feat: add mathematical formulas example article and update categories for existing blog posts

Author: EveSunMaple

docs/CHANGELOG.md

@@ -905,4 +905,14 @@
 ### Fix
 
 - 修复了分类页面中展开动画的样式
-- 修复了分类页面中 `post` 缺失的过渡效果
+- 修复了分类页面中 `post` 缺失的过渡效果
+
+## [3.1.4] - 2025-5-31
+
+### Chore
+
+- 新增一篇数学公式示例文章
+
+### Fix
+
+- 修复了数学公式的渲染问题（先前缺少了必要的 CSS 文件）

package.json

@@ -28,6 +28,7 @@
     "dayjs": "^1.11.13",
     "dotenv": "^16.5.0",
     "js-yaml": "^4.1.0",
+    "katex": "^0.16.22",
     "marked": "^14.1.4",
     "mdast": "^3.0.0",
     "mdast-util-to-string": "^4.0.0",

pnpm-lock.yaml

@@ -1,5 +1,6 @@
 ---
 import "../styles/global.scss";
+import "/node_modules/katex/dist/katex.min.css";
 import type { HeaderProps } from "@interfaces/data";
 
 const canonicalURL = new URL(Astro.url.pathname, Astro.site);

src/components/Header.astro

@@ -4,7 +4,7 @@ description: A comprehensive guide on how to integrate the Waline comment system
 pubDate: 04 15 2025
 image: /image/image4.jpg
 categories:
-  - tech
+  - Documentation
 tags:
   - Frosti
   - Comments

src/content/blog/adding-comment-systems.md

@@ -4,7 +4,8 @@ description: Using MDX in Frosti to enrich article content with more components
 pubDate: 07 12 2024
 image: /image/image2.jpg
 categories:
-  - tech
+  - Documentation
+  - Examples
 tags:
   - Frosti
   - Blog

src/content/blog/frosti-mdx.mdx

@@ -4,7 +4,8 @@ description: "Here is a sample of some basic Markdown syntax that can be used wh
 pubDate: "Jul 01 2024"
 image: /image/image3.png
 categories:
-  - tech
+  - Documentation
+  - Examples
 tags:
   - Makrdown
 badge: Pin

src/content/blog/markdown-style-guide.md

@@ -0,0 +1,102 @@
+---
+title: Testing Mathematical Formulas in Markdown
+description: A demonstration of various mathematical formulas rendered using LaTeX within Markdown.
+pubDate: May 31 2025
+categories:
+  - Documentation
+  - Examples
+tags:
+  - Markdown
+  - LaTeX
+  - Mathematics
+badge: LaTeX
+---
+
+This document serves as a test for rendering mathematical formulas in Markdown using `$$` delimiters.
+
+## Basic Algebra
+
+Let's start with some fundamental algebraic expressions.
+
+The quadratic formula is given by:
+$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
+
+A simple linear equation:
+$$y = mx + c$$
+
+Expansion of a binomial square:
+$$(a+b)^2 = a^2 + 2ab + b^2$$
+
+---
+
+## Calculus
+
+Here are some common expressions from calculus.
+
+The limit definition of a derivative:
+$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$
+
+A definite integral:
+$$\int_{a}^{b} f(x) dx$$
+
+The Taylor series expansion of $e^x$ around $x=0$:
+$$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots$$
+
+---
+
+## Trigonometry
+
+Some basic trigonometric identities.
+
+Pythagorean identity:
+$$\sin^2\theta + \cos^2\theta = 1$$
+
+Angle addition formula for sine:
+$$\sin(\alpha + \beta) = \sin\alpha\cos\beta + \cos\alpha\sin\beta$$
+
+Euler's formula:
+$$e^{i\theta} = \cos\theta + i\sin\theta$$
+
+---
+
+## Statistics and Probability
+
+Formulas commonly used in statistics and probability.
+
+The formula for the mean ($\mu$) of a set of $n$ numbers $x_1, x_2, \ldots, x_n$:
+$$\mu = \frac{1}{n} \sum_{i=1}^{n} x_i$$
+
+The probability density function of a normal distribution:
+$$f(x | \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$
+
+Bayes' theorem:
+$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$
+
+---
+
+## Linear Algebra
+
+Examples from linear algebra.
+
+A 2x2 matrix:
+$$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
+
+The determinant of a 2x2 matrix:
+$$\det(A) = ad - bc$$
+
+Matrix multiplication of two matrices A and B:
+$$C = AB$$
+
+---
+
+## Physics
+
+A couple of well-known physics equations.
+
+Einstein's mass-energy equivalence:
+$$E = mc^2$$
+
+Newton's second law of motion:
+$$F = ma$$
+
+This should provide a good test of how various mathematical formulas are rendered.

src/content/blog/mathematics-examples.md

@@ -4,7 +4,7 @@ description: "Lorem ipsum dolor sit amet"
 pubDate: "Jul 02 2022"
 image: /image/image1.jpg
 categories:
-  - tech
+  - Documentation
 badge: Pin
 ---