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-rw-r--r--Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-angles.tex323
1 files changed, 240 insertions, 83 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-angles.tex b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-angles.tex
index f4516e05d38..d67ea4cc8d8 100644
--- a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-angles.tex
+++ b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-angles.tex
@@ -1,27 +1,27 @@
-\section{Les angles}
+\section{The angles}
-\subsection{Colorier un angle : fill}
+\subsection{Colour an angle: fill}
-L'opération la plus simple
-\begin{NewMacroBox}{tkzFillAngle}{\oarg{local options}\parg{A,O,B}}
-O est le sommet de l'angle. OA et OB sont les côtés. Attention l'angle est déterminé avec l'ordre des points.
+The simplest operation
+\begin{NewMacroBox}{tkzFillAngle}{\oarg{local options}\parg{A,O,B}}%
+$O$ is the vertex of the angle. $OA$ and $OB$ are the sides. Attention the angle is determined by the order of the points.
\medskip
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
-\TOline{size}{1 cm}{cette option détermine le rayon du secteur angulaire colorié}
+\TOline{size}{1 cm}{this option determines the radius of the coloured angular sector.}
\bottomrule
\end{tabular}
\medskip
-Il faut ajouter bien sûr tous les styles de \TIKZ\ comme par exemple l'usage de fill \index{fill} ou encore shade \index{shade}
+Of course, you have to add all the styles of \TIKZ, like the use of fill and shade...
\end{NewMacroBox}
-\subsubsection{Exemple avec \tkzname{size}}
+\subsubsection{Example with \tkzname{size}}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
\tkzInit
@@ -33,7 +33,7 @@ Il faut ajouter bien sûr tous les styles de \TIKZ\ comme par exemple l'usage d
\end{tkzexample}
-\subsubsection{Changement de l'ordre des points}
+\subsubsection{Changing the order of items}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
\tkzInit
@@ -56,8 +56,8 @@ Il faut ajouter bien sûr tous les styles de \TIKZ\ comme par exemple l'usage d
\end{tikzpicture}
\end{tkzexample}
-\begin{NewMacroBox}{tkzFillAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}
-Avec des options communes, il existe une macro pour de mutiples angles
+\begin{NewMacroBox}{tkzFillAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}%
+With common options, there is a macro for multiple angles.
\end{NewMacroBox}
\subsubsection{Multiples angles}
@@ -87,13 +87,12 @@ Avec des options communes, il existe une macro pour de mutiples angles
\end{tikzpicture}
\end{tkzexample}
- \newpage
-\subsection{Marquer un angle mark}
-Opération plus délicate car les options sont nombreuses. Les symboles utilisés pour le marquage outre ceux de TikZ sont définis dans le fichier |tkz-lib-marks.tex| et désignés par les caractères suivants:\begin{tkzltxexample}[]
+\subsection{Mark an angle mark}
+More delicate operation because there are many options. The symbols used for marking in addition to those of \TIKZ\ are defined in the file |tkz-lib-marks.tex| and designated by the following characters:\begin{tkzltxexample}[]
|, ||,|||, z, s, x, o, oo
\end{tkzltxexample}
-Leurs définitions est la suivante
+Their definitions are as follows
\begin{tkzltxexample}[]
\pgfdeclareplotmark{||}
@@ -205,7 +204,6 @@ Leurs définitions est la suivante
}
\end{tkzltxexample}
-\newpage
% \tkzMarkAngle(B, A, C)
@@ -230,25 +228,25 @@ Leurs définitions est la suivante
% mark : none , |, ||,|||, z, s, x, o, oo mais tous les
% % symboles de tikz sont permis
-\begin{NewMacroBox}{tkzMarkAngle}{\oarg{local options}\parg{A,O,B}}
-O est le sommet. Attention les arguments varient en fonction des options. Plusieurs marquages sont possibles. Vous pouvez simplement tracer un arc ou bian ajouter une marque sur cet arc. Le style de l'arc est choisi avec l'option \tkzname{arc}, le rayon de l'arc est donné par \tkzname{mksize}, l'arc peut bien sûr être colorié.
