry is as tedious as learning algebra.

What stage of geometry! Middle school words! It's not hard! If you are a math major at university! The hard part to learn is differential geometry in junior year!

Is it difficult? Actually, it's not difficult at all.

Those who are difficult will not, and those who will will not be difficult.

For me, mathematics is not difficult at all, as long as you like mathematics, mathematics will also like you, for example, if you do a problem that others can't do, there is a joy in your heart

It will not be difficult for those who will be, and it will not be difficult if you put your heart into it.

It's not that hard.

It's not hard to learn anything seriously!!

It's not hard to learn by heart, and it's fun;

If you don't have to learn, it's hard, it's just a sin.

Personally, I think it's not difficult to study hard, and this question varies from person to person.

As long as you work hard and your spatial imagination should be OK.

It's not too difficult, it depends on whether you're in elementary school or junior high school.

If there is a way, it is not difficult to be interested.

It's easy to learn in high school and below! I don't know about the university! Didn't go to college!

AB is equal to the root number 5, BC is equal to the root number 20, and AC is equal to 5, according to the Pythagorean theorem, so it is a right angle.

You're right.

The second question is a right triangle.