只需以 description 节点为基点做平移即可

\documentclass{book}

\usepackage[explicit]{titlesec}

\usepackage[margin = 2cm]{geometry}
\usepackage{enumitem}
\usepackage{tikz}


\usepackage{graphbox} % provide align = c 

\makeatletter
\def\@chapter@description{}
\def\@chapter@objectives{}
\titleformat{name = \chapter}{}{}{0em}
{%
  \begin{tikzpicture}[remember picture, overlay, every node/.style={inner sep = 0pt, outer sep = 0pt}]
    \node[anchor = north west] at ([shift = {(2cm, -2cm)}]current page.north west) {\includegraphics[width = .2\textwidth, height = \textheight]{example-image}};
    \fill[gray!40] ([shift = {(2cm + .2\textwidth, -2.5cm)}]current page.north west) rectangle ++ (.8\textwidth, -4cm);
    \node[anchor = south west, inner sep = 10pt, scale = 2, font = \bfseries] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {#1};
    \fill[gray!70] ([shift = {(-2, -2.5)}]current page.north east) rectangle ++ (-1.5, -4);
    \node[rotate = 90, font=\bfseries\Large]  at ([shift = {(-2.75, -4.5)}]current page.north east) {\chaptername\ \thechapter};
    \node[anchor = north west, inner sep = 10pt] (description) at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@description
      \end{minipage}
    };
    \fill[shading=radial, left color=startcolor, right color=stopcolor] ([shift = {(1, -.5cm)}]description.south west) rectangle ++ (.7\textwidth, -0.8cm);
    \node[anchor = west, inner sep = 10pt, scale = 1, font = \bfseries] at ([shift = {(1, -.9cm)}]description.south west) {Objectives};
    \node[anchor = north west, inner sep = 10pt] at ([shift = {(1, -1.9cm)}]description.south west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@objectives
      \end{minipage}
    };
  \end{tikzpicture}
}
\newcommand{\icon}[1]{\includegraphics[height=1em, align = c]{#1}}
\NewDocumentEnvironment{fancychapter}{m+m+b}{%
  \def\@chapter@objectives{#3}
  \def\@chapter@description{#2}
  \chapter{#1}
  \newpage
}{}
\makeatother

\usetikzlibrary{calc, intersections}
\begin{document}
\setlist[itemize]{noitemsep, leftmargin=*, label=}
% 定义渐变色
\definecolor{startcolor}{RGB}{128,128,128} % 起始颜色为黑色
\definecolor{stopcolor}{RGB}{245,245,245} % 结束颜色为白色
\begin{fancychapter}{Introduction \LaTeX}{
    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.

    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.
    
    The principles of object-oriented programming, such asmodularity and reusability, are quite popular as they helpin reducing the complexity of programs. In order toimplement such principles in real world applications, suchas library management and nventory management, youneed to make use of an object-oriented language, such asJava.

    This chapter focuses on the fundamentals and buildingblocks of the Java programming language. In addition, itexplains how to access the class members.
}
{
  \begin{itemize}
  \item \icon{example-image} Some test text.
  \item \icon{example-image} Some test text.
  \item \icon{example-image} Some test text.
  \item\icon{example-image}  Some test text.
\end{itemize}
}
\end{fancychapter}



