Grandes thématiques

Mathématiques

Informatique

LaTeX

Enseignement

Mathématiques
Seconde • Première spé • Terminale exp

Informatique
Première spé • Terminale spé

Galerie Tikz

Une collection de figure créées à l'aide de la bibliothèque TikZ pour le langage de composition LaTeX. Le code source des figures est disponible !

Consulter la galerie

Quelques figures

Angles associés

Mathématiques Analyse

\usepackage{tikz}
\usepackage{amsmath}

\begin{tabular}{|c|c|c|c|c|c|} \hline
	\multicolumn{2}{|p{5.2cm}|}{
		\vspace{-0.3cm} \begin{center}
			\begin{tikzpicture}[scale=1.5]
				\filldraw[fill=white,->] (0,0) circle (1);
				\draw[->] (-1.25,0) -- (1.25,0);
				\draw[->] (0,-1.25) -- (0,1.25);
				\draw[color=red,very thick] (0,0) -- (0.7071067812,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0.7071067812,0);
				\draw[color=red,very thick] (0,0) -- (0.7071067812,-0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,-0.7071067812) -- (0,-0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,-0.7071067812) -- (0.7071067812,0);
				\draw (0.7071067812,0.7071067812) node {\scriptsize $\bullet$} node[anchor=south west] {\small $M_x$};
				\draw (0.7071067812,-0.7071067812) node {\scriptsize $\bullet$} node[anchor=north west] {\small $M_{-x}$};
				\draw (0.7071067812,0) node[anchor=south east] {\tiny $\cos x$};
				\draw (0.7071067812,0) node[anchor=north east] {\tiny $\cos(-x)$};
				\draw (0,0.7071067812) node[anchor=east] {\tiny $\sin x$};
				\draw (0,-0.7071067812) node[anchor=east] {\tiny $\sin(-x)$};
			\end{tikzpicture}
		\end{center}} &
	\multicolumn{2}{|p{5.2cm}|}{
		\vspace{-0.3cm} \begin{center}
			\begin{tikzpicture}[scale=1.5]
				\filldraw[fill=white,->] (0,0) circle (1);
				\draw[->] (-1.25,0) -- (1.25,0);
				\draw[->] (0,-1.25) -- (0,1.25);
				\draw[color=red,very thick] (0,0) -- (0.7071067812,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0.7071067812,0);
				\draw[color=red,very thick] (0,0) -- (-0.7071067812,0.7071067812);
				\draw[color=red,very thick,dashed] (-0.7071067812,0.7071067812) -- (0,0.7071067812);
				\draw[color=red,very thick,dashed] (-0.7071067812,0.7071067812) -- (-0.7071067812,0);
				\draw (0.7071067812,0.7071067812) node {\scriptsize $\bullet$} node[anchor=south west] {\small $M_x$};
				\draw (-0.7071067812,0.7071067812) node {\scriptsize $\bullet$} node[anchor=south east] {\small $M_{\pi-x}$};
				\draw (0.7071067812,0) node[anchor=north] {\tiny $\cos x$};
				\draw (-0.5,0.03) node[anchor=north] {\tiny $\cos(\pi-x)$};
				\draw (0,0.7071067812) node[anchor=south west] {\tiny $\sin x$};
				\draw (0.08,0.7071067812) node[anchor=north east] {\tiny $\sin\left(\pi-x\right)$};
			\end{tikzpicture}
		\end{center}} &
	\multicolumn{2}{|p{5.2cm}|}{
		\vspace{-0.3cm} \begin{center}
			\begin{tikzpicture}[scale=1.5]
				\filldraw[fill=white,->] (0,0) circle (1);
				\draw[->] (-1.25,0) -- (1.25,0);
				\draw[->] (0,-1.25) -- (0,1.25);
				\draw[color=red,very thick] (0,0) -- (0.7071067812,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0.7071067812,0);
				\draw[color=red,very thick] (0,0) -- (-0.7071067812,-0.7071067812);
				\draw[color=red,very thick,dashed] (-0.7071067812,-0.7071067812) -- (0,-0.7071067812);
				\draw[color=red,very thick,dashed] (-0.7071067812,-0.7071067812) -- (-0.7071067812,0);
				\draw (0.7071067812,0.7071067812) node {\scriptsize $\bullet$} node[anchor=south west] {\small $M_x$};
