<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%// -*- coding: utf-8 -*-
%!TEX encoding = UTF-8 Unicode
\documentclass[a4paper]{amsart}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english,francais]{babel}
\usepackage{ae,aeguill,icomma}
\usepackage{amssymb}
\usepackage{enumerate}
\usepackage{url}
\usepackage[notcite, notref]{showkeys}

\usepackage{tikz}
\usepackage[babel=true,kerning=true]{microtype}
% sinon incompatibilitÃ© entre babel et tikz
\usetikzlibrary{calc,through,shapes}

\newcommand\N{\mathbb N}
\newcommand\Z{\mathbb Z}
\newcommand\Q{\mathbb Q}
\newcommand\R{\mathbb R}
\newcommand\C{\mathbb C}
\newcommand\ep\varepsilon
\newcommand\al\alpha

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{notation}[theorem]{Notation}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{example}[theorem]{Example}

\newcommand\pos[1]{#1_{&gt;0}}
\newcommand\pd[2]{\frac{\partial #1}{\partial #2}}

\DeclareMathOperator\Hom{Hom}

\begin{document}
\tikz{\draw (0,0) -- (1.5,0);\draw[color=orange](0,0)circle(2ex);}
un autre cercle
\tikz\draw[color=blue]circle(2ex);
et encore un cercle $8+9$
\tikz\draw[color=green]circle(1cm);
\tikz\draw[color=blue]circle(2cm);

\tikz \draw[thick,rounded corners=8pt] 
(0,0) -- (0,2) -- (1,3.25) -- (2,2) -- (2,0) -- (0,2) -- (2,2) -- (0,0) -- (2,0);

\begin{tikzpicture} 
\draw (-1.5,0) -- (1.5,0); 
\draw (0,-1.5) -- (0,1.5); 
\end{tikzpicture}

\begin{tikzpicture} 
\filldraw [gray] (0,0) circle (2pt) 
(1,1) circle (2pt) 
(2,1) circle (2pt) 
(2,0) circle (2pt); 
\draw (0,0) .. controls (1,1) and (3,3) .. (2,0); 
\end{tikzpicture} 

\tikz \draw (0,0) circle (10pt);
\tikz \filldraw[fill=red!60!green,draw=blue,very thick] (0,0) circle (10pt);

\begin{tikzpicture}
\clip[rotate=30] (0,0) ellipse (40pt and 10pt); 
\draw[step=.3cm,very thin, gray] (-1.4,-1.4) grid (1.4,1.4); 
\end{tikzpicture}

\begin{tikzpicture}
\draw[&lt;-&gt;&gt;,very thick] (3,0) arc (0:30:3);
\fill[green!20!white] (0,0) -- (3,0) arc (0:30:3) -- cycle;
\draw (30:1) node{M} ++(40:1) node{U} +(50:1) node{L};
\draw[very thick,orange] (1,0) -- (intersection of 1,0--1,1 and 0,0--30:1); 
\end{tikzpicture}

\begin{tikzpicture} 
\draw (0,0) -- (90:1cm) arc (90:360:1cm) arc (0:30:1cm) -- cycle; 
\draw (60:5pt) -- +(30:1cm) arc (30:90:1cm) -- cycle; 
\draw (3,0) +(0:1cm) -- +(72:1cm) -- +(144:1cm) -- +(216:1cm) -- +(288:1cm) -- cycle; 
\end{tikzpicture} 

\begin{tikzpicture} 
\coordinate (A) at (0,1); 
\coordinate (B) at (1.25,0.25); 
\draw[blue] (A) -- (B); 
\end{tikzpicture}

\begin{tikzpicture} 
\coordinate [label=left:\textcolor{blue}{$A$}] (A) at (0,0); 
\coordinate [label=right:\textcolor{blue}{$B$}] (B) at (1.25,0.25); 
\draw[blue] (A) -- (B); 
\end{tikzpicture} 

\begin{tikzpicture}[scale=1.5]
\draw[-&gt;] (-1,0) -- (2.5,0) node[above]{$y$};
\draw[-&gt;] (0,-2) -- (0,2) node[right]{$x$};
\draw (1,-2) -- (1,2) node[above]{$x=1$};
\draw[very thin, color=gray] (2,2) -- (-1,-1) node[left]{$y=x$};
\draw[very thin, color=gray] (2,-2) -- (-1,1) node[left]{$y=-x$};
\draw[smooth,domain=0:6500] plot
({(\x/6600)*cos(\x)},{(\x/6600)*sin(\x)});
\end{tikzpicture}

