> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/advanced-math/algebra-geometry.md).

# 代数与平面几何

### 方程

* **一元一次方程** ax + b = 0，解 x = -b / a（a ≠ 0）
* **二元一次方程组**：代入消元或加减消元

```cpp
// 解 ax + by = c, dx + ey = f
double det = a * e - b * d;
double x = (c * e - b * f) / det;
double y = (a * f - c * d) / det;
```

### 平面几何基础

| 图形  | 公式                     |
| --- | ---------------------- |
| 长方形 | 面积 = 长 × 宽，周长 = 2(长+宽) |
| 三角形 | 面积 = 底 × 高 / 2         |
| 圆   | 面积 = πr²，周长 = 2πr      |

### 两点距离

d = sqrt((x1-x2)² + (y1-y2)²)

```cpp
double dist(double x1, double y1, double x2, double y2) {
    return sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
}
```

### 计算几何常用

* 向量叉积判断方向 / 求面积
* 判断三点共线、点在多边形内
* 注意浮点误差，用 eps = 1e-9 比较


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