\end{document}

贴一下代码，看不懂的下面评论吧

\documentclass{book}

\usepackage[explicit]{titlesec}

\usepackage[margin = 2cm]{geometry}

\usepackage{tikz}

\makeatletter
\def\@chapter@description{}
\titleformat{name = \chapter}{}{}{0em}
{%
  \begin{tikzpicture}[remember picture, overlay, every node/.style={inner sep = 0pt, outer sep = 0pt}]
    \node[anchor = north west] at ([shift = {(2cm, -2cm)}]current page.north west) {\includegraphics[width = .2\textwidth, height = \textheight]{example-image-a}};
    \fill[gray!40] ([shift = {(2cm + .2\textwidth, -2.5cm)}]current page.north west) rectangle ++ (.8\textwidth, -4cm);
    \node[anchor = south west, inner sep = 10pt, scale = 2, font = \bfseries] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {#1};
    \fill[gray!70] ([shift = {(-2, -2.5)}]current page.north east) rectangle ++ (-1.5, -4);
    \node[rotate = 90, font=\bfseries\Large] at ([shift = {(-2.75, -4.5)}]current page.north east) {\chaptername\ \thechapter};
    \node[anchor = north west, inner sep = 10pt] at ([shift = {(2cm + .2\textwidth, -6.5cm)}]current page.north west) {
      \begin{minipage}{\dimexpr .8\textwidth - 10pt\relax}
        \parindent=2em
        \@chapter@description
      \end{minipage}
    };
  \end{tikzpicture}
}

\NewDocumentEnvironment{fancychapter}{m+b}{%
  \def\@chapter@description{#2}
  \chapter{#1}
  \newpage
}{}
\makeatother
\begin{document}


\begin{fancychapter}{Introduction \LaTeX}
  \foreach \x in {1, ..., 100} {Some test text. }
  
  \begin{itemize}
    \item Some test text.
    \item Some test text.
    \item Some test text.
    \item Some test text.
  \end{itemize}
\end{fancychapter}

\end{document}

你能提供一个 mwe 吗

可以尝试先画出这些多面体，然后拿表格对齐

你这个没有 mwe 解决不了的

提供 MWE 吧，这样看不出来.

% 定义一个新的背景模板
\defbeamertemplate{background}{overlay}{
    \begin{tikzpicture}[remember picture,overlay]
    \pgfmathtruncatemacro{\colorindex}{mod(\insertframenumber,10)}
    % 设置纯色背景
    \fill[bgcolor] (current page.south west) rectangle (current page.north east);
    % 计算要绘制圆角矩形的位置
    \coordinate (SW) at ($(current page.south west) + (0.275cm,0.275cm)$);
    \coordinate (NE) at ($(current page.north east) + (-0.275cm,-0.275cm)$);
    % 添加一个圆角矩形
    \filldraw[fill=incolor\colorindex, rounded corners=0.64cm, draw=bdcolor, line width=0.6pt]
    (SW) rectangle (NE);
\end{tikzpicture}
}

\mode<beamer>{%
\setbeamertemplate{background}[overlay]
}

article.cls 中

\DeclareOption{a4paper}
{\setlength\paperheight{297mm}%
\setlength\paperwidth{210mm}%
}

可以通过判断 \paperwidth 和 \paperheight

'恢复回来'，其实并不是一个好的解决办法，毕竟没有人知道你原来是什么样的格式. 在 \LaTeX 中有 分组(group) 这个概念，在分组内做一些操作不会对分组外的内容有影响(前提是你没有用 \global)，请看如下场景

\centering
first paragraph ...

second paragraph ...

那么 第一段第二段都会具有 \centering 居中效果，如果是

{\centering
first paragraph ...}

second paragraph ...

只是第一段居中，第二段按原来的方式正常显示，不受 \centering 的影响. 这里的 {...} 用花括号包裹的代码块其实就是一个分组，能够有效的避免后面的内容也受到影响.

首先是你的提问不是很规范，建议熟悉 md 语法，代码使用
```tex
LaTeX
...
```

包裹.

接下来说说问题，在 TeX 中 "<number> 表示 16 进制, 也即是 "3900 转换为 10 进制是 14592

可以更改你的代码为

\foreach \y in {3900,3901,...,4000}{\char "\y \quad}

请提供MWE, 我这边没有问题

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\section{$\bar{s},\underline{aa}$}
\subsection{$r_1>\bar{\mu}_1$and$r_2<\underline{\mu}_2$}
\subsection{The worst case prior in $[\underline{\mu}, \bar{\mu}] \times[\underline{\sigma}, \bar{\sigma}]$}
\end{document}

texlive2023 + PDFLaTeX

帮你召唤一下大佬哈哈哈@u10307

tikz实现

\documentclass[margin=1cm]{standalone}
\usepackage{tikz,ctex}

\begin{document}

\begin{tikzpicture}[x = 1cm,y = .5cm]
    \tikzset{circle/.pic = {
        \draw[] (0,0)circle (2pt);
    },
    triangle/.pic = {
        \draw[] (90:2pt) -- (210:2pt) -- (-30:2pt) -- cycle;
    }
    }


