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Diffstat (limited to 'macros/latex/contrib/profcollege/latex/PfCRappelsFormules.tex')
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diff --git a/macros/latex/contrib/profcollege/latex/PfCRappelsFormules.tex b/macros/latex/contrib/profcollege/latex/PfCRappelsFormules.tex new file mode 100644 index 0000000000..2c22e2b45a --- /dev/null +++ b/macros/latex/contrib/profcollege/latex/PfCRappelsFormules.tex @@ -0,0 +1,1028 @@ +%%% +% Formules +%%% +\setKVdefault[ClesFormule]{Perimetre=false,Aire=false,Volume=false,Surface=carr\'e,Solide=pav\'e,Angle=0,Ancre={(0,0)},Largeur=5cm,Couleur=white,EchelleEspace=70,Echelle=1cm} + +\def\MPFigureCarre{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0); + C=rotation(A,B,-90); + D-C=A-B; + draw polygone(A,B,C,D); + draw codeperp(A,B,C,5); + draw codeperp(B,C,D,5); + draw codeperp(C,D,A,5); + draw codeperp(D,A,B,5); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $c$ etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0); + C=rotation(A,B,-90); + D-C=A-B; + draw polygone(A,B,C,D); + draw codeperp(A,B,C,5); + draw codeperp(B,C,D,5); + draw codeperp(C,D,A,5); + draw codeperp(D,A,B,5); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $c$ etex); + \end{mpost} + \fi +} + +\def\MPFigurePolygone{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + pair A,B,C,D,E,F; + A=u*(1,1); + B-A=u*(2,0); + C=3/5[B,rotation(A,B,-120)]; + D-C=u*(0,1); + E-D=u*(-1.25,-1); + F-E=u*(-1,1); + draw polygone(A,B,C,D,E,F); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + pair A,B,C,D,E,F; + A=u*(1,1); + B-A=u*(2,0); + C=3/5[B,rotation(A,B,-120)]; + D-C=u*(0,1); + E-D=u*(-1.25,-1); + F-E=u*(-1,1); + draw polygone(A,B,C,D,E,F); + \end{mpost} + \fi +} + +\def\MPFigureParallelogramme{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=\useKV[ClesFormule]{Echelle}; + vardef marque_para(expr dd,ee,pa)= + save im; + picture im; + pair kk,ll,mn,mo; + kk=point(pa*length dd) of dd; + ll=projection(kk,point(0.25*length ee) of ee,point(0.5*length ee) of ee); + mn=iso(kk,ll); + mo=(mn--kk) intersectionpoint cercles(mn,3mm); + im=image( + drawarrow mo--kk; + drawarrow symetrie(mo,mn)--ll; + label(btex $//$ etex,mn); + ); + im + enddef; + + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2.25,0.25); + D=4/5[A,rotation(B,A,40)]; + C-D=B-A; + draw polygone(A,B,C,D); + drawoptions(withcolor gris); + draw marque_para(droite(A,B),droite(C,D),0.455); + draw marque_para(droite(B,C),droite(A,D),0.43); + draw segment(B,2.5[C,B]) dashed evenly; + draw segment(A,1.5[D,A]) dashed evenly; + draw segment(A,1.55[B,A]) dashed evenly; + draw segment(D,2[C,D]) dashed evenly; + drawoptions(); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + vardef marque_para(expr dd,ee,pa)= + save im; + picture im; + pair kk,ll,mn,mo; + kk=point(pa*length dd) of dd; + ll=projection(kk,point(0.25*length ee) of ee,point(0.5*length ee) of ee); + mn=iso(kk,ll); + mo=(mn--kk) intersectionpoint cercles(mn,3mm); + im=image( + drawarrow mo--kk; + drawarrow symetrie(mo,mn)--ll; + label(btex $//$ etex,mn); + ); + im + enddef; + + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2.25,0.25); + D=4/5[A,rotation(B,A,40)]; + C-D=B-A; + draw polygone(A,B,C,D); + drawoptions(withcolor gris); + draw marque_para(droite(A,B),droite(C,D),0.455); + draw marque_para(droite(B,C),droite(A,D),0.43); + draw segment(B,2.5[C,B]) dashed evenly; + draw segment(A,1.5[D,A]) dashed evenly; + draw segment(A,1.55[B,A]) dashed evenly; + draw segment(D,2[C,D]) dashed evenly; + drawoptions(); + \end{mpost} + \fi +} + +\def\MPFigureParallelogrammeAire{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,10u,5u); + pair A,B,C,D,I,J; + A=u*(1,1); + B-A=u*(2,0.5); + D=3/5[A,rotation(B,A,40)]; + C-D=B-A; + I=projection(D,A,B); + draw polygone(A,B,C,D) withcolor gris; + draw segment(A,B); + draw segment(D,I); + draw codeperp(D,I,B,5); + A:=A+3*u*(1,0); + B:=A+u*(2,0.5); + D:=3/5[A,rotation(B,A,40)]; + C:=D+B-A; + J=projection(B,A,D); + draw polygone(A,B,C,D) withcolor gris; + draw segment(D,1.5[A,D]) dashed evenly withcolor gris; + draw segment(A,D); + draw segment(B,J); + draw codeperp(B,J,A,5); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,10u,5u); + pair A,B,C,D,I,J; + A=u*(1,1); + B-A=u*(2,0.5); + D=3/5[A,rotation(B,A,40)]; + C-D=B-A; + I=projection(D,A,B); + draw polygone(A,B,C,D) withcolor gris; + draw segment(A,B); + draw segment(D,I); + draw codeperp(D,I,B,5); + A:=A+3*u*(1,0); + B:=A+u*(2,0.5); + D:=3/5[A,rotation(B,A,40)]; + C:=D+B-A; + J=projection(B,A,D); + draw polygone(A,B,C,D) withcolor gris; + draw segment(D,1.5[A,D]) dashed evenly withcolor gris; + draw segment(A,D); + draw segment(B,J); + draw codeperp(B,J,A,5); + \end{mpost} + \fi +} + +\def\MPFigureSphere{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + Initialisation(5,0,10,\useKV[ClesFormule]{EchelleEspace}); + color O,A,B,C; + O=(0,0,0); + A-O=(0,1/2,0); + C-O=(-1/2,0,0); + B-O=(0,0,1/2); + path cc,cd; + cc=cercles(O,A,O,A,C); + cd=cercles(O,A,O,A,B); + draw cd; + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw cotationmil(O,A,0,18,btex rayon $r$ etex); + marque_p:="plein"; + pointe(O); + marque_p:="non"; + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,0,10,v); + color O,A,B,C; + O=(0,0,0); + A-O=(0,1/2,0); + C-O=(-1/2,0,0); + B-O=(0,0,1/2); + path cc,cd; + cc=cercles(O,A,O,A,C); + cd=cercles(O,A,O,A,B); + draw cd; + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw cotationmil(O,A,0,18,btex rayon $r$ etex); + marque_p:="plein"; + pointe(O); + marque_p:="non"; + \end{mpost} + \fi +} + +\def\MPFigurePave{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,115); + color A,B,C,D,E,F,G,H; + draw Pave(A,B,C,D,E,F,G,H)(0.5,1,1/3) withcolor gris; + draw segment(A,B); + draw segment(E,F); + draw segment(A,F); + draw appelation(A,B,-2mm,btex $\ell$ etex); + draw appelation(F,E,2mm,btex $p$ etex); + draw appelation(A,F,2mm,btex $h$ etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,115); + color A,B,C,D,E,F,G,H; + draw Pave(A,B,C,D,E,F,G,H)(0.5,1,1/3) withcolor gris; + draw segment(A,B); + draw segment(E,F); + draw segment(A,F); + draw