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-rw-r--r--macros/latex/contrib/profcollege/latex/PfCPythagore.tex119
1 files changed, 49 insertions, 70 deletions
diff --git a/macros/latex/contrib/profcollege/latex/PfCPythagore.tex b/macros/latex/contrib/profcollege/latex/PfCPythagore.tex
index ae8dda031e..45a20b80c7 100644
--- a/macros/latex/contrib/profcollege/latex/PfCPythagore.tex
+++ b/macros/latex/contrib/profcollege/latex/PfCPythagore.tex
@@ -270,6 +270,48 @@
\newcommand\RedactionCalculsReciPythagore{}%
\newcommand\RedactionConclusionReciPythagore{}%
+\NewDocumentCommand\CalculsPythagore{o m m m m}{
+ \xintifboolexpr{#3<#4 || #3==#4}{%\ifnum#3<#4%
+ \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}%
+ \begin{align*}
+ \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
+ \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
+ \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
+ \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
+ \ifboolKV[ClesPythagore]{AvantRacine}{}{%
+ \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
+ \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
+ }
+ \end{align*}
+ }{%\else
+ \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}%
+ \ifboolKV[ClesPythagore]{Soustraction}{%
+ \begin{align*}
+ \NomA\NomB^2&=\NomA\NomC^2-\NomB\NomC^2\\
+ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}-\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
+ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
+ \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
+ \ifboolKV[ClesPythagore]{AvantRacine}{}{%
+ \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
+ \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
+ }
+ \end{align*}
+ }{%
+ \begin{align*}
+ \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
+ \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
+ \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
+ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
+ \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
+ \ifboolKV[ClesPythagore]{AvantRacine}{}{%
+ \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}%
+ \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
+ }
+ \end{align*}
+ }%
+ }%\fi%
+}
+
% \newcommand\Pythagore[5][]{%
\NewDocumentCommand\Pythagore{o m m m m}{%
% #1 Param\`etres sous forme de cl\'es
@@ -277,8 +319,8 @@
% #3 Premi\`ere longueur
% #4 Deuxi\`eme longueur
% #5 Troisi\`eme longueur (\'eventuellement vide)
- \useKVdefault[ClesPythagore]%obligatoire car la macro n'est pas dans un groupe.
- \setKV[ClesPythagore]{#1}%On lit les arguments optionnels
+ \useKVdefault[ClesPythagore]%
+ \setKV[ClesPythagore]{#1}%
\DeclareSIUnit{\PfCPythaUnit}{\useKV[ClesPythagore]{Unite}}%
\ifboolKV[ClesPythagore]{Reciproque}{%
% On retient les noms des sommets
@@ -407,14 +449,14 @@
\xdef\NomSommetC{\NomC}%
% On trace une figure ou pas ?
\ifboolKV[ClesPythagore]{FigureSeule}{%
- \xintifboolexpr{#3<#4 || #3==#4}{%\ifnum#3<#4%
+ \xintifboolexpr{#3<#4 || #3==#4}{%
\xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}%
}{%
\xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}%
}%
\MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}
}{%
- \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation
+ \ifboolKV[ClesPythagore]{Figure}{%
\begin{multicols}{2}%
{\em La figure est donn\'ee \`a titre indicatif.}%
\[\MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}\]
@@ -430,33 +472,8 @@
\ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :%
}%
}
- \xintifboolexpr{#3<#4 || #3==#4}{%\ifnum#3<#4%
- \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}%
- \begin{align*}
- \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
- \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
- \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
- \ifboolKV[ClesPythagore]{AvantRacine}{}{%
- \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
- \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
- }%
- \end{align*}
- }{%\else%
- \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}%
- \begin{align*}
- \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
- \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
- \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
- \ifboolKV[ClesPythagore]{AvantRacine}{}{%
- \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
- \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
- }%
- \end{align*}
- }%\fi%
- }
+ \CalculsPythagore[#1]{#2}{#3}{#4}{}
+ }%
\end{multicols}
}{%
% On d\'emarre la r\'esolution
@@ -469,45 +486,7 @@
}{%
\ifboolKV[ClesPythagore]{Perso}{\RedactionPythagore}{\ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :%
}}%
- \xintifboolexpr{#3<#4 || #3==#4}{%\ifnum#3<#4%
- \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}%
- \begin{align*}
- \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
- \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
- \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
- \ifboolKV[ClesPythagore]{AvantRacine}{}{%
- \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
- \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
- }
- \end{align*}
- }{%\else
- \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}%
- \ifboolKV[ClesPythagore]{Soustraction}{%
- \begin{align*}
- \NomA\NomB^2&=\NomA\NomC^2-\NomB\NomC^2\\
- \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}-\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
- \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
- \ifboolKV[ClesPythagore]{AvantRacine}{}{%
- \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}
- \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
- }
- \end{align*}
- }{%
- \begin{align*}
- \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\
- \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\
- \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\
- \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\
- \ifboolKV[ClesPythagore]{AvantRacine}{}{%
- \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}%
- \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}}%\\
- }
- \end{align*}
- }%
- }%\fi%
+ \CalculsPythagore[#1]{#2}{#3}{#4}{}
}%
}%
}%