+\begin{NewMacroBox}{tkzMarkAngle}{\oarg{local options}\parg{A,O,B}}%
+$O$ is the vertex. Attention the arguments vary according to the options. Several markings are possible. You can simply draw an arc or add a mark on this arc. The style of the arc is chosen with the option \tkzname{arc}, the radius of the arc is given by \tkzname{mksize}, the arc can, of course, be colored.
\medskip
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
-\TOline{arc}{l}{choix parmi l, ll et lll simple, double ou triple.}
-\TOline{size}{1 cm}{rayon de l'arc.}
-\TOline{mark}{none}{choix parmi s.}
-\TOline{mksize}{4pt}{taille du symbol (mark).}
-\TOline{mkcolor}{black}{couleur du symbole (mark).}
-\TOline{mkpos}{0.5}{position du symbole sur l'arc.}
+\TOline{arc}{l}{choice of l, ll and lll (single, double or triple).}
+\TOline{size}{1 cm}{arc radius.}
+\TOline{mark}{none}{choice of mark.}
+\TOline{mksize}{4pt}{symbol size (mark).}
+\TOline{mkcolor}{black}{symbol color (mark).}
+\TOline{mkpos}{0.5}{position of the symbol on the arc.}
\end{tabular}
\end{NewMacroBox}
-\subsubsection{Exemple avec \tkzname{mark = x}}
+\subsubsection{Example with \tkzname{mark = x}}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.75]
\tkzDefPoints{0/0/O,5/0/A,3/4/B}
@@ -259,7 +257,7 @@ options & default & definition \\
\end{tikzpicture}
\end{tkzexample}
\DeleteShortVerb{\|}
-\subsubsection{Exemple avec \tkzname{mark =||}}
+\subsubsection{Example with \tkzname{mark =||}}
\MakeShortVerb{\|}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.75]
@@ -271,29 +269,29 @@ options & default & definition \\
\end{tikzpicture}
\end{tkzexample}
-\begin{NewMacroBox}{tkzMarkAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}
-Avec des options communes, il existe une macro pour de mutiples angles
+\begin{NewMacroBox}{tkzMarkAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}%
+With common options, there is a macro for multiple angles.
\end{NewMacroBox}
-\subsection{Label dans un angle}
+\subsection{Label at an angle}
-\begin{NewMacroBox}{tkzLabelAngle}{\oarg{local options}\parg{A,O,B}}
-Une seule option \tkzname{dist} qui n'est pas indispensable car l'option \tkzname{pos} de \TIKZ\ fonctionne très bien.
+\begin{NewMacroBox}{tkzLabelAngle}{\oarg{local options}\parg{A,O,B}}%
+There is only one option, dist (with or without unit), which can be replaced by the TikZ's pos option (without unit for the latter). By default, the value is in centimeters.
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
-\TOline{pos}{1}{ ou dist, permet de contrôler la distance du sommet au label.}
+\TOline{pos}{1}{ or dist, controls the distance from the top to the label.}
\bottomrule
\end{tabular}
\medskip
-Il est possible de déplacer le label avec toutes les options de TikZ : rotate, shift, below, etc.
+It is possible to move the label with all TikZ options : rotate, shift, below, etc.
\end{NewMacroBox}
-\subsubsection{Exemple avec \tkzname{pos}}
+\subsubsection{Example with \tkzname{pos}}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.75]
\tkzDefPoints{0/0/O,5/0/A,3/4/B}
@@ -330,42 +328,43 @@ Il est possible de déplacer le label avec toutes les options de TikZ : rotate,
\end{tikzpicture}
\end{tkzexample}
-\begin{NewMacroBox}{tkzLabelAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}
-Avec des options communes, il existe une macro pour de mutiples angles
- \end{NewMacroBox}
+\begin{NewMacroBox}{tkzLabelAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}%
+With common options, there is a macro for multiple angles.