    \foreach \y[count = \x] in {
        0.9, 0.9, 1.5, 2.1,
        2.1, 2.5, 2.7, 2.5,
        2.8, 2.1, 1.6, 1.8
    }{
        \coordinate (m-\x) at (\x,\y);
        \pic at (\x,\y) {circle};
        \node[above = 2pt, scale = .75] at (\x,\y) {\y};
    }


    \foreach \y[count = \x] in {
        0.4, 0.6, 0.0, 0.4,
       -0.2, 0.0, 0.5,-0.1,
        0.3, 0.1,-0.2, 0.0
    }{
        \coordinate (n-\x) at (\x,\y);
        \pic at (\x,\y) {triangle};
        \node[below = 2pt, scale = .75] at (\x,\y) {\y};
    }

    \foreach \x[evaluate=\x as \y using \x+1] in {1,2,...,11} {
        \draw[] (m-\x) -- (m-\y);
        \draw[] (n-\x) -- (n-\y);
    }

    \draw[] (0.5,-3) rectangle (12.5,6);

    \foreach \x[count = \xc] in {{1月},{2月},{3月},{4月},{5月},{6月},{7月},{8月},{9月},{10月},{11月},{12月}} {
        \node[below,scale = .75] at (\xc, -3) {\x};
        \draw[] (\xc + .5,-3) --++ (0,.2);
    }

    \foreach \y in {-3.0,0.0,3.0,6.0} {
        \draw[] (0.5,\y)node[left, scale = .75]{\y} --++ (.1,0);
    }

    \node[scale = .75] at (6.5,6.5) {2022年居民消费价格月度涨跌幅度};

    \node[scale = .75] at (0.5,6.5) {\%};

    \node[anchor = north west] at (0.5,6.0) {
        \tikz {
            \draw[] (0,0) -- (1,0);
            \pic at (.5,0) {circle};
            \node[anchor = west, scale = .75] at (1.1,0) {月度同比};
            \draw[] (2.5,0) -- (3.5,0);
            \pic at (3,0) {circle};
            \node[anchor = west, scale = .75] at (3.6,0) {月度环比};
        }
    };
\end{tikzpicture}
\end{document}

texdoc texdef

example

latexdef -c book -s mainmatter

你可以使用

\def\sab#1{%
\expandafter\ifcase\csname c@#1\endcsname%
  \or 甲%
  \or 乙%
  \or 丙%
  \or 丁%
  \or 戊%
  \or 己%
  \or 庚%
  \or 辛%
  \or 壬%
  \or 癸%
\fi%
}

定义一种计数器(\sab) Stems-and-Branches(天干地支), 然后修改 \thefigure

\def\thefigure{\sab{figure}}

源码如下：

\documentclass{ctexart}
\usepackage{caption}
% Stems-and-Branches

\def\sab#1{%
\expandafter\ifcase\csname c@#1\endcsname%
  \or 甲\or 乙\or 丙\or 丁\or 戊\or 己\or 庚\or 辛\or 壬\or 癸
\fi%
}
\def\thefigure{\sab{figure}}
\usepackage{graphicx}
\begin{document}
\begin{figure}
    \centering
    \includegraphics[width = 5cm]{example-image}
    \caption{this is a picture.}\label{fig:a}
\end{figure}
\begin{center}
    \includegraphics[width = 5cm]{example-image-a}
    \captionof{figure}{this is a fig.}\label{fig:b}
\end{center}

\verb|hahahhahahha and this is \ref{fig:a} and \ref{fig:b}| $==>$

hahahhahahha and this is \ref{fig:a} and \ref{fig:b}
\end{document}

• 下次提问希望能够尽可能提供最小工作示例
• 楼上用了 LaTeX3 我就用 TeX 吧(