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"중첩된" 수학 세트를 그리는 방법은 무엇입니까?

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"중첩된" 수학 세트를 그리는 방법은 무엇입니까?

다음과 같이 중첩된 원을 사용하여 수학적 숫자 집합(R,Z,N)을 표현하고 싶습니다.

여기에 이미지 설명을 입력하세요

이것은 gimp를 사용하여 매우 빠르게 생성되었지만 tikz에서 제대로 수행하려고 시도하고 있지만 주로 원과 관련 레이블을 배치하는 데 몇 가지 문제가 있습니다. 확장 가능한 솔루션이 필요합니다. 어떤 배치 전략을 사용해야 할까요?

위 =2

등이 있지만 제대로 확장되지 않습니까?

답변1

다음은 circle \nodes와 positioning라이브러리를 사용하여 레이블을 배치하는 하나의 옵션입니다. scale=<factor>,transform shape스케일링을 제공합니다:

\documentclass{article} 
\usepackage{amssymb} 
\usepackage{tikz} 
\usetikzlibrary{positioning}

\tikzset{set/.style={draw,circle,inner sep=0pt,align=center}}

\begin{document} 

\begin{tikzpicture}
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea,text opacity=1]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\begin{tikzpicture}[scale=0.7,transform shape]
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\begin{tikzpicture}[scale=2.5,transform shape]
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\end{document}

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답변2

positioning다음은 , fit및 라이브러리를 사용하는 솔루션입니다 backgrounds.

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전문:

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning,fit,backgrounds}

매크로 \drawnestedsets:

\newcommand\drawnestedsets[4]{
  % initial position
  \def\position{#1}
  % number of sets
  \def\nbsets{#2}
  % list of sets
  \def\listofnestedsets{#3}
  % reversed list of colors
  \def\reversedlistofcolors{#4}

  % position and draw labels of sets
  \coordinate (circle-0) at (#1);
  \coordinate (set-0) at (#1);
  \foreach \set [count=\c] in \listofnestedsets {
    \pgfmathtruncatemacro{\cminusone}{\c - 1}
    % label of current set (below previous nested set)
    \node[below=3pt of circle-\cminusone,inner sep=0]
    (set-\c) {$\mathbb{\set}$};
    % current set (fit current label and previous set)
    \node[circle,inner sep=0,fit=(circle-\cminusone)(set-\c)]
    (circle-\c) {};
  }

  % draw and fill sets in reverse order
  \begin{scope}[on background layer]
    \foreach \col[count=\c] in \reversedlistofcolors {
      \pgfmathtruncatemacro{\invc}{\nbsets-\c}
      \pgfmathtruncatemacro{\invcplusone}{\invc+1}
      \node[circle,draw,fill=\col,inner sep=0,
      fit=(circle-\invc)(set-\invcplusone)] {};
    }
  \end{scope}
}

문서:

\begin{document}
\begin{tikzpicture}
  \drawnestedsets{0,0}{4}{N,Z,R,C}{lime,orange,yellow,cyan}

  \begin{scope}[font=\tiny]
    \drawnestedsets{2,0}{3}{N,Z,R}{orange,yellow,cyan}
  \end{scope}
\end{tikzpicture}
\end{document}

편집하다:다음은 타원이 있는 수평 변형입니다.

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그리고 코드(참고: 매크로 \drawnestedsets는 수정된 버전입니다):

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning,fit,backgrounds,shapes.geometric}

\newcommand\drawnestedsets[4]{
  % initial position
  \def\position{#1}
  % number of sets
  \def\nbsets{#2}
  % list of sets
  \def\listofnestedsets{#3}
  % reversed list of colors
  \def\reversedlistofcolors{#4}

  % position and draw labels of sets
  \coordinate (circle-0) at (#1);
  \coordinate (set-0) at (#1);
  \foreach \set [count=\c] in \listofnestedsets {
    \pgfmathtruncatemacro{\cminusone}{\c - 1}
    % label of current set (below previous nested set)
    \node[right=3pt of circle-\cminusone,inner sep=0]
    (set-\c) {$\mathbb{\set}$};
    % current set (fit current label and previous set)
    \node[ellipse,inner sep=0,fit=(circle-\cminusone)(set-\c)]
    (circle-\c) {};
  }

  % draw and fill sets in reverse order
  \begin{scope}[on background layer]
    \foreach \col[count=\c] in \reversedlistofcolors {
      \pgfmathtruncatemacro{\invc}{\nbsets-\c}
      \pgfmathtruncatemacro{\invcplusone}{\invc+1}
      \node[ellipse,draw,fill=\col,inner sep=0,
      fit=(circle-\invc)(set-\invcplusone)] {};
    }
  \end{scope}
}

\begin{document}
\begin{tikzpicture}
  \drawnestedsets{0,0}{4}{N,Z,R,C}{lime,orange,yellow,cyan}

  \begin{scope}[font=\tiny]
    \drawnestedsets{0,-1}{3}{N,Z,R}{orange,yellow,cyan}
  \end{scope}
\end{tikzpicture}
\end{document}

답변3

Gonzalo와 Paul의 답변은 훌륭합니다. 다양성을 위해 여기에 내 버전을 추가하고 있습니다. 여러모로 열악하지만 색상 선택에 심혈을 기울였습니다.

