Extension:
In the related branches of geometry, topology and mathematics, a point in space is used to describe a special object in a given space, where there are similar volumes, areas, lengths or other high-dimensional analogues. Points are zero-dimensional objects.
As the simplest geometric concept, point is usually the most basic component in geometry, physics, vector graphics and other fields. Points form lines, lines form surfaces, and points are the most basic components in geometry.
A point can also be regarded as a two-dimensional infinitesimal area, a three-dimensional infinitesimal volume and so on.
A point in a point set topology is defined as an element of a set in a topological space.
Although the point is regarded as a basic concept in major geometry and topology, some geometry and topology theories do not need the concept of the point. Such as noncommutative geometry and non-point set topology. Non-point space is not defined as a set, but through a structure (algebraic or logical) similar to geometric function space: continuous function algebra or set algebra.
In Euclidean geometry, a point is a figure with only position but no size in space. Point is the basis of the whole Euclidean geometry, which is the science of studying points, lines, surfaces and bodies.
Euclid initially vaguely defined a point as "something without parts". In two-dimensional Euclidean space, points are represented as ordered pairs, in which the first number customarily represents the horizontal position, usually X, and the second number customarily represents the vertical position, usually Y. ..
This idea can be easily extended to the three-dimensional case, when a point is represented as an ordered triple, and the third number represents the depth, usually Z. More generally, a point is represented as an ordered n-tuple, where n is the dimension of the space where the point is located.