appelation(A,B,-2mm,\btex $\ell$ etex); + draw appelation(F,E,2mm,\btex $p$ etex); + draw appelation(A,F,2mm,\btex $h$ etex); + \end{mpost} + \fi +} + +\def\MPFigurePrisme{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,\useKV[ClesFormule]{EchelleEspace}); + color A,B,C,D,E,F,G,H; + D=(0.75,0,0); + G=(0,1,0); + H=(0,0,0); + A-D=(0,0,0.5); + C-D=G-H; + E-H=A-D; + F-E=(0,0.6,0); + B-A=F-E; + NbS:=8; + Sommet1:=A; + Sommet2:=B; + Sommet3:=C; + Sommet4:=D; + Sommet5:=E; + Sommet6:=F; + Sommet7:=G; + Sommet8:=H; + NF:=6; + Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2; + Fc[200]:=4;Fc[201]:=4;Fc[202]:=1;Fc[203]:=5;Fc[204]:=8; + Fc[300]:=4;Fc[301]:=4;Fc[302]:=8;Fc[303]:=7;Fc[304]:=3; + Fc[400]:=4;Fc[401]:=8;Fc[402]:=5;Fc[403]:=6;Fc[404]:=7; + Fc[500]:=4;Fc[501]:=1;Fc[502]:=2;Fc[503]:=6;Fc[504]:=5; + Fc[600]:=4;Fc[601]:=2;Fc[602]:=3;Fc[603]:=7;Fc[604]:=6; + CoulTrace:=gris; + DessineObjet; + drawoptions(withcolor gris); + draw codeperp(B,A,E,5); + draw codeperp(A,B,F,5); + draw codeperp(H,D,C,5); + draw codeperp(D,C,G,5); + drawoptions(); + draw polygone(A,B,C,D); + draw hachurage(polygone(A,B,C,D),60,0.3,0); + draw segment(A,E); + draw appelation(A,E,3mm,btex hauteur etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,115); + color A,B,C,D,E,F,G,H; + D=(0.75,0,0); + G=(0,1,0); + H=(0,0,0); + A-D=(0,0,0.5); + C-D=G-H; + E-H=A-D; + F-E=(0,0.6,0); + B-A=F-E; + NbS:=8; + Sommet1:=A; + Sommet2:=B; + Sommet3:=C; + Sommet4:=D; + Sommet5:=E; + Sommet6:=F; + Sommet7:=G; + Sommet8:=H; + NF:=6; + Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2; + Fc[200]:=4;Fc[201]:=4;Fc[202]:=1;Fc[203]:=5;Fc[204]:=8; + Fc[300]:=4;Fc[301]:=4;Fc[302]:=8;Fc[303]:=7;Fc[304]:=3; + Fc[400]:=4;Fc[401]:=8;Fc[402]:=5;Fc[403]:=6;Fc[404]:=7; + Fc[500]:=4;Fc[501]:=1;Fc[502]:=2;Fc[503]:=6;Fc[504]:=5; + Fc[600]:=4;Fc[601]:=2;Fc[602]:=3;Fc[603]:=7;Fc[604]:=6; + CoulTrace:=gris; + DessineObjet; + drawoptions(withcolor gris); + draw codeperp(B,A,E,5); + draw codeperp(A,B,F,5); + draw codeperp(H,D,C,5); + draw codeperp(D,C,G,5); + drawoptions(); + draw polygone(A,B,C,D); + draw hachurage(polygone(A,B,C,D),60,0.3,0); + draw segment(A,E); + draw appelation(A,E,3mm,btex hauteur etex); + \end{mpost} + \fi +} + +\def\MPFigureCylindre{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,0,20,\useKV[ClesFormule]{EchelleEspace}); + color O,O',A,A',B,B',C,C'; + O=(0,0,0); + O'-O=(0,0,1); + A-O=(0,1,0); + A'-A=O'-O; + C=symetrie(A,O); + C'-C=O'-O; + B-O=(-1/2,0,0); + B'-B=O'-O; + path cc,cd; + cc=cercles(O,A,O,A,B); + cd=cercles(O',A',O',A',B'); + draw cd; + draw segment(C,C'); + draw segment(A,A'); + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw segment(O,A); + draw cotationmil(C,C',3mm,25,btex hauteur $h$ etex); + draw appelation(O,A,2mm,btex rayon $r$ etex); + marque_p:="croix"; + pointe(O); + marque_p:="non"; + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,0,20,70); + color O,O',A,A',B,B',C,C'; + O=(0,0,0); + O'-O=(0,0,1); + A-O=(0,1,0); + A'-A=O'-O; + C=symetrie(A,O); + C'-C=O'-O; + B-O=(-1/2,0,0); + B'-B=O'-O; + path