From eb3caa8b7d115c0b8173f300516fb101e51e1c3c Mon Sep 17 00:00:00 2001 From: hanyujie2002 Date: Sat, 28 Oct 2023 17:20:29 +0800 Subject: [PATCH] zh-cn: init the translation of mathml three famous formula (#16684) Co-authored-by: Jason Ren <40999116+jasonren0403@users.noreply.github.com> Co-authored-by: A1lo --- .../index.md | 121 ++++++++++++++++++ .../xelatex-output.png | Bin 0 -> 37750 bytes 2 files changed, 121 insertions(+) create mode 100644 files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md create mode 100644 files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/xelatex-output.png diff --git a/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md b/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md new file mode 100644 index 00000000000000..03858bb7025826 --- /dev/null +++ b/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md @@ -0,0 +1,121 @@ +--- +title: 三个著名的数学公式 +slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas +--- + +{{LearnSidebar}}{{PreviousMenu("Learn/MathML/First_steps/Tables", "Learn/MathML/First_steps")}} + + + + + + + + + + + + +
前提: + 在尝试本测验之前,你应该已经完成本单元中的所有文章,并且对 HTML 基础知识有所了解(请参阅 HTML 简介)。 +
目标:尝试使用 MathML 并测试你的新技能。
+ +## 一篇数学小文章 + +目标是使用 HTML 和 MathML 重写以下数学文章: + +![通过 XeLaTeX 生成的 PDF 输出的屏幕截图](xelatex-output.png) + +尽管你不需要熟悉 [LaTeX](https://zh.wikipedia.org/wiki/LaTeX),但知道生成它的 LaTeX 源代码可能会对你有帮助: + +```latex +\documentclass{article} + +\usepackage{amsmath} +\usepackage{amssymb} + +\begin{document} + +要解决三次方程 $t^3 + pt + q = 0$(其中实数 $p, q$ 满足 ${4p^3 + 27q^2} > 0$),可以使用卡尔达诺公式: + +\[ + \sqrt[{3}]{ + -\frac{q}{2} + +\sqrt{\frac{q^2}{4} + {\frac{p^{3}}{27}}} + }+ + \sqrt[{3}]{ + -\frac{q}{2} + -\sqrt{\frac{q^2}{4} + {\frac{p^{3}}{27}}} + } +\] + +对于任意 $u_1, \dots, u_n \in \mathbb{C}$ 和 $v_1, \dots, v_n \in \mathbb{C}$,柯西—布尼亚科夫斯基—施瓦茨不等式可以写成如下形式: + +\[ + \left| \sum_{k=1}^n {u_k \bar{v_k}} \right|^2 + \leq + { + \left( \sum_{k=1}^n {|u_k|} \right)^2 + \left( \sum_{k=1}^n {|v_k|} \right)^2 + } +\] + +最后,范德蒙行列式可以使用以下表达式计算: + +\[ + \begin{vmatrix} + 1 & x_1 & x_1^2 & \dots & x_1^{n-1} \\ + 1 & x_2 & x_2^2 & \dots & x_2^{n-1} \\ + 1 & x_3 & x_3^2 & \dots & x_3^{n-1} \\ + \vdots & \vdots & \vdots & \ddots & \vdots \\ + 1 & x_n & x_n^2 & \dots & x_n^{n-1} \\ + \end{vmatrix} + = {\prod_{1 \leq {i,j} \leq n} {(x_i - x_j)}} +\] + +\end{document} +``` + +## 起始点 + +要开始这个测验,你可以使用我们常用的 HTML 模板。默认情况下,它使用 UTF-8 编码,在 `` 和 `` 标签上使用特殊的 Web 字体(具有与 LaTeX 输出类似的界面外观)。目标是将问号 `???` 替换为实际的 MathML 内容。 + +```html + + + + + 三个著名的数学公式 + + + +

+ 要解决三次方程 ???(其中实数 ??? 满足 ???),可以使用卡尔达诺公式:??? +

+ +

+ 对于任意 ??? 和 ???,柯西—布尼亚科夫斯基—施瓦茨不等式可以写成如下形式:??? +

+ +

最后,范德蒙行列式可以使用以下表达式计算:???

+ + +``` + +## 提示和技巧 + +- 首先插入空的 `` 标签,并决定它们是否应该有 `display="block"` 属性。 +- 检查所使用的文本,并找到它们的 [Unicode 字符](https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode)(“−”、“ℂ”、“∑”等)。 +- 分析每个文本部分的语义(变量?运算符?数字?),并确定每个部分应使用的正确的标记元素。 +- 查找高级结构(分数?根号?上下标?矩阵?),并确定每个结构应使用的正确的 MathML 元素。 +- 别忘了使用 `` 对子表达式进行分组。 +- 注意可伸缩和大型运算符! +- 使用 [W3C 验证器](https://validator.w3.org/nu/)检查你的 HTML/MathML 标记中是否有意外的错误。 +- 如果你陷入困境,或感到手动编写 MathML 有多么痛苦,请随时使用[编写 MathML 的工具](/zh-CN/docs/Web/MathML/Authoring)(如 [TeXZilla](https://fred-wang.github.io/TeXZilla/))。 + +{{LearnSidebar}}{{PreviousMenu("Learn/MathML/First_steps/Tables", "Learn/MathML/First_steps")}} diff --git a/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/xelatex-output.png b/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/xelatex-output.png new file mode 100644 index 0000000000000000000000000000000000000000..78515673dc63812bf36fd8935f00116c7c7b7d24 GIT binary patch literal 37750 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