				\draw (-0.7071067812,-0.7071067812) node {\scriptsize $\bullet$} node[anchor=north east] {\small $M_{\pi-x}$};
				\draw (0.7071067812,0) node[anchor=north] {\tiny $\cos x$};
				\draw (-0.5,0) node[anchor=south] {\tiny $\cos\left(\pi+x\right)$};
				\draw (0,0.7071067812) node[anchor=east] {\tiny $\sin x$};
				\draw (0,-0.7071067812) node[anchor=west] {\tiny $\sin\left(\pi+x\right)$};
			\end{tikzpicture}
		\end{center}} \\
	\multicolumn{2}{|p{5.2cm}|}{\vspace{-0.6cm} \centering
		$\cos(-x)=\cos x$ \par $\sin(-x)=-\sin x$ \vspace{-0.2cm} \par} &
	\multicolumn{2}{|p{5.2cm}|}{\vspace{-0.6cm} \centering
		$\cos\left(\pi-x\right)=-\cos x$ \par $\sin\left(\pi-x\right)=-\sin x$ \vspace{-0.2cm} \par} &
	\multicolumn{2}{|p{5.2cm}|}{\vspace{-0.6cm} \centering
		$\cos\left(\pi+x\right)=-\cos x$ \par $\sin\left(\pi+x\right)=-\sin x$ \vspace{-0.2cm} \par} \\ \hline
	\multicolumn{3}{|p{8cm}|}{
		\vspace{-0.3cm} \begin{center}
			\begin{tikzpicture}[scale=1.5]
				\filldraw[fill=white,->] (0,0) circle (1);
				\draw[->] (-1.25,0) -- (1.25,0);
				\draw[->] (0,-1.25) -- (0,1.25);
				\draw[color=red,very thick] (0,0) -- (1/2,0.8660254038);
				\draw[color=red,very thick,dashed] (0,0.8660254038) -- (1/2,0.8660254038) -- (1/2,0);
				\draw[color=red,very thick,dashed] (0,1/2) -- (0.8660254038,1/2) -- (0.8660254038,0);
				\draw[color=red,very thick] (0,0) -- (0.8660254038,1/2);
				\draw (0.8660254038,1/2) node {\scriptsize $\bullet$} node[anchor=south west] {\small $M_x$};
				\draw (1/2,0.8660254038) node {\scriptsize $\bullet$} node[anchor=south west] {\small $M_{\frac{\pi}{2}-x}$};
				\draw (1,0) node[anchor=north] {\tiny $\cos x$};
				\draw (0.2,0) node[anchor=north] {\tiny $\cos\left(\frac{\pi}{2}-x\right)$};
				\draw (0,1/2) node[anchor=east] {\tiny $\sin x$};
				\draw (0,0.8660254038) node[anchor=east] {\tiny $\sin\left(\frac{\pi}{2}-x\right)$};
			\end{tikzpicture}
		\end{center}} &
	\multicolumn{3}{|p{8cm}|}{
		\vspace{-0.3cm} \begin{center}
			\begin{tikzpicture}[scale=1.5]
				\filldraw[fill=white,->] (0,0) circle (1);
				\draw[->] (-1.25,0) -- (1.25,0);
				\draw[->] (0,-1.25) -- (0,1.25);
				\draw[color=red,very thick] (0,0) -- (0.7071067812,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0,0.7071067812);
				\draw[color=red,very thick,dashed] (0.7071067812,0.7071067812) -- (0.7071067812,0);
				\draw[color=red,very thick] (0,0) -- (-1/2,0.8660254038);
				\draw[color=red,very thick,dashed] (-1/2,0.8660254038) -- (0,0.8660254038);
				\draw[color=red,very thick,dashed] (-1/2,0.8660254038) -- (-1/2,0);
				\draw (0.7071067812,0.7071067812) node {\scriptsize $\bullet$} node[anchor=west] {\small $M_x$};
				\draw (-1/2,0.8660254038) node {\scriptsize $\bullet$} node[anchor=south east] {\small $M_{\frac{\pi}{2}+x}$};
				\draw (0.7071067812,0) node[anchor=north] {\tiny $\cos x$};
				\draw (-0.5,0) node[anchor=north] {\tiny $\cos\left(\frac{\pi}{2}+x\right)$};
				\draw (0,0.7071067812) node[anchor=south west] {\tiny $\sin\left(\frac{\pi}{2}+x\right)$};
				\draw (0,0.7071067812) node[anchor=east] {\tiny $\sin x$};
			\end{tikzpicture}
		\end{center}} \\
	\multicolumn{3}{|p{8cm}|}{\vspace{-0.6cm} \centering
		$\cos\left(\frac{\pi}{2}-x\right)=\sin x$ \par $\sin\left(\frac{\pi}{2}-x\right)=\cos x$ \vspace{-0.2cm} \par} &
	\multicolumn{3}{|p{8cm}|}{\vspace{-0.6cm} \centering
		$\cos\left(\frac{\pi}{2}+x\right)=-\sin x$ \par $\sin\left(\frac{\pi}{2}+x\right)=\cos x$ \vspace{-0.2cm} \par} \\ \hline
\end{tabular}