cc,cd; + cc=cercles(O,A,O,A,B); + cd=cercles(O',A',O',A',B'); + draw cd; + draw segment(C,C'); + draw segment(A,A'); + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw segment(O,A); + draw cotationmil(C,C',3mm,25,btex hauteur $h$ etex); + draw appelation(O,A,2mm,btex rayon $r$ etex); + marque_p:="croix"; + pointe(O); + marque_p:="non"; + \end{mpost} + \fi +} + +\def\MPFigureCone{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,0,10,\useKV[ClesFormule]{EchelleEspace}); + color O,O',A,B,C; + O=(0,0,0); + O'-O=(0,0,1.5); + A-O=(0,1,0); + C=symetrie(A,O); + B-O=(-1/2,0,0); + path cc; + cc=cercles(O,A,O,A,B); + draw chemin(C,O',A); + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw chemin(O',O,A); + draw appelation(O,O',2mm,btex hauteur etex); + draw appelation(O,A,1mm,btex rayon $r$ etex); + marque_p:="croix"; + pointe(O); + marque_p:="non"; + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,0,10,70); + color O,O',A,B,C; + O=(0,0,0); + O'-O=(0,0,1.5); + A-O=(0,1,0); + C=symetrie(A,O); + B-O=(-1/2,0,0); + path cc; + cc=cercles(O,A,O,A,B); + draw chemin(C,O',A); + draw (subpath(0,length cc/2) of cc) dashed evenly; + draw subpath(length cc/2,length cc) of cc; + draw chemin(O',O,A); + draw appelation(O,O',2mm,btex hauteur etex); + draw appelation(O,A,1mm,btex rayon $r$ etex); + marque_p:="croix"; + pointe(O); + marque_p:="non"; + \end{mpost} + \fi +} + +\def\MPFigurePyramide{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + u:=0.5cm; + z0=(-0.5,0)*u; + z1=(2.5,0.5)*u; + z2=(4,2)*u; + z3=(-0.5,2.75)*u; + z4=(-3,1.5)*u; + z5=(0.5,6)*u; + z6=(0.5,1.5)*u; + z7=z6 shifted (5u,0); + draw z5--z0 withcolor gris; + draw z5--z1 withcolor gris; + draw z5--z2 withcolor gris; + draw z5--z4 withcolor gris; + draw z5--z3 dashed evenly withcolor gris; + draw hachurage(polygone(z4,z0,z1,z2,z3,z4),60,0.4,0); + remplis codeperp(z7,z6,z5,8)--z6--cycle withcolor white; + draw z4--z0--z1--z2; + draw z2--z3--z4 dashed evenly; + draw z5--z6 dashed evenly; + draw codeperp(z7,z6,z5,8); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + Figure(-10u,-10u,10u,10u); + u:=0.5cm; + z0=(-0.5,0)*u; + z1=(2.5,0.5)*u; + z2=(4,2)*u; + z3=(-0.5,2.75)*u; + z4=(-3,1.5)*u; + z5=(0.5,6)*u; + z6=(0.5,1.5)*u; + z7=z6 shifted (5u,0); + draw z5--z0 withcolor gris; + draw z5--z1 withcolor gris; + draw z5--z2 withcolor gris; + draw z5--z4 withcolor gris; + draw z5--z3 dashed evenly withcolor gris; + draw hachurage(polygone(z4,z0,z1,z2,z3,z4),60,0.4,0); + remplis codeperp(z7,z6,z5,8)--z6--cycle withcolor white; + draw z4--z0--z1--z2; + draw z2--z3--z4 dashed evenly; + draw z5--z6 dashed evenly; + draw codeperp(z7,z6,z5,8); + \end{mpost} + \fi +} + +\def\MPFigureCube{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,80); + color A,B,C,D,E,F,G,H; + draw Cube(A,B,C,D,E,F,G,H) withcolor gris; + draw segment(E,H); + draw appelation(E,H,2mm,btex $a$ etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={v:=\useKV[ClesFormule]{EchelleEspace};}] + typetrace:="3D"; + typerepre:="persp"; + Figure(-10u,-10u,10u,10u); + Initialisation(5,30,20,80); + color A,B,C,D,E,F,G,H; + draw