In the same plane, 1 can be drawn by drawing the perpendicular of a known straight line at a point, and the relevant contents are as follows:

Simple concept of 1. plane

Geometry originated from the field survey in ancient Egypt, and related mathematical concepts such as figures (such as triangles and quadrangles) and areas are needed in the survey. It can be inferred that the ancient Egyptians had an intuitive understanding of the geometric "surface".

Surface is a key step to transition to "plane". However, limited by the times, the ancient Egyptians did not do more, so the key step was to take a step on the fertile soil of ancient Greece.

The first scholar who abstracted the concept of "plane" was parmenides, a philosopher who lived in the 5th century BC. He divided geometric objects into three categories: straight, curved and mixed. Among them, if a two-dimensional image is a "straight surface" and a straight line can coincide with it in any direction, it is a "plane".

Parmenides and Euclid's definition of "plane" is very simple, which is based on people's intuitive understanding of plane, but there is also a shortcoming: the words are not clear enough to be used for propositional reasoning.

Later mathematicians in ancient Greece (such as Helen) tried to change the definition of Europe, but it also brought other shortcomings-repeated judgment (Leibniz). In the more than 1000 years after Helen, geometry has not developed much, so people naturally talk less about the concept of "plane". This situation did not change until17-18th century.

2. Constructive definition of plane

/kloc-Leibniz, a great mathematician in the 0/7th century, noticed the defects of Euclid's definition of "plane" and the verbosity of Helen's definition (Helen's definition: a plane is a surface with the following properties, which extends to all sides indefinitely, and all straight lines on the plane coincide with it. If two points on a straight line coincide with it, the whole straight line coincides with it at any position).

This definition is completely "constructive", not only concise, but also gives the definition from three-dimensional space, which is a great innovation of plane definition. During this period and the18th century, under the guidance of Leibniz's definition, many mathematicians gave other forms of "constructive definition" of plane.