使用 TikZ 绘制勾股定理的演示

Question

我必须绘制毕达哥拉斯定理的视觉表示。我最初采用的方法是绘制中间的三角形，然后逐步处理正方形。但这似乎需要大量蛮力工作。那么，有没有简单的方法可以做到这一点，从而避免使用蛮力方法？（也许使用一些库）。某种解释或有用的提示就足够了。

Answer 1

这真的只是为了好玩，无法与 Alain Matthes 的出色宏和例程相媲美。然而，让 Ti钾Z 在给定线上方/下方绘制正方形，使得该线成为正方形的一条边。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc,positioning}
\begin{document}
\tikzset{square/.style={minimum size=#1,draw},
measureme/.style={execute at begin to={
\path let \p1=($ (\tikztostart) - (\tikztotarget) $),\n1={veclen(\x1,\y1)}
in \pgfextra{\xdef#1{\n1}};}}}
\begin{tikzpicture}
\draw[measureme=\mylen](0,0) 
to node[midway,sloped,above,square=\mylen,fill=blue!20]{\xdef\mylenC{\mylen}} node[midway,left=3pt]{$c$} (2,4)
to node[midway,sloped,above,square=\mylen,fill=red!20]{\xdef\mylenB{\mylen}} node[midway,right=3pt]{$b$} (2,0) 
to node[midway,sloped,below,square=\mylen,fill=purple!20]{\xdef\mylenA{\mylen}} node[midway,below=3pt]{$a$} (0,0);
\begin{scope}[yshift=-5cm]
 \node[square=\mylenB,fill=red!20](B) {$b^2$};
 \node[left=2pt of B] (plus) {$+$};
 \node[left=2pt of plus,square=\mylenA,fill=purple!20](A) {$a^2$};
 \node[right=2pt of B] (eq) {$=$};
 \node[right=2pt of eq,square=\mylenC,fill=blue!20](C) {$c^2$};
\end{scope}
\end{tikzpicture}
\end{document}

编辑：使节点标签直立，并添加毕达哥拉斯关系。

解释：measureme风格让 Ti钾Z 测量边的长度（并将结果存储在\mylen示例中调用的宏中）。正方形样式生成一个正方形，放置在给定边的中间，使其与边重合。

Answer 2

\documentclass[pstricks,margin=6pt]{standalone}
\begin{document}
\begin{pspicture}[dimen=m,fillstyle=solid](-4,-3)(7,7)
    \psframe[fillcolor=red](3,-3)
    \psframe[fillcolor=green](3,0)(7,4)
    \rput{!4 3 atan}(0,0){\psframe[fillcolor=blue](5,5)}
\end{pspicture}
\end{document}

Answer 3

\input tikz.tex
\input pgfmath.tex

{\vskip 5mm plus 2mm minus 2mm
\leftskip=0mm plus 1fil
\rightskip=0mm plus 1fil
\parindent=0pt
\parfillskip=0pt
\tikzpicture
    \def\xa{0}
    \def\ya{0}

    \def\xb{0}
    \def\yb{3}

    \def\xc{-1}
    \def\yc{0}

    \coordinate (A) at (\xa,\ya);
    \coordinate (B) at (\xb,\yb);
    \coordinate (C) at (\xc,\yc);

    \pgfmathanglebetweenpoints{\pgfpointanchor{A}{center}}{\pgfpointanchor{B}{center}}
    \edef\angleab{\pgfmathresult}

    \pgfmathanglebetweenpoints{\pgfpointanchor{B}{center}}{\pgfpointanchor{C}{center}}
    \edef\anglebc{\pgfmathresult}

    \pgfmathanglebetweenpoints{\pgfpointanchor{C}{center}}{\pgfpointanchor{A}{center}}
    \edef\angleca{\pgfmathresult}

    \pgfmathparse{veclen(abs(\xa-\xb),abs(\ya-\yb))}
    \edef\lenab{\pgfmathresult}

    \pgfmathparse{veclen(abs(\xb-\xc),abs(\yb-\yc))}
    \edef\lenbc{\pgfmathresult}

    \pgfmathparse{veclen(abs(\xc-\xa),abs(\yc-\ya))}
    \edef\lenca{\pgfmathresult}

    \draw[fill=green,opacity=0.5]
        (A) -- (B) -- ++ (\angleab-90:\lenab) -- ++ (\angleab-180:\lenab) -- cycle;

    \draw[fill=blue,opacity=0.5]
        (B) -- (C) -- ++ (\anglebc-90:\lenbc) -- ++ (\anglebc-180:\lenbc) -- cycle;

    \draw[fill=red,opacity=0.5]
        (C) -- (A) -- ++ (\angleca-90:\lenca) -- ++ (\angleca-180:\lenca) -- cycle;

\endtikzpicture
\vskip 2mm plus 1mm minus 1mm
\line{\hfil{Figure. My Lovely Picture}\hfil}
\par}

\bye