여기에 이미지 설명을 입력하세요

% author: Patrick TOCHE, 21 Jan 2024.
\documentclass[border=3pt]{standalone}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage{amsfonts}
\usepackage{kpfonts}

\newcommand{\N}{\ensuremath{\mathbb{N}} }% set of natural numbers
\newcommand{\Z}{\ensuremath{\mathbb{Z}} }% set of integers
\newcommand{\Q}{\ensuremath{\mathbb{Q}} }% set of rational numbers
\newcommand{\R}{\ensuremath{\mathbb{R}} }% set of real numbers
\newcommand{\C}{\ensuremath{\mathbb{C}} }% set of complex numbers
\renewcommand{\H}{\ensuremath{\mathbb{H}} }% set of hypercomplex numbers
\newcommand{\T}{\ensuremath{\mathbb{T}} }% set of transcendental numbers

\newcommand{\e}{\mathrm{e}}% exponential number

\newcommand{\definitions}{%
  % color of set of Natural numbers
  \colorlet{colN}{OrangeRed!60}
  % color of set of Integers
  \colorlet{colZ}{Orange!60}
  % color of set of Rational numbers
  \colorlet{colQ}{Gold!60}
  % color of set of Real numbers
  \colorlet{colR}{ForestGreen!50}
  % color of set of Complex numbers
  \colorlet{colC}{CornflowerBlue!80}
  % color of set of Hypercomplex numbers
  \colorlet{colH}{BlueViolet!50}
  % color of set of Transcendental numbers
  \colorlet{colT}{Green!30}

  % center coordinate of Natural numbers
  \coordinate (oN) at (0.0, 0.0);
  % center coordinate of Integers
  \coordinate (oZ) at (0.5, 0.5);
  % center coordinate of Rational numbers
  \coordinate (oQ) at (1.0, 1.0);
  % center coordinate of Real numbers
  \coordinate (oR) at (1.5, 1.5);
  % center coordinate of Complex numbers
  \coordinate (oC) at (2.0, 2.0);
  % center coordinate of Hypercomplex numbers
  \coordinate (oH) at (2.5, 2.5);
  % center coordinate of Transcendental numbers
  \coordinate (oT) at (0.5, 4.7);

  % set of Natural numbers
  \def\setN{(oN) ellipse (2.5 and 1.0)}
  % set of Integers
  \def\setZ{(oZ) ellipse (3.5 and 2.0)}
  % set of Rational numbers
  \def\setQ{(oQ) ellipse (4.5 and 3.0)}
  % set of Real numbers
  \def\setR{(oR) ellipse (5.5 and 4.0)}
  % set of Complex numbers
  \def\setC{(oC) ellipse (6.5 and 5.0)}
  % set of Hypercomplex numbers
  %\def\setH{(oH) ellipse (7.5 and 6.0)}
  % set of Transcendental numbers
  \def\setT{(oT) ellipse (1.5 and 0.67)}
}

\begin{document}
\begin{tikzpicture}
  
  % define colors and sets
  \definitions

  % fill sets in reverse order of size
  %\filldraw[fill=colH]\setH;
  \filldraw[fill=colC]\setC;
  \filldraw[fill=colR]\setR;
  \filldraw[fill=colQ]\setQ;
  \filldraw[fill=colZ]\setZ;
  \filldraw[fill=colN]\setN;
  %\filldraw[fill=colT]\setT;

  % add set label for each set
  \node[font=\huge] (N) at (-.2, 0.5) {\N};
  \node[font=\huge] (Z) at (0.8, 2.0) {\Z};
  \node[font=\huge] (Q) at (1.8, 3.5) {\Q};
  \node[font=\huge] (R) at (2.8, 4.9) {\R};
  \node[font=\huge] (C) at (3.8, 6.3) {\C};
  %\node[font=\huge] (H) at (4.8, 7.8) {\H};
  %\node[font=\large] (T) at (0.8, 4.9) {\T};

  % add name label for each set
  \node[font=\large] [below=0ex of N] {Natural};
  \node[font=\large] [below=0ex of Z] {Integer};
  \node[font=\large] [below=0ex of Q] {Rational};
  \node[font=\large] [below=0ex of R] {Real};
  \node[font=\large] [below=0ex of C] {Complex};
  %\node[font=\large] [below=0ex of H] {Hypercomplex};
  %\node[font=\small] [below=-1ex of T] {Transcendental};

  % add number examples for each set
  \node[font=\small] [below right=3.5ex and -1em of N] {$1,2,3,4$};
  \node[font=\small] [below right=3.5ex and 1.5em of Z] {$-4,-3,-2,-1$};
  \node[font=\small] [below right=3.5ex and 2em of Q] {$-\frac{1}{2},\frac{22}{7},\frac{355}{113}$};
  \node[font=\small,align=left] [below right=1.5ex and 1em of R] {$\sqrt{2},\sqrt{3},\varphi$,\\ \quad$\pi,\e,\gamma$};
  \node[font=\small] [below right=3.5ex and 1em of C] {$\sqrt{-1},i,\sqrt{i},\e^{i}$};
  %\node[font=\small] [below right=3.5ex and -1em of H] {Hypercomplex};
  %\node[font=\small] [below=1ex of T] {$\pi,\e,\gamma$};

\end{tikzpicture}
\end{document}

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