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# 括號與圓括號

## 簡介

括號和中括號在數學公式中非常常見。你可以很容易地在 LaTeX 中控制括號的大小和樣式；本文將說明方法。

以下是一個列出 LaTeX 中一些常見數學括號和括弧的表格：

| 類型      | LaTeX 標記              | 顯示為                        |
| ------- | --------------------- | -------------------------- |
| 括號；圓括號  | `(x+y)`               | $$(x+y)$$                  |
| 中括號；方括號 | `[x+y]`               | $$\[x+y]$$                 |
| 大括號；花括號 | `\{ x+y \}`           | $${ x+y }$$                |
| 尖括號     | `\langle x+y \rangle` | $$\langle x+y\rangle$$     |
| 豎線；垂直線  | `\|x+y\|`             | $$\displaystyle\| x+y \|$$ |
| 雙豎線     | \`\\                  | x+y\\                      |

## 一些範例

括號的大小可以手動設定，也可以在文件中動態調整，如下一個範例所示：

```latex
\[
F = G \left( \frac{m_1 m_2}{r^2} \right)
\]
```

[在 Overleaf 中開啟此 LaTeX 片段](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+1\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B+%0AF+%3D+G+%5Cleft%28+%5Cfrac%7Bm_1+m_2%7D%7Br%5E2%7D+%5Cright%29%0A%5C%5D%0A%5Cend%7Bdocument%7D)

上述範例會產生以下輸出：

$$F = G \left( \frac{m\_1 m\_2}{r^2} \right)$$ 請注意，要插入括號或中括號， `\left` 以及 `\right` 命令會被使用。即使你只使用一個括號， *兩個* 命令都是必要的。 `\left` 以及 `\right` 可以動態調整大小，如下一個範例所示：

```latex
\[
 \left[  \frac{ N } { \left( \frac{L}{p} \right)  - (m+n) }  \right]
\]
```

[在 Overleaf 中開啟此 LaTeX 片段](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+2\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B+%0A+%5Cleft%5B++%5Cfrac%7B+N+%7D+%7B+%5Cleft%28+%5Cfrac%7BL%7D%7Bp%7D+%5Cright%29++-+%28m%2Bn%29+%7D++%5Cright%5D%0A%5C%5D%0A%5Cend%7Bdocument%7D)

上述範例會產生以下輸出：

$$\left\[ \frac{ N } { \left( \frac{L}{p} \right) - (m+n) } \right]$$

在撰寫多行方程式時，使用 `align`, `align*` 或 `aligned` 環境時， `\left` 以及 `\right` 命令必須平衡 *於每一行的同一側 `&`*。因此，以下程式碼片段會產生錯誤：

```latex
\begin{align*}
y  = 1 + & \left(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \ldots  \\
  & \quad  + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)
\end{align*}
```

[在 Overleaf 中開啟此 LaTeX 片段（含錯誤）](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+with+errors\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0Ay++%3D+1+%2B+%26+%5Cleft%28++%5Cfrac%7B1%7D%7Bx%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E2%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E3%7D+%2B+%5Cldots++%5C%5C%0A++%26+%5Cquad++%2B+%5Cfrac%7B1%7D%7Bx%5E%7Bn-1%7D%7D+%2B+%5Cfrac%7B1%7D%7Bx%5En%7D+%5Cright%29%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D)

解法是使用「隱形」括號來平衡，也就是在第一行末尾加上一個 `\right.` ，並在 `\left.` 第二行開頭加上一個 `&`:

```latex
\begin{align*}
y  = 1 + & \left(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \ldots \right. \\
  &\left. \quad + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)
\end{align*}
```

[在 Overleaf 中開啟此 LaTeX 片段](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+4\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0Ay++%3D+1+%2B+%26+%5Cleft%28++%5Cfrac%7B1%7D%7Bx%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E2%7D+%2B+%5Cfrac%7B1%7D%7Bx%5E3%7D+%2B+%5Cldots+%5Cright.+%5C%5C%0A++%26%5Cleft.+%5Cquad+%2B+%5Cfrac%7B1%7D%7Bx%5E%7Bn-1%7D%7D+%2B+%5Cfrac%7B1%7D%7Bx%5En%7D+%5Cright%29%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D)

