From 62de965f9f1025cd72b3380e68c12cd61aeb2c05 Mon Sep 17 00:00:00 2001 From: hanyujie2002 <84226578+hanyujie2002@users.noreply.github.com> Date: Mon, 23 Oct 2023 23:15:53 +0800 Subject: [PATCH 1/9] zh-cn: init localization of mathml three famous formula --- .../index.md | 119 ++++++++++++++++++ 1 file changed, 119 insertions(+) create mode 100644 files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md 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..1c7d84122cc0ac --- /dev/null +++ b/files/zh-cn/learn/mathml/first_steps/three_famous_mathematical_formulas/index.md @@ -0,0 +1,119 @@ +--- +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: + 在尝试本评估之前,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:尝试一下使用 MathML 并测试你的新技能。
+ +## 一篇小型数学文章 + +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(Cardano's formula): + +\[ + \sqrt[{3}]{ + -\frac{q}{2} + +\sqrt{\frac{q^2}{4} + {\frac{p^{3}}{27}}} + }+ + \sqrt[{3}]{ + -\frac{q}{2} + -\sqrt{\frac{q^2}{4} + {\frac{p^{3}}{27}}} + } +\] + +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(Cauchy–Bunyakovsky–Schwarz inequality)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,范德蒙德矩阵(Vandermonde matrix)的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} +``` + +要开始这个评估,你可以使用我们通常的 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 输出类似的外观和感觉)。目标是将问号 `???` 替换为实际的 MathML 内容。 + + + + + + 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(Cardano's formula):??? +

+ +

+ 对于任意 ??? 和 ???,柯西-布尼亚科夫斯基-施瓦茨不等式(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式:??? +

+ +

+ 最后,范德蒙德矩阵(Vandermonde matrix)的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")}} From ce3e0b473453c1d497c9becc12344d571a26ff80 Mon Sep 17 00:00:00 2001 From: Jason Ren <40999116+jasonren0403@users.noreply.github.com> Date: Tue, 24 Oct 2023 10:08:16 +0800 Subject: [PATCH 2/9] solve linter problem --- .../first_steps/three_famous_mathematical_formulas/index.md | 2 ++ 1 file changed, 2 insertions(+) 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 index 1c7d84122cc0ac..0f169386b6e59a 100644 --- 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 @@ -81,6 +81,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas 要开始这个评估,你可以使用我们通常的 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 输出类似的外观和感觉)。目标是将问号 `???` 替换为实际的 MathML 内容。 +```html @@ -104,6 +105,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas

+``` ## 提示和技巧 From 18806fd47c788807e7b542f3e823cb1af9ac34ab Mon Sep 17 00:00:00 2001 From: Jason Ren <40999116+jasonren0403@users.noreply.github.com> Date: Tue, 24 Oct 2023 10:11:24 +0800 Subject: [PATCH 3/9] fixup --- .../first_steps/three_famous_mathematical_formulas/index.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) 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 index 0f169386b6e59a..8f0bbad2396b25 100644 --- 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 @@ -10,7 +10,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas 前提: - 在尝试本评估之前,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)。 @@ -79,6 +79,8 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas \end{document} ``` +## 起始点 + 要开始这个评估,你可以使用我们通常的 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 输出类似的外观和感觉)。目标是将问号 `???` 替换为实际的 MathML 内容。 ```html From 37e782fab730f6aafbb57dd5844d07e9514df2ce Mon Sep 17 00:00:00 2001 From: hanyujie2002 <84226578+hanyujie2002@users.noreply.github.com> Date: Tue, 24 Oct 2023 12:42:32 +0800 Subject: [PATCH 4/9] fix --- .../three_famous_mathematical_formulas/index.md | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) 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 index 8f0bbad2396b25..71a6de3a02b76c 100644 --- 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 @@ -63,7 +63,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas } \] -最后,范德蒙德矩阵(Vandermonde matrix)的行列式可以使用以下表达式计算: +最后,范德蒙行列式可以使用以下表达式计算: \[ \begin{vmatrix} @@ -95,16 +95,17 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas

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

- 对于任意 ??? 和 ???,柯西-布尼亚科夫斯基-施瓦茨不等式(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式:??? + 对于任意 ??? 和 + ???,柯西-布尼亚科夫斯基-施瓦茨不等式(Cauchy–Bunyakovsky–Schwarz + inequality)可以写成如下形式:???

-

- 最后,范德蒙德矩阵(Vandermonde matrix)的行列式可以使用以下表达式计算:??? -

+

最后,范德蒙的行列式可以使用以下表达式计算:???

``` From 9868e711cce6e65e55a0d03c02e2e9b0bcfe07b8 Mon Sep 17 00:00:00 2001 From: hanyujie2002 <84226578+hanyujie2002@users.noreply.github.com> Date: Tue, 24 Oct 2023 12:47:00 +0800 Subject: [PATCH 5/9] fix --- .../first_steps/three_famous_mathematical_formulas/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) 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 index 71a6de3a02b76c..a06585d48bc57a 100644 --- 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 @@ -52,7 +52,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas } \] -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(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式: +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(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式: \[ \left| \sum_{k=1}^n {u_k \bar{v_k}} \right|^2 @@ -101,7 +101,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas

对于任意 ??? 和 - ???,柯西-布尼亚科夫斯基-施瓦茨不等式(Cauchy–Bunyakovsky–Schwarz + ???,柯西—布尼亚科夫斯基—施瓦茨不等式(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式:???

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2023 16:50:52 +0800 Subject: [PATCH 7/9] apply suggestion from code reviewer --- .../index.md | 13 +++++-------- .../xelatex-output.png | Bin 84899 -> 77125 bytes 2 files changed, 5 insertions(+), 8 deletions(-) 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 index a06585d48bc57a..07f3766d83be84 100644 --- 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 @@ -39,7 +39,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas \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(Cardano's formula): +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: \[ \sqrt[{3}]{ @@ -52,7 +52,7 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas } \] -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(Cauchy–Bunyakovsky–Schwarz inequality)可以写成如下形式: +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 @@ -95,17 +95,14 @@ slug: Learn/MathML/First_steps/Three_famous_mathematical_formulas

- 要解决三次方程 ???(其中实数 ??? 满足 - ???),可以使用卡尔达诺公式(Cardano's formula):??? + 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(Cauchy–Bunyakovsky–Schwarz - inequality)可以写成如下形式:??? + 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,范德蒙的行列式可以使用以下表达式计算:???

+

最后,范德蒙行列式可以使用以下表达式计算:???

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