Geometry编辑历史

# Overview

Geometry is a branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. Originating in ancient civilizations for land measurement and construction, geometry has evolved into a formal deductive system, with Euclidean geometry as its classical foundation. Modern geometry extends into non-Euclidean and abstract spaces, playing a fundamental role in fields such as physics, engineering, computer graphics, and topology.

# 1 Fundamentals of Geometry

## 1.1 Basic Primitives

### 1.1.1 Points and Lines
A point is a fundamental object in geometry, representing a specific location in space with no dimension (length, width, or height). It is typically denoted by a dot and labeled with a capital letter. A line is a straight, one-dimensional set of points extending infinitely in both directions. It has no thickness and is the shortest path between any two points. In Euclidean geometry, a line is defined by two distinct points.

### 1.1.2 Planes and Space
A plane is a two-dimensional flat surface that extends infinitely in all directions. It contains an infinite number of points and lines. Space, in geometry, refers to three-dimensional (or higher-dimensional) environments where points, lines, and planes interact. In Euclidean space, three dimensions are defined by length, width, and height.

## 1.2 Angles and Measurement

### 1.2.1 Types of Angles
An angle is formed by two rays sharing a common endpoint called the vertex. Angles are classified by their measure in degrees or radians: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (180°), reflex (between 180° and 360°), and full rotation (360°).

### 1.2.2 Angle Relationships
Angles can be related through their positions and measures. Complementary angles sum to 90°, supplementary angles sum to 180°, adjacent angles share a vertex and a side, and vertical angles are formed by intersecting lines and