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chatgpt
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‎chatgpt1/chatgpt1.fls‎

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‎chatgpt1/chatgpt1.pdf‎

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‎chatgpt1/chatgpt1.tex‎

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‎chatgpt1/figures/cosinus-01.tikz‎

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\begin{tikzpicture}[scale=1]
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\begin{scope}
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% Axes
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\draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (0,0)--(5.5,0) node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,0)--(0,4.5) node[left,black] {$y$};
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\fill[] (0,0) circle (2pt) node[below]{$0$};
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\fill[] (1,0) circle (2pt) node[below]{$1$};
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\fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (2,3);
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\coordinate (Y) at (4,4);
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\draw[very thick, blue] (X) -- (Y) node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\fill[red] (X) circle (2pt) node[black,below left]{$X$};
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\fill[red] (Y) circle (2pt) node[black,below right]{$Y$};
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\node[align=center] at (2.5,-1.2) {\bf Distance euclidienne \\ $\|X-Y\|$};
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\end{scope}
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\begin{scope}[xshift=9cm]
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% Axes
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\draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (0,0)--(5.5,0) node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,0)--(0,4.5) node[left,black] {$y$};
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\fill[] (0,0) circle (2pt) node[below]{$0$};
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\fill[] (1,0) circle (2pt) node[below]{$1$};
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\fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (2,3);
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\coordinate (Y) at (4,4);
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\draw[->,>=latex,very thick, red] (0,0) -- (X) node[black,above left,scale=0.8]{$X$};
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\draw[->,>=latex,very thick, red] (0,0) -- (Y) node[black,below right,scale=0.8]{$Y$};
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\draw[blue,very thick,double] ({atan(3/2)}:3) arc ({atan(3/2)}:{atan(4/4)}:3) node[midway,above right]{$\theta$};
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%node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\node[align=center] at (2.5,-1.2) {\bf Similarité cosinus \\ $\cos(\theta)$};
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\end{scope}
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\end{tikzpicture}

‎chatgpt1/figures/cosinus-02.tikz‎

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\begin{tikzpicture}[scale=1]
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\begin{scope}
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (0,0)--(5.5,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,0)--(0,4.5); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (1,3);
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\coordinate (Y) at (4,2);
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\draw[very thick, blue] (X) -- (Y) node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\fill[red] (X) circle (2pt) node[black,below left]{$Y$};
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\fill[red] (Y) circle (2pt) node[black,below right]{$X$};
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\node[align=center] at (2.5,-1.2) {\bf Distance euclidienne \\ $\|X-Y\|$};
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\end{scope}
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\begin{scope}[xshift=9cm]
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (0,0)--(5.5,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,0)--(0,4.5); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (1,3);
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\coordinate (Y) at (4,2);
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\draw[->,>=latex,very thick, red] (0,0) -- (X) node[black,above left,scale=0.8]{$Y$};
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\draw[->,>=latex,very thick, red] (0,0) -- (Y) node[black,below right,scale=0.8]{$X$};
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\draw[blue,very thick,double] ({atan(2/4)}:2.5) arc ({atan(2/4)}:{atan(3/1)}:2.5) node[midway,above right]{$\theta$};
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%node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\node[align=center] at (2.5,-1.2) {\bf Similarité cosinus \\ $\cos(\theta)$};
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\end{scope}
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\end{tikzpicture}