+\end{NewMacroBox}
-\subsection{Marquer un angle droit}
+\subsection{Marking a right angle}
+
+\begin{NewMacroBox}{tkzMarkRightAngle}{\oarg{local options}\parg{A,O,B}}%
+The \tkzname{german} option allows you to change the style of the drawing. The option \tkzname{size} allows to change the size of the drawing.
-\begin{NewMacroBox}{tkzMarkRightAngle}{\oarg{local options}\parg{A,O,B}}
-L'option \tkzname{german} permet de changer le style du dessin. L'option \tkzname{size} permet de modifier la taille du dessin.
-\begin{tabular}{lll}
+\medskip
+\begin{tabular}{lll}%
\toprule
-options & default & definition \\
+options & default & definition \\
\midrule
-\TOline{german}{normal}{ german arc avec point intérieur.}
-\TOline{size}{0.2}{ taille d'un coté.}
+\TOline{german}{normal}{ german arc with inner point.}
+\TOline{size}{0.2}{ side size.}
\end{tabular}
\end{NewMacroBox}
-\subsubsection{Exemple de marquage d'un angle droit}
+\subsubsection{Example of marking a right angle}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}
\tkzDefPoints{0/0/A,3/1/B,0.9/-1.2/P}
\tkzDefPointBy[projection = onto B--A](P) \tkzGetPoint{H}
\tkzDrawLines[add=.5 and .5](P,H)
\tkzMarkRightAngle[fill=blue!20,size=.5,draw](A,H,P)
- \tkzDrawPoints[](A,B,P,H)
\tkzDrawLines[add=.5 and .5](A,B)
- \tkzMarkRightAngle[fill=red!20,size=.8](B,H,P)
+ \tkzMarkRightAngle[fill=red!20,size=.8](B,H,P)
+ \tkzDrawPoints[](A,B,P,H)
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Exemple de marquage d'un angle droit, german style}
+\subsubsection{Example of marking a right angle, german style}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}
\tkzDefPoints{0/0/A,3/1/B,0.9/-1.2/P}
\tkzDefPointBy[projection = onto B--A](P) \tkzGetPoint{H}
- \pgfresetboundingbox
\tkzDrawLines[add=.5 and .5](P,H)
\tkzMarkRightAngle[german,size=.5,draw](A,H,P)
\tkzDrawPoints[](A,B,P,H)
@@ -374,7 +373,7 @@ options & default & definition \\
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Mélange de styles}
+\subsubsection{Mix of styles}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.75]
\tkzDefPoint(0,0){A}
@@ -392,7 +391,7 @@ options & default & definition \\
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Exemple complet}
+\subsubsection{Full example}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[rotate=-90]
@@ -422,21 +421,72 @@ options & default & definition \\
\end{tkzexample}
\subsection{\tkzcname{tkzMarkRightAngles}}
-\begin{NewMacroBox}{tkzMarkRightAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}
-Avec des options communes, il existe une macro pour de mutiples angles
- \end{NewMacroBox}
-
-\subsection{\tkzcname{tkzGetAngle}}
-\begin{NewMacroBox}{tkzGetAngle}{\parg{macro}}
-Attribue la valeur d'un angle à une macro.
- \end{NewMacroBox}
-
-\subsection{\tkzcname{tkzFindAngle}}
-\begin{NewMacroBox}{tkzFindAngle}{\parg{A,O,B}}
-Détermine la valeur de l'angle en degrés.
- \end{NewMacroBox}
+\begin{NewMacroBox}{tkzMarkRightAngles}{\oarg{local options}\parg{A,O,B}\parg{A',O',B'}etc.}%
+With common options, there is a macro for multiple angles.
+\end{NewMacroBox}
+
+\section{Angles tools}
+
+\subsection{Recovering an angle \tkzcname{tkzGetAngle}}
+\begin{NewMacroBox}{tkzGetAngle}{\parg{name of macro}}%
+Assigns the value in degree of an angle to a macro. This macro retrieves \tkzcname{tkzAngleResult} and stores the result in a new macro.