\begin{tikzpicture} 
\coordinate [label=left:$A$] (A) at (0,0); 
\coordinate [label=right:$B$] (B) at (1.25,0.25); 
\draw (A) -- (B); 
\draw (A) let 
             \p1 = ($ (B) - (A) $) 
          in 
             circle ({veclen(\x1,\y1)}); 
\end{tikzpicture} 

\begin{tikzpicture} 
\coordinate [label=left:$A$] (A) at (0,0); 
\coordinate [label=right:$B$] (B) at (1.25,0.25); 
\draw (A) -- (B); 
\draw let \p1 = ($ (B) - (A) $), 
\n2 = {veclen(\x1,\y1)} 
in 
(A) circle (\n2) 
(B) circle (\n2); 
\end{tikzpicture} 

\begin{tikzpicture} 
\coordinate [label=left:$A$] (A) at (0,0); 
\coordinate [label=right:$B$] (B) at (1.25,0.25); 
\draw (A) -- (B); 
\node (D) [draw,circle through=(B),label=left:$D$] at (A) {}; 
\node (E) [draw,circle through=(A),label=right:$E$] at (B) {}; 
\coordinate [label=above:$C$] (C) at (intersection 2 of D and E); 
\draw [red] (A) -- (C); 
\draw [red] (B) -- (C); 
\end{tikzpicture} 

\begin{tikzpicture} 
\draw[fill=yellow] (0,0) -- (60:.75cm) arc (60:180:.75cm); 
\draw(120:0.4cm) node {$\alpha$}; 
\draw[fill=green!30] (0,0) -- (right:.75cm) arc (0:60:.75cm); 
\draw(30:0.5cm) node {$\beta$}; 
\begin{scope}[shift={(60:2cm)}] 
\draw[fill=green!30] (0,0) -- (180:.75cm) arc (180:240:.75cm); 
\draw (30:-0.5cm) node {$\gamma$}; 
\draw[fill=yellow] (0,0) -- (240:.75cm) arc (240:360:.75cm); 
\draw (-60:0.4cm) node {$\delta$}; 
\end{scope} 
\begin{scope}[thick] 
\draw (60:-1cm) node[fill=white] {$E$} -- (60:3cm) node[fill=white] {$F$}; 
\draw[red] (-2,0) node[left] {$A$} -- (3,0) node[right]{$B$}; 
\draw[blue,shift={(60:2cm)}] (-3,0) node[left] {$C$} -- (2,0) node[right]{$D$}; 
\draw[shift={(60:1cm)},xshift=4cm] 
node [right,text width=6cm,rounded corners,fill=red!20,inner sep=1ex] 
{ 
When we assume that $\color{red}AB$ and $\color{blue}CD$ are 
parallel, i.\,e., ${\color{red}AB} \mathbin{\|} \color{blue}CD$, 
then $\alpha = \delta$ and $\beta = \gamma$. 
}; 
\end{scope} 
\end{tikzpicture} 

\begin{tikzpicture} 
\node (start) [draw,shape=ellipse] {start}; 
\foreach \angle in {-90, -80, ..., 90} 
\draw (node cs:name=start,angle=\angle) 
.. controls +(\angle:1cm) and +(-1,0) .. (2.5,0); 
\end{tikzpicture} 

\tikz \draw (0,0) .. controls +(left:3.5cm) and +(right:3.5cm) .. (0,3)
\foreach \p in {0,0.125,...,1} {node[pos=\p]{\p}};

\begin{tikzpicture}[domain=0:4] 
\draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9); 
\draw[-&gt;] (-0.2,0) -- (4.2,0) node[right] {$x$}; 
\draw[-&gt;] (0,-1.2) -- (0,4.2) node[above] {$f(x)$}; 
\draw[color=red] plot (\x,\x) node[right] {$f(x) =x$}; 
\draw[color=blue] plot (\x,{sin(\x r)}) node[right] {$f(x) = \sin x$}; 
\draw[color=orange] plot (\x,{0.05*exp(\x)}) node[right] {$f(x) = \frac{1}{20} \mathrm e^x$}; 
\end{tikzpicture} 
\end{document}</pre></body></html>