‎chatgpt1/figures/cosinus-03.tikz‎

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\begin{tikzpicture}[scale=1]
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\begin{scope}[xshift=0cm]
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (-1,0)--(4,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,-1)--(0,4); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (3,2);
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\coordinate (Y) at (3,3);
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\draw[->,>=latex,very thick, red] (0,0) -- (X) node[black,below right,scale=0.8]{$X$};
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\draw[->,>=latex,very thick, red] (0,0) -- (Y) node[black,above,scale=0.8]{$Y$};
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\draw[blue,very thick,double] ({atan(3/3)}:2.5) arc ({atan(3/3)}:{atan(2/3)}:2.5) node[midway,above right]{$\theta$};
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%node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\node[align=center] at (2,-1.2) {\bf $\cos(\theta) \simeq 1$};
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\end{scope}
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\begin{scope}[xshift=9cm]
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (-2.5,0)--(4,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,-1)--(0,4); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (3,1);
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\coordinate (Y) at (-2,-1);
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\draw[->,>=latex,very thick, red] (0,0) -- (X) node[black,above,scale=0.8]{$X$};
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\draw[->,>=latex,very thick, red] (0,0) -- (Y) node[black,below,scale=0.8]{$Y$};
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\draw[blue,very thick,double] ({atan(1/3)}:1) arc ({atan(1/3)}:{180+atan(1/2)}:1) node[midway,above]{$\theta$};
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%node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\node[align=center] at (1.5,-1.2) {\bf $\cos(\theta) \simeq -1$};
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\end{scope}
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\begin{scope}[xshift=16cm]
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (-1,0)--(4,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,-1)--(0,4); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (3,0.5);
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\coordinate (Y) at (-1,3);
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\draw[->,>=latex,very thick, red] (0,0) -- (X) node[black,above right,scale=0.8]{$X$};
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\draw[->,>=latex,very thick, red] (0,0) -- (Y) node[black,above,scale=0.8]{$Y$};
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\draw[blue,very thick,double] ({atan(0.5/3)}:2.5) arc ({atan(0.5/3)}:{180-atan(3/1)}:2.5) node[midway,above right]{$\theta$};
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%node[midway,sloped,above,scale=0.7] {$\|X-Y\|$};
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\node[align=center] at (2,-1.2) {\bf $\cos(\theta) \simeq 0$};
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\end{scope}
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\end{tikzpicture}

‎chatgpt1/figures/cosinus-04.tikz‎

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\begin{tikzpicture}[scale=1]
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% Axes
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% \draw[gray] (0,0) grid ++ (5,4);
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\draw[->,>=latex, gray] (-1,0)--(5,0); % node[below,black] {$x$};
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\draw[->,>=latex, gray] (0,-1)--(0,5); % node[left,black] {$y$};
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% \fill[] (0,0) circle (2pt) node[below]{$0$};
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% \fill[] (1,0) circle (2pt) node[below]{$1$};
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% \fill[] (0,1) circle (2pt) node[left]{$1$};
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\coordinate (X) at (20:5);
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\coordinate (Y) at (60:5);
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\draw[->,>=latex,line width = 6pt, red!20] (0,0) -- (X);
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\draw[->,>=latex,line width = 6pt, blue!20] (0,0) -- (Y);
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\fill[red] (20:4) circle (2pt) node[below, align=center, scale=0.8] {{\bf chat} \\ {\small très confiant}};
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\fill[red] (20:2.5) circle (2pt) node[below, align=center, scale=0.8] {{\bf chat} \\ \small confiant};
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\fill[red] (20:1) circle (2pt) node[below, align=center, scale=0.8] {{\bf chat} \\ \small peu confiant};
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\fill[blue] (60:4) circle (2pt) node[above left, align=center, scale=0.8] {{\bf chien} \\ \small très confiant};
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\fill[blue] (60:2.5) circle (2pt) node[above left, align=center, scale=0.8] {{\bf chien} \\ \small confiant};
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\fill[blue] (60:1) circle (2pt) node[left, align=center, scale=0.8] {{\bf chien} \\ \small peu confiant};
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\end{tikzpicture}

‎chatgpt1/figures/cube-01.tikz‎

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\begin{tikzpicture}[scale=1, cube/.style={very thick,black}]
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\draw[cube] (0,0) -- (0,2) -- (2,2) -- (2,0) -- cycle;
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\node at (1,-0.5) {\bf Carré};
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\end{tikzpicture}