+
+\medskip
+
+\begin{tabular}{lll}%
+\toprule
+arguments & example & explication \\
+\midrule
+\TAline{name of macro} {\tkzcname{tkzGetAngle}\{ang\}}{\tkzcname{ang} contains the value of the angle.}
+\end{tabular}
+\end{NewMacroBox}
+
+\subsection{Example of the use of \tkzcname{tkzGetAngle}}
+
+ The point here is that $(AB)$ is the bisector of $\widehat{CAD}$, such that the $AD$ slope is zero. We recover the slope of $(AB)$ and then rotate twice.
+
+
+\begin{tkzexample}[vbox,small]
+\begin{tikzpicture}
+ \tkzInit
+ \tkzDefPoint(1,5){A} \tkzDefPoint(5,2){B}
+ \tkzDrawSegment(A,B)
+ \tkzFindSlopeAngle(A,B)\tkzGetAngle{tkzang}
+ \tkzDefPointBy[rotation= center A angle \tkzang ](B)
+ \tkzGetPoint{C}
+ \tkzDefPointBy[rotation= center A angle -\tkzang ](B)
+ \tkzGetPoint{D}
+ \tkzCompass[length=1,dashed,color=red](A,C)
+ \tkzCompass[delta=10,brown](B,C)
+ \tkzDrawPoints(A,B,C,D)
+ \tkzLabelPoints(B,C,D)
+ \tkzLabelPoints[above left](A)
+ \tkzDrawSegments[style=dashed,color=orange!30](A,C A,D)
+\end{tikzpicture}
+\end{tkzexample}
+
+
+
+\subsection{Angle formed by three points}
+
+\begin{NewMacroBox}{tkzFindAngle}{\parg{pt1,pt2,pt3}}%
+The result is stored in a macro \tkzcname{tkzAngleResult}.
+
+\medskip
+
+\begin{tabular}{lll}%
+\toprule
+arguments & example & explication \\
+\midrule
+\TAline{(pt1,pt2,pt3)} {\tkzcname{tkzFindAngle}(A,B,C)}{\tkzcname{tkzAngleResult} gives the angle ($\overrightarrow{BA},\overrightarrow{BC}$)}
+\bottomrule
+\end{tabular}
+
+\medskip
+The result is between -180 degrees and +180 degrees. pt2 is the vertex and \tkzcname{tkzGetAngle} can retrieve the angle.
+\end{NewMacroBox}
-\subsubsection{Vérication de la mesure d'un angle}
+\subsubsection{Verification of angle measurement}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.75]
@@ -456,7 +506,32 @@ Détermine la valeur de l'angle en degrés.
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Détermination des trois angles d'un triangle}
+\subsection{Example of the use of \tkzcname{tkzFindAngle} }
+
+\begin{tkzexample}[vbox,small]
+\begin{tikzpicture}
+ \tkzInit[xmin=-1,ymin=-1,xmax=7,ymax=7]
+ \tkzClip
+ \tkzDefPoint (0,0){O} \tkzDefPoint (6,0){A}
+ \tkzDefPoint (5,5){B} \tkzDefPoint (3,4){M}
+ \tkzFindAngle (A,O,M) \tkzGetAngle{an}
+ \tkzDefPointBy[rotation=center O angle \an](A)
+ \tkzGetPoint{C}
+ \tkzDrawSector[fill = blue!50,opacity=.5](O,A)(C)
+ \tkzFindAngle(M,B,A) \tkzGetAngle{am}
+ \tkzDefPointBy[rotation = center O angle \am](A)
+ \tkzGetPoint{D}
+ \tkzDrawSector[fill = red!50,opacity = .5](O,A)(D)
+ \tkzDrawPoints(O,A,B,M,C,D)
+ \tkzLabelPoints(O,A,B,M,C,D)
+ \edef\an{\fpeval{round(\an,2)}}\edef\am{\fpeval{round(\am,2)}}
+ \tkzDrawSegments(M,B B,A)
+ \tkzText(4,2){$\widehat{AOC}=\widehat{AOM}=\an^{\circ}$}
+ \tkzText(1,4){$\widehat{AOD}=\widehat{MBA}=\am^{\circ}$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\subsubsection{Determination of the three angles of a triangle}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=1.25,rotate=30]
@@ -484,32 +559,114 @@ Détermine la valeur de l'angle en degrés.