Cube(A,B,C,D,E,F,G,H) withcolor gris; + draw segment(E,H); + draw appelation(E,H,2mm,btex $a$ etex); + \end{mpost} + \fi +} + +\def\MPFigureLosange{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0.5); + D=rotation(B,A,40); + C-D=B-A; + draw polygone(A,B,C,D); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $c$ etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0.5); + D=rotation(B,A,40); + C-D=B-A; + draw polygone(A,B,C,D); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $c$ etex); + \end{mpost} + \fi +} + +\def\MPFigureLosangeAire{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0.5); + D=rotation(B,A,40); + C-D=B-A; + draw polygone(A,B,C,D) withcolor gris; + draw segment(A,C); + draw segment(B,D); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0.5); + D=rotation(B,A,40); + C-D=B-A; + draw polygone(A,B,C,D) withcolor gris; + draw segment(A,C); + draw segment(B,D); + marque_s:=marque_s/3; + draw Codelongueur(A,B,B,C,C,D,D,A,2); + marque_s:=marque_s*3; + \end{mpost} + \fi +} + +\def\MPFigureRectangle{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(3,0); + C=2/3[B,rotation(A,B,-90)]; + D-C=A-B; + draw polygone(A,B,C,D); + draw codeperp(A,B,C,5); + draw codeperp(B,C,D,5); + draw codeperp(C,D,A,5); + draw codeperp(D,A,B,5); + marque_s:=marque_s/3; + draw Codelongueur(A,B,C,D,2); + draw Codelongueur(A,D,C,B,5); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $L$ etex); + label.lft(btex $\ell$ etex,iso(A,D)); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + pair A,B,C,D; + A=u*(1,1); + B-A=u*(3,0); + C=2/3[B,rotation(A,B,-90)]; + D-C=A-B; + draw polygone(A,B,C,D); + draw codeperp(A,B,C,5); + draw codeperp(B,C,D,5); + draw codeperp(C,D,A,5); + draw codeperp(D,A,B,5); + marque_s:=marque_s/3; + draw Codelongueur(A,B,C,D,2); + draw Codelongueur(A,D,C,B,5); + marque_s:=marque_s*3; + draw appelation(A,B,-3mm,btex $L$ etex); + label.lft(btex $\ell$ etex,iso(A,D)); + \end{mpost} + \fi +} + +\def\MPFigureTriangle{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(1,1); + B-A=u*(3,0); + C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + draw polygone(A,B,C); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(1,1); + B-A=u*(3,0); + C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + draw polygone(A,B,C); + \end{mpost} + \fi +} + +\def\MPFigureCercle{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(2.5,2.5); + path cc; + cc=cercles(A,1.25u); + B=pointarc(cc,195); + C=symetrie(B,A); + draw cc withcolor gris; + draw segment(B,C); + marque_p:="croix"; + pointe(A); + draw appelation(B,C,3mm,btex diam\`etre etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(2.5,2.5); + path cc; + cc=cercles(A,1.25u); + B=pointarc(cc,195); + C=symetrie(B,A); + draw cc withcolor gris; + draw segment(B,C); + marque_p:="croix"; + pointe(A); + draw appelation(B,C,3mm,\btex diam\`etre etex); + \end{mpost} + \fi +} + +\def\MPFigureDisque{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(2.5,2.5); + path cc; + cc=cercles(A,1.25u); + B=pointarc(cc,195); + C=symetrie(B,A); + draw cc withcolor gris; + draw