From 2d234af911ec062a36b45701b19b1065c765eb4e Mon Sep 17 00:00:00 2001 From: Jean-Michel Sarlat Date: Sat, 19 Nov 2011 23:28:53 +0100 Subject: [PATCH] =?utf8?q?Mise=20en=20place=20de=20la=20page=20de=20garde,?= =?utf8?q?=20style=20=C2=AB=20Syracuse=20=C2=BB=20:),=20de=20la=20document?= =?utf8?q?ation?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- doc.pdf | Bin 3130640 -> 3144151 bytes doc/christ5.tex | 420 ++++++++++++++++++++++++++++++++++++++++++ doc/doc.pdf | Bin 0 -> 3144151 bytes doc/doc.tex | 27 +++ doc/fond.pdf | Bin 0 -> 1309 bytes doc/mp-solid.pdf | Bin 0 -> 4359 bytes doc/mp-solid.w | 6 + doc/syracuse-crop.pdf | Bin 0 -> 9168 bytes 8 files changed, 453 insertions(+) create mode 100644 doc/christ5.tex create mode 100644 doc/doc.pdf create mode 100644 doc/fond.pdf create mode 100644 doc/mp-solid.pdf create mode 100644 doc/mp-solid.w create mode 100644 doc/syracuse-crop.pdf diff --git a/doc.pdf b/doc.pdf index 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b/doc/christ5.tex @@ -0,0 +1,420 @@ +%========================================= +%Macros personnelles +%christophe.poulain@melusine.eu.org +%création : 25 Septembre 1999 +%dernière modification : 28 Avril 2005 +%========================================= + +\RequirePackage{xlop,fancybox,color,amssymb,ifthen} +\input{xlopsqrt} +\newtheorem{ppte}{Propri\'et\'e} +\newtheorem{theo}{Th\'eor\`eme} +\newtheorem{defi}{D\'efinition} +\newtheorem{lemme}{Lemme} +\newtheorem{coro}{Corollaire} +\newtheorem{prop}{Proposition} +\newtheorem{reg}{R\`egle} +\newtheorem{conj}{Conjecture} +\newtheorem{remar}{Remarque} +\newtheorem{exem}{Exemple} + +\newcommand{\rema}{\underline{Remarque} } +\newcommand{\exe}{\underline{Exemple} } +\newcommand{\pre}{\underline{Preuve}} +\newcommand{\cas}{\underline{Cas particulier}} +\newcommand{\cass}{\underline{Cas particuliers}} +\newcommand{\Not}{\underline{Notation} } +\newcommand{\Si}{\underline{Si} } +\newcommand{\si}{\underline{si} } +\newcommand{\alors}{\underline{alors} } +\newcommand{\cons}{\underline{Conséquence}} +\newcommand{\Comme}{\underline{Comme} } +\newcommand{\comme}{\underline{comme} } + +\def\qed{\hfill\raise -2pt\hbox{\vrule\vbox to 10pt{\hrule width4pt\vfill\hrule}\vrule}} +\def\cqfd{\hfill\unskip\kern 6pt\penalty 500\qed\par} + +\catcode`\@=11 +\def\Eqalign#1{\null\,\vcenter{\openup\jot\m@th\ialign{ +\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil +&&\quad\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$ +\hfil\crcr #1\crcr}}\,} +\catcode`\@=12 + +\newcommand{\vecteur}[1] +{\overrightarrow{\strut #1}} + +\font\tenbb=msbm10 +\font\sevenbb=msbm7 +\font\fivebb=msbm5 +\newfam\bbfam +\textfont\bbfam=\tenbb +\scriptfont\bbfam=\sevenbb +\scriptscriptfont\bbfam=\fivebb +\def\bb{\fam\bbfam\tenbb} +\let\oldbb=\bb +\def\bb #1{{\oldbb #1}} + +\def\tvi{\vrule height 12pt depth 5pt width 0pt} +\def\tvj{\vrule height 12pt depth 5pt width 1pt} +\def\hfq{\hfill\,\,} +\def\cc#1{\hfq #1\hfq} +\def\tv{\tvi\vrule} +\def\tw{\tvj\vrule} +\def\traithorizontal{\noalign{\hrule}} +\def\traithorizontale{\noalign{\hrule height 1pt}} + +\newcommand{\encadre}[1] +{\begin{center} +\fbox{\begin{minipage}{\linewidth} +{#1} +\end{minipage}} +\end{center} +} + +\def\pgcd{\mathop{\rm PGCD}\nolimits} +\def\ppcm{\mathop{\rm PPCM}\nolimits} + +\def\cut{{}\hfill\cr \hfill{}} + +\newcommand{\biindice}[3]% +{ +\renewcommand{\arraystretch}{0.5} +\begin{array}[t]{c} +#1\\ +{\scriptstyle #2}\\ +{\scriptstyle #3} +\end{array} +\renewcommand{\arraystretch}{1} +} + +\newlength{\ltxt} +\newcommand{\compo}[4]{ +\setlength{\ltxt}{\linewidth} +\setbox#1=\hbox{\includegraphics[scale=#3]{#2.