Geometric mathematical meaning, what is geometric meaning

The ancient meaning refers to how much, the year is geometric; Nowadays, it is mostly used in mathematical terminology and a sub-subject in mathematics.

Geometric ideas are the most important class of ideas in mathematics. The development of all branches of mathematics has a tendency towards geometry, that is, the use of geometric viewpoints and thinking methods to improve the mathematical theories. Common theorems are the Pythagorean theorem.

Euler's theorem, Steult's theorem, etc.

Chinese civilization. It may have had the same advanced mathematics as its counterpart, but there are no traces of that era that allow us to confirm this. Perhaps this was partly due to the early Chinese use of primitive paper, rather than the use of clay or stone carvings to record their achievements.

Extended Information: Geometry has a long and rich history. It is extremely closely related to algebra, analysis, number theory, and so on.

Geometric ideas are the most important class of ideas in mathematics. The development of all branches of mathematics has a tendency towards geometry, that is, the use of geometric viewpoints and thinking methods to improve the mathematical theories.

Euclidean geometry.

The axiom essentially describes the geometric properties of flat spaces, and the fifth axiom in particular raises doubts about its correctness. This led to the attention paid to the geometry of its curved space, known as "non-Euclidean geometry". Non-Euclidean geometry includes the most classical geometry topics, such as "spherical geometry" and "Roche geometry".

Wait a minute. On the other hand, in order to bring into the scope of observation those ethereal points at infinity, people began to think about projective geometry. These early non-Euclidean geometries.

In general, it is the study of non-metric properties, i.e., those that have little to do with metrics, but only focus on the position of geometric objects - such as parallelism, intersection, and so on. The spatial background studied by these types of geometry is curved space.

Thursday, 17 November, 2022.

1. Watch the online live class midterm exam essay section and complete the composition:

The historical figures in the texts in Unit 4 and the recently read "Journey to the West" show the ups and downs on the road to growth, but also highlight the brilliance and personality strength of ideals, which may trigger your memories of some undone past events and inspire you with the meaning of life in different aspects.

Please choose one of the following protagonists and write him a letter of 500 words:

1) A person has great or small abilities, but as long as he has this spirit, he is a noble person, a pure person, a moral person, a person who is free from low tastes, and a person who is beneficial to the people.

2) The war did not disturb his life. This shepherd has been planting trees. Oak trees, beech trees, and birch trees.

3) The walker said: "You monster, how do you know" "one day as a teacher, a lifetime as a father" and "father and son have no enmity between each other"! You hurt my master, why don't I come to him? ”p230

Geometric significance.

1. What is the meaning of the nature from the image?

2. For example, the derivative itself is a function, and its geometric meaning is the slope of the tangent of a point in the image.

3. It is an abstract geometric figure and geometric language such as algebraic formulas, equations, functions, etc.

Being able to convert geometry problems into algebraic problems, this game is quite fun, you can try it. This should be visible, so let's see for yourself.

Geometry is the clear and bright figure, and the figure is the plane figure composed of line segments, such as three envy side angles, quadrilaterals, pentagons, etc. Solid geometry, on the other hand, is a three-dimensional figure composed of planes or line segments.

Geometry includes four main traditional geometry disciplines: plane and solid geometry, differential geometry, intrinsic geometry, and topology.

In addition to the above-mentioned disciplines, there are also those established by Minkowski"The geometry of the number";A new discipline closely related to modern physics"Tropical geometry";Dimensionality theory"Fractal geometry";And there is"Convex geometry"、"Combined geometry"、"Calculate geometry"、"Arrange the geometry"、"Intuitive geometry"Wait.

Hello, it is an honor to serve you, the following are my answers to your questions, I hope it will be helpful to you! 1. It is a discipline that studies the structure and nature of space. 2. For example, three hail rent angles, socks lack squares, circles, parallelograms, cuboids, cubes, etc., these are all geometric

1. What is geometry?

Geometry is a discipline that studies the structure and properties of space. It is one of the most basic research contents in mathematics, and it is as important as analysis, algebra, etc., and is extremely closely related. Originated in ancient Egypt.

In high school mathematics, the main research is solid geometry and plane analytic geometry.

Solid geometry is the study of the structure and relationship of points, lines, and surfaces in space. Plane analytic geometry is mainly the study of geometric problems using algebraic methods.

2. What is a geometric representation?

Geometric representation is the representation of abstract problems in algebra with geometric figures.