segment(A,C); + marque_p:="croix"; + pointe(A); + draw appelation(A,C,3mm,btex rayon $r$ etex); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C; + A=u*(2.5,2.5); + path cc; + cc=cercles(A,1.25u); + B=pointarc(cc,195); + C=symetrie(B,A); + draw cc withcolor gris; + draw segment(A,C); + marque_p:="croix"; + pointe(A); + draw appelation(A,C,3mm,\btex rayon $r$ etex); + \end{mpost} + \fi +} + +\def\MPFigureTriangleAire{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} +u:=\useKV[ClesFormule]{Echelle}; + drawoptions( dashed dashpattern(on1cm)); + pair A,B,C,H,I,J; + A=u*(0.5,1); + B-A=u*(1.4,0); + C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + H=projection(C,A,B); + I=projection(A,B,C); + J=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(C,H); + draw segment(A,B); + draw codeperp(C,H,B,5); + drawoptions(); + A:=A+u*(2.5,0); + B:=A+u*(1.4,0); + C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + I:=projection(A,B,C); + J:=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(A,I); + draw segment(C,B); + draw codeperp(A,I,B,5); + drawoptions(); + A:=A-u*(1.25,1); + B:=A+u*(1.4,0); + C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + J:=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(B,J); + draw segment(C,A); + draw codeperp(B,J,C,5); + drawoptions(); + \end{mplibcode} + \else + \begin{mpost}[mpsettings={u:=\useKV[ClesFormule]{Echelle};}] + Figure(-5u,-5u,5u,5u); + pair A,B,C,H,I,J; + A=u*(0.5,1); + B-A=u*(1.4,0); + C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + H=projection(C,A,B); + I=projection(A,B,C); + J=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(C,H); + draw segment(A,B); + draw codeperp(C,H,B,5); + drawoptions(); + A:=A+u*(2.5,0); + B:=A+u*(1.4,0); + C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + I:=projection(A,B,C); + J:=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(A,I); + draw segment(C,B); + draw codeperp(A,I,B,5); + drawoptions(); + A:=A-u*(1.25,1); + B:=A+u*(1.4,0); + C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45)); + J:=projection(B,C,A); + draw polygone(A,B,C) withcolor gris; + drawoptions(); + draw segment(B,J); + draw segment(C,A); + draw codeperp(B,J,C,5); + drawoptions(); + \end{mpost} + \fi +}% + +\newcommand\Formule[1][]{% + \useKVdefault[ClesFormule]% + \setKV[ClesFormule]{#1}% + \setlength{\RoundedBoxWidth}{\useKV[ClesFormule]{Largeur}}% + \xdef\ColorFill{\useKV[ClesFormule]{Couleur}}% + \ifboolKV[ClesFormule]{Perimetre}{% + \begin{tikzpicture}[remember picture, overlay] + \node[draw,fill=\ColorFill,dashed,rounded corners,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \IfStrEqCase{\useKV[ClesFormule]{Surface}}{% + {carre}{\begin{center} + \MPFigureCarre\par + P\'erim\`etre d'un carr\'e :\par$4\times c$ + \end{center}}% + {polygone}{% + \begin{center} + \MPFigurePolygone\par + P\'erim\`etre d'un polygone : \par$\text{Somme des c\^ot\'es}$ + \end{center} + }% + {rectangle}{% + \begin{center} + \MPFigureRectangle\par + P\'erim\`etre d'un rectangle : \par$2\times(L+\ell)$ + \end{center} + }% + {losange}{% + \begin{center} + \MPFigureLosange\par + P\'erim\`etre d'un losange : \par$4\times c$ + \end{center} + }% + {triangle}{% + \begin{center} + \MPFigureTriangle\par + P\'erim\`etre d'un triangle : \par Somme des c\^ot\'es + \end{center} + }% + {cercle}{% + \begin{center} + \MPFigureCercle\par + P\'erim\`etre d'un cercle : \par$\pi\times\text{diam\`etre}$ + \end{center} + }% + {parallelogramme}{% + \begin{center} + \MPFigureParallelogramme\par + P\'erim\`etre d'un parall\'elogramme : \par Somme des c\^ot\'es + \end{center} + }} + \end{minipage}}; + \end{tikzpicture} + }{\ifboolKV[ClesFormule]{Aire}{% + \begin{tikzpicture}[remember picture, overlay] + \node[draw,fill=\ColorFill,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \IfStrEqCase{\useKV[ClesFormule]{Surface}}{% + {carre}{\begin{center} + \MPFigureCarre\par + Aire d'un carr\'e :\par$c\times c$ + \end{center}}% + {rectangle}{% + \begin{center} + \MPFigureRectangle\par + Aire d'un rectangle :\par$L\times\ell$ + \end{center} + }% + {losange}{% + \begin{center} + \MPFigureLosangeAire\par + Aire d'un losange :\par$\dfrac{\text{grande diagonale}\times\text{petite diagonale}}{2}$ + \end{center} + }% + {triangle}{% + \begin{center} + \MPFigureTriangleAire\par\vspace{1em}\par + Aire d'un triangle : $\displaystyle\frac{\text{c\^ot\'e}\times\text{hauteur relative \`a ce c\^ot\'e}}{2}$ + \end{center} + }% + {disque}{% + \begin{center} + \MPFigureDisque\par + Aire d'un disque :\par$\pi\times r\times r$ + \end{center} + }% + {parallelogramme}{% + \begin{center} + \MPFigureParallelogrammeAire\par + Aire d'un parall\'elogramme : $\text{c\^ot\'e}\times\text{hauteur relative \`a ce c\^ot\'e}$ + \end{center} + } + {sphere}{% + \begin{center} + \MPFigureSphere\par + Aire d'une sph\`ere : $4\times\pi\times r^2$ + \end{center} + }} + \end{minipage}}; + \end{tikzpicture} + }{%Volume + \begin{tikzpicture}[remember picture, overlay] + \node[draw,fill=\ColorFill,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \IfStrEqCase{\useKV[ClesFormule]{Solide}}{% + {boule}{\begin{center} + \MPFigureSphere\par + Volume d'une boule : $\dfrac{4\times\pi\times r^3}{3}$ + \end{center}}% + {cube}{% + \begin{center} + \MPFigureCube\par + Volume d'un cube : $a^3\quad(a\times a\times a)$ + \end{center} + }% + {pave}{% + \begin{center} + \MPFigurePave\par + Volume d'un pav\'e droit : $\ell\times h\times p$ + \end{center} + } + {prisme}{% + \begin{center} + \MPFigurePrisme\par + Volume d'un prisme droit : $\text{Aire de la base}\times\mbox{hauteur}$ + \end{center} + } + {cylindre}{% + \begin{center} + \MPFigureCylindre\par + Volume d'un cylindre de r\'evolution : $\pi\times r^2\times h$ + \end{center} + } + {pyramide}{% + \begin{center} + \MPFigurePyramide\par + Volume d'une pyramide : $\dfrac{\text{Aire de la base}\times\text{hauteur}}{3}$ + \end{center} + } + {cone}{% + \begin{center} + \MPFigureCone\par + Volume d'un c\^one de r\'evolution : $\displaystyle\dfrac{\pi\times r^2\times h}{3}$ + \end{center} + } + } + \end{minipage}}; + \end{tikzpicture} + }% + }% +}%
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