Arbre pondéré

Mathématiques Probabilité

\usepackage{tikz}
\usepackage{amsmath}

\begin{tikzpicture}[grow=right,level distance=3cm,scale=.75]
	\coordinate
		child[sibling distance=2.75cm] {
			node {$\overline{A}$}
			child[sibling distance=1cm] {
				node {$\overline{B}$}
				child{
					node[right] {
						$\overline{A}\cap\overline{B} \qquad p(\overline{A}\cap\overline{B})=p(\overline{A})\times p_{\overline{A}}(\overline{B})$}
					edge from parent[dashed]}
				edge from parent node[below=2pt] {$p_{\overline{A}}(\overline{B})$}}
			child[sibling distance=1cm] {
				node {$B$}
				child{
					node[right]{
						$\overline{A} \cap B\qquad p(\overline{A} \cap B)=p(\overline{A})\times p_{\overline{A}}(B)$}
					edge from parent[dashed]}
 				edge from parent node[above=2pt] {$p_{\overline{A}}(B)$}}
			edge from parent node[below=4pt] {$p(\overline{A}$}}
		child[sibling distance=2.75cm] {
			node {$A$}
 			child[sibling distance=1cm] {
				node {$\overline{B}$}
				child {
					node[right]{
						$A\cap\overline{B}\qquad p(A\cap\overline{B})=p(A)\times p_{A}(\overline{B})$}
					edge from parent[dashed]}
				edge from parent node[below=2pt] {$p_A(\overline{B})$}}
			child[sibling distance=1cm] {
				node {$B$}
				child{
					node[right]{
						$A\cap B\qquad p(A\cap B)=p(A)\times p_A(B)$}
					edge from parent[dashed]}
				edge from parent node[above=2pt] {$p_A(B)$}}
			edge from parent node[above=4pt] {$p(A)$}};
\end{tikzpicture}