For example, any real number has a one-to-one correspondence with a point on the number line, so the two expressions "real number a" and "point a on the number line" are often regarded as having the same meaning without distinction (Mathematical Analysis, East China Normal University, 2nd Edition, p. 2).

In high school, algebra is usually associated with geometry through the plane Cartesian coordinate system, which is consistent with what we call the idea of combining numbers and shapes.

For example, find the minimum value of the function y= [(x-2) 2+1]+ x+2) 2+4]. We can convert this to find the minimum value of the sum of distances from points (x,0) to points (2,1) and (-2,2) on the x-axis.

Then: y=|ac|+|ab|。As the point c with respect to the x-axis of the symmetry point c', then |ac|=|ac’|, so y=|ab|+|ac’|, connecting BC', then a, b, and c' form a triangle (or on a line), and the sum of the two sides of the triangle is greater than the third side, we can know |ab|+|ac’|>=|bc’|, if and only if a,b,c' is in a straight line (i.e., when a and d coincide) y reaches a minimum value, then the minimum value is the length of the line segment bc'.

The minimum value can then be found.

Another example: find the number of solutions when lgx=cosx.

It can be converted to the number of points where y=lgx and y=cosx intersect two function images. Just look at how many intersections there are in (0,10).

3. Commonly used geometric representations:

In high school, several commonly used geometric representations are as follows, through the following ways, complex and abstract problems are transformed into simple and intuitive geometric problems, so as to solve problems well.

1. Functions or equations can be represented by images, which are often used to solve or the number of intersection points, and to judge the value range and maximum value of the function definition domain or equation;

2. Problems used in linear programming (or nonlinear programming) to find the optimal solution;

3. It is used for geometric generalizations to find the probability of events;

4. Algebraic problems and geometric problems are transformed into each other, so as to simplify the problems, etc.

Geometric meaning is elaborated from a graphic point of view, that is, it can be described graphically.

Geometry (Ancient Greek: also known as geometry. It is a basic branch of mathematics that mainly studies the relationship between spatial regions such as shape, size, and the relative position of figures, as well as the measurement of spatial forms.

Geometry has developed in many cultures, including much about length, area, and volume, and in the time of Thales in the sixth century BC, the Western world began to consider geometry as part of mathematics. In the third century BC, Euclid's axioms were added to geometry, and the resulting Euclidean geometry was the standard of geometry for the following centuries [1]. Archimedes developed methods for calculating area and volume, many of which used the concept of integrals.

In astronomy, the relative positions of stars and planets on the celestial sphere, and their relative motions, were the subject of the next 1,500 years. Geometry and astronomy are listed among the four arts in Western liberal arts education, and were one of the contents taught in Western universities in the Middle Ages.

René Descartes's invention of the coordinate system and the development of epochs led to a new phase in geometry, where geometric shapes such as plane curves could be represented analytically by functions or equations. This had an important influence on the introduction of calculus in the 17th century. The theory of perspective projection has led to the idea that geometry is not just a measure of the properties of objects, and that perspective projection later derived projective geometry.

Euler and Gauss began to study the ontological properties of geometric objects, which further expanded the subject of geometry, and finally gave rise to topology and differential geometry.

In Euclid's time, there was no clear distinction between physical and geometric space, but since the discovery of non-Euclidean geometry in the nineteenth century, the concept of space has been greatly adjusted, and the question of which geometric space is most suitable for real space has also begun to arise. After the rise of formal mathematics in the twentieth century, space (including points, lines, and planes) no longer had its intuitive concept. Today it is necessary to distinguish between physical space, geometric space (where points, lines, and surfaces do not yet have an intuitive concept), and abstract space.

Contemporary geometry considers manifolds, and the concept of space is more abstract than Euclid's, and the two are approximate to each other only at very small sizes. These spaces can be joined with additional structure, so their length can be considered. Modern geometry and physics are closely related, just as pseudo-Riemannian manifolds are to general relativity.

The youngest string theory in physical theory is also closely related to geometry.

The visible properties of geometry make it more accessible than mathematical fields such as algebra and number theory, but some geometric languages have become more and more distant from the traditional definition of Euclidean geometry, such as fragmentary geometry and analytic geometry [2].

Geometry in modern concepts has greatly increased in its degree of abstraction and generalization, and is closely integrated with analysis, abstract algebra and topology.

Geometry is used in many fields, including art, architecture, physics, and other fields of mathematics.