‎chatgpt1/figures/cube-02.tikz‎

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\begin{tikzpicture}
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[scale=1, cube/.style={very thick,black},
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grid/.style={very thin,gray},
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axis/.style={->,blue,thick}]
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%draw a grid in the x-y plane
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% \foreach \x in {-0.5,0,...,2.5}
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% \foreach \y in {-0.5,0,...,2.5}
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% {
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% \draw[grid] (\x,-0.5) -- (\x,2.5);
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% \draw[grid] (-0.5,\y) -- (2.5,\y);
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% }
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%draw the axes
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% \draw[axis] (0,0,0) -- (3,0,0) node[anchor=west]{$x$};
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% \draw[axis] (0,0,0) -- (0,3,0) node[anchor=west]{$y$};
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% \draw[axis] (0,0,0) -- (0,0,3) node[anchor=west]{$z$};
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%draw the top and bottom of the cube
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\draw[cube] (0,0,0) -- (0,2,0) -- (2,2,0) -- (2,0,0) -- cycle;
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\draw[cube] (0,0,2) -- (0,2,2) -- (2,2,2) -- (2,0,2) -- cycle;
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%draw the edges of the cube
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\draw[cube] (0,0,0) -- (0,0,2);
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\draw[cube] (0,2,0) -- (0,2,2);
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\draw[cube] (2,0,0) -- (2,0,2);
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\draw[cube] (2,2,0) -- (2,2,2);
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\node at (0.5,-1.5) {\bf Cube};
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\end{tikzpicture}

‎chatgpt1/figures/cube-03.tikz‎

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% https://tex.stackexchange.com/questions/598573/
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\begin{tikzpicture}[scale=0.7]
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\begin{scope}[thick,
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every node/.style={circle, draw, fill, minimum size=5pt, inner sep=0pt, font=\tiny}]
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\pgfsetxvec{\pgfpoint{0.9cm}{0.0cm}}
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\pgfsetyvec{\pgfpoint{0.0cm}{0.9cm}}
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\foreach \point / \id / \angle in {
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% outer cube
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(0,0)/0001/270,
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(0,5)/0011/90,
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(5,0)/1001/270,
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(5,5)/1011/90,
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(2,2)/0101/180,
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(2,7)/0111/90,
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(7,2)/1101/270,
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(7,7)/1111/90,
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% inner cube
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(2.5,1.5)/0000/270,
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(2.5,3.5)/0010/90,
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(4.5,1.5)/1000/250,
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(4.5,3.5)/1010/120,
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(3.5,2.5)/0100/170,
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(3.5,4.5)/0110/180,
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(5.5,2.5)/1100/10,
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(5.5,4.5)/1110/0}
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{
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\node (\id) at \point [label=\angle:\id] {};
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}
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% Here you have some specific nodes coloured in blue.
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\foreach \id in {0011, 0101, 1011, 1101}
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{
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%\node[blue] at (\id){};
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}
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% And here some other nodes couloured in red
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\foreach \id in {0001, 0100, 1001, 1110}
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{
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%\node[red] at (\id){};
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}
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\path
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(0011) edge (1011) edge (0111) edge (0001)
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(1001) edge (0001) edge (1101) edge (1011)
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(1111) edge (1101) edge (1011) edge (0111)
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(0010) edge (1010) edge (0110) edge (0000)
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(1000) edge (0000) edge (1100) edge (1010)
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(1110) edge (1100) edge (1010) edge (0110);
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\path%[dashed]
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(0101) edge (1101) edge (0001) edge (0111)
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(0100) edge (1100) edge (0000) edge (0110);
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\path%[dotted]
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(0000) edge (0001)
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(0010) edge (0011)
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(0100) edge (0101)
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(0110) edge (0111)
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(1000) edge (1001)
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(1010) edge (1011)
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(1100) edge (1101)
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(1110) edge (1111);
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\end{scope}
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every node/.style={}
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\node at (3,-1.5) {\bf Hypercube};
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\end{tikzpicture}

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