Cercle trigonométrique

Mathématiques Analyse

\usepackage{tikz}
\usepackage{amsmath}

\begin{tikzpicture}[scale=2.5]
	\draw[color=red,dashed] (-1/2,-0.8660254038) -- (1/2,-0.8660254038) -- (1/2,0.8660254038) -- (-1/2,0.8660254038) -- (-1/2,-0.8660254038);
	\draw[color=blue,dashed] (-0.7071067812,-0.7071067812) -- (0.7071067812,-0.7071067812) -- (0.7071067812,0.7071067812) -- (-0.7071067812,0.7071067812) -- (-0.7071067812,-0.7071067812);
	\draw[color=teal,dashed] (-0.8660254038,-1/2) -- (0.8660254038,-1/2) -- (0.8660254038,1/2) -- (-0.8660254038,1/2) -- (-0.8660254038,-1/2);
	\draw (1,0) node {\footnotesize$+$} node[anchor=south west] {\footnotesize $0$};
	\draw (-1,0) node {\footnotesize$+$} node[anchor=south east] {\footnotesize $\pi$};
	\draw (-1,0) node {\footnotesize$+$} node[anchor=north east] {\footnotesize $-\pi$};
	\draw (0,1) node[anchor=south west] {\footnotesize $\frac{\pi}{2}$};
	\draw (1/2,0.8660254038) node {\footnotesize$+$} node[anchor=south west] {\footnotesize $\frac{\pi}{3}$};
	\draw (0.7071067812,0.7071067812) node {\footnotesize$+$} node[anchor=south west] {\footnotesize $\frac{\pi}{4}$};
	\draw (0.8660254038,1/2) node {\footnotesize$+$} node[anchor=south west] {\footnotesize $\frac{\pi}{6}$};
	\draw (-1/2,0.8660254038) node {\footnotesize$+$} node[anchor=south east] {\footnotesize $\frac{2\pi}{3}$};
	\draw (-0.7071067812,0.7071067812) node {\footnotesize$+$} node[anchor=south east] {\footnotesize $\frac{3\pi}{4}$};
	\draw (-0.8660254038,1/2) node {\footnotesize$+$} node[anchor=south east] {\footnotesize $\frac{5\pi}{6}$};
	\draw (0,-1) node {\footnotesize$+$} node[anchor=north west] {\footnotesize $-\frac{\pi}{2}$};
	\draw (1/2,-0.8660254038) node {\footnotesize$+$} node[anchor=north west] {\footnotesize $-\frac{\pi}{3}$};
	\draw (0.7071067812,-0.7071067812) node {\footnotesize$+$} node[anchor=north west] {\footnotesize $-\frac{\pi}{4}$};
	\draw (0.8660254038,-1/2) node {\footnotesize$+$} node[anchor=north west] {\footnotesize $-\frac{\pi}{6}$};
	\draw (-1/2,-0.8660254038) node {\footnotesize$+$} node[anchor=north east] {\footnotesize $-\frac{2\pi}{3}$};
	\draw (-0.7071067812,-0.7071067812) node {\footnotesize$+$} node[anchor=north east] {\footnotesize $-\frac{3\pi}{4}$};
	\draw (-0.8660254038,-1/2) node {\footnotesize$+$} node[anchor= east] {\footnotesize $-\frac{5\pi}{6}$};
	\draw (1/2,0) node[anchor=north,inner sep=1.5pt,fill=white] {\tiny \textcolor{red}{$\frac{1}{2}$}};
	\draw (0.7071067812,0) node[anchor=north,inner sep=1.5pt,fill=white] {\tiny \textcolor{blue}{$\frac{\sqrt{2}}{2}$}};
	\draw (0.8660254038,0) node[anchor=north,inner sep=1.5pt,fill=white] {\tiny \textcolor{teal}{$\frac{\sqrt{3}}{2}$}};
	\draw (0,1/2) node[anchor=east,inner sep=1.5pt,fill=white] {\tiny \textcolor{teal}{$\frac{1}{2}$}};
	\draw (0,0.7071067812) node[anchor=east,inner sep=1.5pt,fill=white] {\tiny \textcolor{blue}{$\frac{\sqrt{2}}{2}$}};
	\draw (0,0.8660254038) node[anchor=east,inner sep=1.5pt,fill=white] {\tiny \textcolor{red}{$\frac{\sqrt{3}}{2}$}};
	\filldraw[fill opacity=0,->] (0,0) circle (1);
	\draw[>=latex,->] (0,-1.15) -- (0,1.15);
	\draw[>=latex,->] (-1.15,0) -- (1.15,0);
\end{tikzpicture}

Produit matriciel

Mathématiques Algèbre

\usepackage{tikz}
\usepackage{nicematrix}
\usetikzlibrary{angles,quotes,matrix,shapes.geometric}