上述範例會產生以下輸出：

![Paren-ex03.png](/files/eea9b423c64250de04cfcb11c2784536f0f3496b)

## 控制類型與大小

括號的大小可以明確控制，如下列 LaTeX 程式片段所示：

```latex
\[
 \Biggl \langle 3x+7 \biggr \rangle
\]
```

[在 Overleaf 中開啟此 LaTeX 片段](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=brackets+and+parentheses+example+5\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0A%5C%5B%0A+%5CBiggl+%5Clangle+3x%2B7+%5Cbiggr+%5Crangle%0A%5C%5D%0A%5Cend%7Bdocument%7D)

上述範例會產生以下輸出：

$$\Biggl \langle 3x+7 \biggr \rangle$$

這些 `\Biggl` 以及 `\biggr` 命令可分別設定定界符的大小 `<` 以及 `>` ，搭配 `l` 或 `r` 表示它是左括號還是右括號。有關括號與大小的完整清單，請參見 [參考指南](#reference-guide).

## 參考指南

| LaTeX 標記                                                    | 顯示為                                                       |
| ----------------------------------------------------------- | --------------------------------------------------------- |
| `\bigl( \Bigl( \biggl( \Biggl(`                             | $$\big( \Big( \bigg( \Bigg($$                             |
| `\bigr] \Bigr] \biggr] \Biggr]`                             | $$\big] \Big] \bigg] \Bigg]$$                             |
| `\bigl\{ \Bigl\{ \biggl\{ \Biggl\{`                         | $$\big{ \Big{ \bigg{ \Bigg{$$                             |
| `\bigl \langle \Bigl \langle \biggl \langle \Biggl \langle` | $$\big \langle \Big \langle \bigg \langle \Bigg \langle$$ |
| `\bigr \rangle \Bigr \rangle \biggr \rangle \Biggr \rangle` | $$\big \rangle \Big \rangle \bigg \rangle \Bigg \rangle$$ |
| `\big\| \Big\| \bigg\| \Bigg\|`                             | $$\big\| ; \Big\| ; \bigg\| ; \Bigg\|$$                   |
| \`\big\\                                                    | \Big\\                                                    |
| `\bigl \lceil \Bigl \lceil \biggl \lceil \Biggl \lceil`     | $$\big \lceil \Big \lceil \bigg \lceil \Bigg \lceil$$     |
| `\bigr \rceil \Bigr \rceil \biggr \rceil \Biggr \rceil`     | $$\big \rceil \Big \rceil \bigg \rceil \Bigg \rceil$$     |
| `\bigl \lfloor \Bigl \lfloor \biggl \lfloor \Biggl \lfloor` | $$\big \lfloor \Big \lfloor \bigg \lfloor \Bigg \lfloor$$ |
| `\bigr \rfloor \Bigr \rfloor \biggr \rfloor \Biggr \rfloor` | $$\big \rfloor \Big \rfloor \bigg \rfloor \Bigg \rfloor$$ |

## 延伸閱讀

* [數學表達式](/latex/zh-tw/shu-xue/01-mathematical-expressions.md)
* [下標與上標](/latex/zh-tw/shu-xue/02-subscripts-and-superscripts.md)
* [使用 amsmath 對齊方程式](/latex/zh-tw/shu-xue/06-aligning-equations-with-amsmath.md)
* [數學模式中的顯示樣式](/latex/zh-tw/shu-xue/10-display-style-in-math-mode.md)
* [運算子](/latex/zh-tw/shu-xue/07-operators.md)
* [LaTeX2ε 的不算太短的入門介紹](http://www.ctan.org/tex-archive/info/lshort/)


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