#1}} +\addtolength{\ltxt}{-\wd#1} +\addtolength{\ltxt}{-10pt} +\begin{minipage}{\wd#1} +\includegraphics[scale=#3]{#2.#1} +\end{minipage} +\hfill +\begin{minipage}{\ltxt} +#4 +\end{minipage} +} + +\newcommand{\compog}[4]{ +\setlength{\ltxt}{\linewidth} +\setbox#1=\hbox{\includegraphics[scale=#3]{#2.#1}} +\addtolength{\ltxt}{-\wd#1} +\addtolength{\ltxt}{-10pt} +\begin{minipage}{\ltxt} +#4 +\end{minipage} +\hfill +\begin{minipage}{\wd#1} +\includegraphics[scale=#3]{#2.#1} +\end{minipage} +} + +\newlength{\lntxt} +\newcommand{\Compo}[4]{ +\setlength{\lntxt}{\linewidth} +\setbox#1=\hbox{\includegraphics[scale=#3]{#2}} +\addtolength{\lntxt}{-\wd#1} +\addtolength{\lntxt}{-10pt} +\begin{minipage}{\wd#1} +\includegraphics[scale=#3]{#2} +\end{minipage} +\hfill +\begin{minipage}{\lntxt} +#4 +\end{minipage} +} + +\newlength{\lnttxt} +\newcommand{\dispo}[3]{ +\setlength{\lnttxt}{\linewidth} +\setbox#1=\hbox{#2} +\addtolength{\lnttxt}{-\wd#1} +\addtolength{\lnttxt}{-20pt} +\begin{minipage}{\wd#1} +#2 +\end{minipage} +\hfill +\begin{minipage}{\lnttxt} +#3 +\end{minipage} +} + +\newcounter{num}[section] +\newcommand{\exo}{\addtocounter{num}{1} +\par\underline{\bf Exercice~\thenum} } + +\newcommand{\titrage}[2]{ +{\Large #1}\hfill#2 +\par\rule[+6pt]{\linewidth}{0.5mm} +\par +} + +\newcommand{\titragedossier}[1]{ +{\small #1}\hfill{\small www.melusine.eu.org/syracuse/poulecl/} +\par\rule[+6pt]{\linewidth}{0.5mm} +\par +} + +\newcommand{\partie}[2]{ +\begin{center} +\begin{minipage}{#1pt} +\begin{center} +\boxput*(0,0){\colorbox{white}{#2}} +{\rule{\linewidth}{0.5mm}} +\end{center} +\end{minipage} +\end{center} +\par +} + +\newenvironment{myenumerate}{ +\renewcommand{\theenumi}{\arabic{enumi}} +\def\labelenumi{{\bf \theenumi /}} +\begin{enumerate}}{\end{enumerate}} + +\newenvironment{Myenumerate}{ +\renewcommand{\theenumi}{\arabic{enumi}} +\def\labelenumi{$\rhd${\bf \theenumi /}} +\begin{enumerate}}{\end{enumerate}} + +\newdimen\shadeshift\shadeshift=1pt +\def\shadedtext#1{{\setbox0=\hbox{#1}\leavevmode + \vtop to 0pt{\rlap{\special{color push rgb 0.75 0.75 0.75}% + \kern0.1em\lower0.1em\copy0 + \special{color pop}}\vss}\box0}}% +\long\def\shadedparagraph#1\par{{\setbox0=\vbox{\hsize=\hsize#1}% + \noindent\leavevmode + \vtop to 0pt{\rlap{\special{color push rgb 0.75 0.75 0.75}% + \kern0.1em\lower0.1em\copy0 + \special{color pop}}\vss}\box0\par}}% + +\newboolean{exact} +\setboolean{exact}{true} +\newboolean{racine} +\setboolean{racine}{false} + +\newcommand{\pythahypo}[5]{ +\opset{decimalsepsymbol={,}} +\opcopy{#4}{A1} +\opcopy{#5}{A2} +Dans le triangle $#1#2#3$ rectangle en $#2$, le théorème de Pythagore permet d'écrire : +\[\Eqalign{ +#1#3^2&=#1#2^2+#2#3^2\cr +#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr +#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr +#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr +#1#3&=\sqrt{\opprint{a3}}\cr +\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{2}{a4}\opunzero{a4} +\opprint{a4}}}\cr +}\] +} + +\newcommand{\pythadroit}[5]{ +\opset{decimalsepsymbol={,}} +\opcopy{#4}{A1} +\opcopy{#5}{A2} +Dans le triangle $#1#2#3$ rectangle en $#2$, le théorème de Pythagore permet d'écrire : +\[\Eqalign{ +#1#3^2&=#1#2^2+#2#3^2\cr +\opprint{A1}^2&=#1#2^2+\opprint{A2}^2\cr +\opmul*{A1}{A1}{a1}\opprint{a1}&=#1#2^2+\opmul*{A2}{A2}{a2}\opprint{a2}\cr +#1#2^2&=\opmul*{A1}{A1}{a1}\opprint{a1}-\opmul*{A2}{A2}{a2}\opprint{a2}\cr +#1#2^2&=\opsub*{a1}{a2}{a3}\opprint{a3}\cr +#1#2&=\sqrt{\opprint{a3}}\cr +\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#2&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#2&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{2}{a4}\opunzero{a4} +\opprint{a4}}}\cr +}\] +} + +\newcommand{\Recipytha}[6]{ +\opset{decimalsepsymbol={,}} +\opcopy{#4}{A1} +\opcopy{#5}{A2} +\opcopy{#6}{A3} +Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté. +\[\left. + \begin{array}{l} + #1#3^2=\opprint{A1}^2=\opmul*{A1}{A1}{a1}\opprint{a1}\cr + #1#2^2+#2#3^2=\opprint{A2}^2+\opprint{A3}^2=\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}=\opadd*{a2}{a3}{a4}\opprint{a4}\cr + \end{array} +\right\}#1#3^2=#1#2^2+#2#3^2 +\] +Comme $#1#3^2=#1#2^2+#2#3^2$ alors le triangle $#1#2#3$ est rectangle en $#2$ d'après la réciproque du théorème de Pythagore.} + +\newcommand{\Recipythacol}[6]{ +\opset{decimalsepsymbol={,}} +\opcopy{#4}{A1} +\opcopy{#5}{A2} +\opcopy{#6}{A3} +Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté. +\[\Eqalign{ + #1#3^2&\kern0.15\linewidth#2^2+#2#3^2\cr + \opprint{A1}^2&&\opprint{A2}^2+\opprint{A3}^2\cr + \opmul*{A1}{A1}{a1}\opprint{a1}&&\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}\cr + &&\opadd*{a2}{a3}{a4}\opprint{a4}\cr +}\] +Comme $#1#3^2=#1#2^2+#2#3^2$ alors le triangle $#1#2#3$ est rectangle en $#2$ d'après la réciproque du théorème de Pythagore.} + +\newcommand{\Thales}[5]{% +Dans le triangle $#1#2#3$, $#4$ est un point de la + droite $(#1#2)$, $#5$ est un point de la droite + $(#1#3)$ ; les droites $(#4#5)$ et $(#2#3)$ sont parallèles. + Le théorème de Thalès permet d'écrire : +\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\]% +} + +\newcommand{\Thalesf}[5]{ +Dans le triangle $#1#2#3$, $#4$ est un point du + segment $[#1#2]$, $#5$ est un point du segment + $[#1#3]$ ; les droites $(#4#5)$ et $(#2#3)$ sont parallèles. + L'égalité des 3 rapports permet d'écrire : +\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\] +} + +\newcommand{\ResolThales}[6]{% +\opset{decimalsepsymbol={,}}% +\opcopy{#3}{a3}% +\opcopy{#4}{a4}% +\opcopy{#5}{a5}% +On utilise % +\[\Eqalign{% +\frac{#1#2}{\opprint{a3}}&=\frac{\opprint{a4}}{\opprint{a5}}\cr% +#1#2&=\frac{\opprint{a3}\times\opprint{a4}}{\opprint{a5}}\cr% +#1#2&=\frac{\opmul*{a3}{a4}{a6}\opunzero{a6}\opprint{a6}}{\opprint{a5}}\cr% +\ifthenelse{\boolean{exact}}{#1#2&=\opdiv*[maxdivstep=3]{a6}{a5}{a7}{a8}\opunzero{a7}\opprint{a7}\cr}{#1#2&\approx\opdiv*[maxdivstep=3]{a6}{a5}{a7}{a8}\opunzero{a7}\opprint{a7}\cr}% +}\]% +\ifthenelse{\boolean{exact}}{La longueur $#1#2$ mesure \opprint{a7}\,#6}{La longueur $#1#2$ mesure environ \opprint{a7}\,#6}% +} + +%%QCM +\newcounter{qqcm} + +%définir un booléen qui permet de choisir la correction ou non +\newboolean{solution} + +%définir une commande \V qui permet de changer le carré en carré coché suivant la valeur du booléen. +\newcommand{\V}[1]{\ifthenelse{\boolean{solution}}{$\boxtimes$\kern2mm #1}{$\Box$\kern2mm #1}} +\newcommand{\F}[1]{$\Box$\kern2mm #1} +\newcommand{\vr}{\ifthenelse{\boolean{solution}}{$\boxtimes$}{$\Box$}} +\newcommand{\fa}{$\Box$} + +%%QCM Version 2 +\newenvironment{Qcm}[1][2]{\par\setboolean{solution}{false} +\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5} +\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/#1}|*{#1}{l|}}\hline}{\hline\end{tabular} +\renewcommand{\arraystretch}{1}} + +\newenvironment{Qcmcor}[1][2]{\par\setboolean{solution}{true}\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5} +\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/#1}|*{#1}{l|}}\hline}{\hline\end{tabular} +\renewcommand{\arraystretch}{1}} + +\newcounter{taill} +\newcommand{\QCM}[3]{\setboolean{solution}{false} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{1.5} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +\multicolumn{\thetaill}{|c|}{{\sc #2}}\\ +#3 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newcommand{\QCMcor}[3]{\setboolean{solution}{true} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{1.5} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +\multicolumn{\thetaill}{|c|}{{\sc #2}}\\ +#3 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newcommand{\QCMvar}[4]{\setboolean{solution}{false} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{#2} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +\multicolumn{\thetaill}{|c|}{{\sc #3}}\\ +#4 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newcommand{\QCMvarcor}[4]{\setboolean{solution}{true} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{#2} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +\multicolumn{\thetaill}{|c|}{{\sc #3}}\\ +#4 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newcommand{\QCMsimple}[2]{\setboolean{solution}{false} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{1.5} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +#2 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newcommand{\QCMsimplevar}[3]{\setboolean{solution}{false} +\setcounter{qqcm}{0} +\renewcommand{\arraystretch}{#2} +\setcounter{taill}{#1} +\addtocounter{taill}{1} +\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}} +\hline +#3 +\hline +\end{tabularx} +\renewcommand{\arraystretch}{1} +} + +\newenvironment{VF}[1]{\par\setboolean{solution}{false} +\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5} +\begin{center} +\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/2}|*{2}{c|}}\hline +\multicolumn{3}{|c|}{#1}\\ +\hline +\multicolumn{1}{|c|}{\bf Question}&\multicolumn{1}{c|}{\bf Vrai}&\multicolumn{1}{c|}{\bf Faux}\\ +\hline +}{\hline\end{tabular} +\end{center}\renewcommand{\arraystretch}{1}} + +\newenvironment{VFcor}[1]{\par\setboolean{solution}{true}\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5} +\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/2}|*{2}{c|}}\hline +\multicolumn{3}{|c|}{#1}\\ +\hline +\multicolumn{1}{|c|}{\bf Question}&\multicolumn{1}{c|}{\bf Vrai}&\multicolumn{1}{c|}{\bf Faux}\\ +\hline +}{\hline\end{tabular} 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