用数学符号写入对齐环境

Question

我尝试多次编写此文本，但发现错误missing $。您能帮我编写此文本吗？

C & = n L \nonumber \\
     & = n 2 R \sin(\phi/n) \nonumber \\ \intertext{As :} \nonumber \\
   \phi & = 2\pi/n \nonumber \\ \intertext{Thus :} \nonumber \\
   C & = 2 n R \sin(\pi/n) \\ \intertext{If n\mapsto\infty (It's mean a polygon with infinite sides) we find :} \nonumber \\
   C_{\infty} & = 2R \lim_{n\to \infty} n\sin(\phi/n) \nonumber \\ \intertext{Thus :} \nonumber \\
   C_{\infty} & = 2\pi R \nonumber

Answer 1

您需要使用数学模式进行内部数学运算\intertext。这样的行既不需要也不\nonumber需要\\。

更适合用于\shortintertext短线。

\documentclass[a4paper]{article}
\usepackage{amsmath,mathtools}

\begin{document}

\begin{align}
         C & = n L \nonumber \\
           & = n 2 R \sin(\phi/n) \nonumber \\
\shortintertext{As:}
      \phi & = 2\pi/n \nonumber \\
\shortintertext{Thus:}
         C & = 2 n R \sin(\pi/n) \\
\intertext{If $n\to\infty$ (meaning a polygon with infinite sides) we find:}
C_{\infty} & = 2R \lim_{n\to \infty} n\sin(\phi/n) \nonumber \\
\shortintertext{Thus:}
C_{\infty} & = 2\pi R \nonumber
\end{align}

\end{document}

计算有误，可能应该\sin{\phi/2)在第二行。\phi极限中的 应该是\pi。

另一方面，没有必要对齐所有内容，某些内容应该内联而不是显示。

\documentclass[a4paper]{article}
\usepackage{amsmath,mathtools}

\begin{document}

\begin{align*}
  C & = n L\\
    & = n\, 2 R \sin(\phi/2)
\end{align*}
As $\phi = 2\pi/n$, we have
\begin{equation}
  C = 2 n R \sin(\pi/n)
\end{equation}
If $n\to\infty$ (meaning a polygon with infinitely many sides) we find
\begin{equation*}
C_{\infty} = 2R \lim_{n\to \infty} n\sin(\pi/n)
\end{equation*}
and therefore
\begin{equation*}
C_{\infty} = 2\pi R
\end{equation*}

\end{document}