\begin{tikzpicture}[scale=0.95, >=latex,
	node style sp/.style={draw,circle,minimum size=1cm},
	node style ge/.style={circle,minimum size=1cm},
	arrow style mul/.style={draw,sloped,midway,fill=white},
	arrow style plus/.style={midway,sloped,fill=white}]
	% Matrice A
	\matrix (A) [matrix of math nodes,nodes={node style ge},left delimiter=(,right delimiter=)] at (0,0) {
		a_{1,1} & a_{1,2} & \ldots & a_{1,p} \\
		|[node style sp]| a_{2,1} & |[node style sp]| a_{2,2} & \ldots & |[node style sp]| a_{2,p} \\
		\vdots & \vdots & \ddots & \vdots \\
		a_{n,1} & a_{n,2} & \ldots & a_{n,p} \\ };
	\node[below=-3pt] at (A.south) {$A$ : \textcolor{red}{\bfseries\boldmath $n$ \unboldmath lignes} $p$ colonnes};
	% Matrice B
	\matrix (B) [matrix of math nodes,nodes={node style ge},left delimiter=(,right delimiter=)] at (6cm,6cm) {
		b_{1,1} & |[node style sp]| b_{1,2} & \ldots & b_{1,q} \\
		b_{2,1} & |[node style sp]| b_{2,2} & \ldots & b_{2,q} \\
		\vdots & \vdots & \ddots & \vdots \\
		b_{p,1} & |[node style sp]| b_{p,2} & \ldots & b_{p,q} \\ };
	\node[above=-3pt] at (B.north) {$B$ : $p$ lignes \textcolor{red}{\bfseries\boldmath $q$ \unboldmath colonnes}};
	% Matrice résultat C
	\matrix (C) [matrix of math nodes,nodes={node style ge},left delimiter=(,right delimiter=)] at (6cm,0) {
		c_{1,1} & c_{1,2} & \ldots & c_{1,q} \\
		c_{2,1} & |[node style sp,red]| \text{\boldmath$c_{2,2}$} & \ldots & c_{2,q} \\
		\vdots & \vdots & \ddots & \vdots \\
		c_{n,1} & c_{n,2} & \ldots & c_{n,q} \\ };
	\node [below=0pt] at (C.south) {$C=A\times B$ : \textcolor{red}{\bfseries\boldmath $n$ lignes $q$ colonnes \unboldmath}};
	% Les fleches
	\draw[red] (A-2-1.north) -- (C-2-2.north);
	\draw[red] (A-2-1.south) -- (C-2-2.south);
	\draw[red] (B-1-2.west) -- (C-2-2.west);
	\draw[red] (B-1-2.east) -- (C-2-2.east);
	\draw[<->,red] (A-2-1) to[in=180,out=90] node[arrow style mul] (x) {$\text{\boldmath $a_{2,1}\times b_{1,2}$}$} (B-1-2);
	\draw[<->,red] (A-2-2) to[in=180,out=90] node[arrow style mul] (y) {$\text{\boldmath $a_{2,2}\times b_{2,2}$}$} (B-2-2);
	\draw[<->,red] (A-2-4) to[in=180,out=90] node[arrow style mul] (z) {$\text{\boldmath $a_{2,p}\times b_{p,2}$}$} (B-4-2);
	\draw[->,red] (x) to node[arrow style plus] {$+$} (y) to node[arrow style plus] {$+\raisebox{.5ex}{\ldots}+$} (z) to (C-2-2.north west);
\end{tikzpicture}

Valeur absolue

Mathématiques Analyse

\usepackage{tikz}
\usepackage{amsmath}

\begin{tikzpicture}
	\draw (-3,0) node {\scriptsize$\bullet$} node[anchor=south] {$B$} node[anchor=north] {$x_B$} coordinate (ae);
	\draw (1,0) node {\scriptsize$\bullet$} node[anchor=south] {$A$} node[anchor=north] {$x_A$} coordinate (ea);
	\draw[->,>=stealth] (-4,0) -- (2,0);
	\draw[<->,>=stealth] (-3,0.5) -- (1,0.5) node[midway,anchor=south] {\small$AB=\lvert x_B-x_A \rvert$};
\end{tikzpicture}

Qui suis-je ?

Clément DEHESDIN

2024

Les amis du Far West

Développement du site web d'une association de danse en ligne.

2023 - 2024

Tutorat

Aide auprès d'élèves de première en spécialité mathématiques et NSI.

24 - 28 avril 2023

Labo de math de Versailles

Stage d'une semaine dans l'univers d'un professeur d'université.

2024

Baccalauréat

Obtention du Baccalauréat, mention Bien, avec 15,34 de moyenne.

Grandes thématiques

Enseignement

Galerie Tikz

Quelques figures

Angles associés

Arbre pondéré

Cercle trigonométrique

Produit matriciel

Valeur absolue

Clément DEHESDIN

Curriculum vitæ

2024

Les amis du Far West

2023 - 2024

Tutorat

24 - 28 avril 2023

Labo de math de Versailles

2024

Baccalauréat

Les articles récents

Le flocon de Koch, entre périmètre infini et aire finie