Introduction to measurement:
Metric, also called distance function, a mathematical concept, is a special function that meets certain conditions in metric space, which is generally expressed by D. Metric space, also called distance space, is a special topological space. Fréchet abstracted the concept of distance in Euclidean space and defined the metric space in 1906.
Put forward the following points:
The most basic and important abstract space in modern mathematics is closest to Euclidean space. At the end of 19, the German mathematician G Cantor founded the set theory, which laid the foundation for the establishment of various abstract spaces. At the beginning of the 20th century, French mathematician M.R. Fréchet found that many analysis results, from a more abstract point of view, all involved the distance relationship between functions, thus abstracting the concept of metric space.
Three-dimensional Euclidean space is most consistent with our intuitive understanding of reality. Euclidean metric in this space defines the distance between two points as the length of the line segment connecting the two points.
Its nature is as follows:
D(x, y) is the distance between x and y, and compactness, countable compactness, sequence compactness and subset compactness are consistent in metric space. Separability, genetic separability, second countability are consistent with Lindelof. Metric space must satisfy the first countable axiom, namely Hausdorff space, completely normal space and paracompact space. Pseudometric spaces satisfy the first countable axiom, but they are generally not Hausdorff spaces.
Angle introduction:
In geometry, it is a geometric object composed of two rays with a common endpoint. These two rays are called the edges of an angle, and their common endpoint is called the vertex of the angle. The general angle is assumed to be in Euclidean plane, but it can also be defined in Euclidean geometry. Angle is widely used in geometry and trigonometry.
Euclid, the father of geometry, once defined an angle as the relative inclination of two non-parallel straight lines in a plane. Proclos thinks that angle may be a trait, a quantifiable quantity, or a relationship. Oldham thinks that an angle is a deviation from a straight line, and Cabus of Antioch thinks that an angle is a space between two intersecting straight lines. Euclid thinks that an angle is a relationship, but its definitions of right angle, acute angle and obtuse angle are quantitative.