\end{tikzpicture}
\end{tkzexample}
-\subsection{\tkzcname{tkzFindSlopeAngle}}
-\begin{NewMacroBox}{tkzFindSlopeAngle}{\parg{A,B}}
-Détermine la pente de la droite (AB).
- \end{NewMacroBox}
+ \subsection{Determining a slope}
+It is a question of determining whether it exists, the slope of a straight line defined by two points. No verification of the existence is made.
+
+\begin{NewMacroBox}{tkzFindSlope}{\parg{pt1,pt2}\marg{name of macro}}%
+The result is stored in a macro.
+
+\medskip
+
+\begin{tabular}{lll}%
+\toprule
+arguments & example & explication \\
+\midrule
+\TAline{(pt1,pt2){pt3}} {\tkzcname{tkzFindSlope}(A,B)\{slope\}}{\tkzcname{slope} will give the result of $\frac{y_B-y_A}{x_B-x_A}$} \\
+\bottomrule
+\end{tabular}
+
+\medskip
+\tkzHandBomb\ Careful not to have $x_B=x_A$.
+\end{NewMacroBox}
+
+
+\begin{tkzexample}[latex=7cm,small]
+\begin{tikzpicture}[scale=1.5]
+ \tkzInit[xmax=4,ymax=5]\tkzGrid[sub]
+ \tkzDefPoint(1,2){A} \tkzDefPoint(3,4){B}
+ \tkzDefPoint(3,2){C} \tkzDefPoint(3,1){D}
+ \tkzDrawSegments(A,B A,C A,D)
+ \tkzDrawPoints[color=red](A,B,C,D)
+ \tkzLabelPoints(A,B,C,D)
+ \tkzFindSlope(A,B){SAB} \tkzFindSlope(A,C){SAC}
+ \tkzFindSlope(A,D){SAD}
+ \pgfkeys{/pgf/number format/.cd,fixed,precision=2}
+ \tkzText[fill=Gold!50,draw=brown](1,4)%
+ {The slope of (AB) is : $\pgfmathprintnumber{\SAB}$}
+ \tkzText[fill=Gold!50,draw=brown](1,3.5)%
+ {The slope of (AC) is : $\pgfmathprintnumber{\SAC}$}
+ \tkzText[fill=Gold!50,draw=brown](1,3)%
+ {The slope of (AD) is : $\pgfmathprintnumber{\SAD}$}
+\end{tikzpicture}
+\end{tkzexample}
+
+\subsection{Angle formed by a straight line with the horizontal axis \tkzcname{tkzFindSlopeAngle}}
+Much more interesting than the last one. The result is between -180 degrees and +180 degrees.
+
+\begin{NewMacroBox}{tkzFindSlopeAngle}{\parg{A,B}}%
+Determines the slope of the straight line (AB). The result is stored in a macro \tkzcname{tkzAngleResult}.
+
+\medskip
+\begin{tabular}{lll}%
+\toprule
+arguments & example & explication \\
+\midrule
+\TAline{(pt1,pt2)} {\tkzcname{tkzFindSlopeAngle}(A,B)}{}
+\bottomrule
+\end{tabular}
+
+\medskip
+\tkzcname{tkzGetAngle} can retrieve the result. If retrieval is not necessary, you can use \tkzcname{tkzAngleResult}.
+\end{NewMacroBox}
- \subsubsection{Pliage}
+ \subsubsection{Folding}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}
\tkzDefPoint(1,5){A}
- \tkzDefPoint(5,2){B} \tkzDrawSegment(A,B)
- \tkzFindSlopeAngle(A,B)\tkzGetAngle{tkzang}
+ \tkzDefPoint(5,2){B}
+ \tkzDrawSegment(A,B)
+ \tkzFindSlopeAngle(A,B)
+ \tkzGetAngle{tkzang}
\tkzDefPointBy[rotation= center A angle \tkzang ](B)
\tkzGetPoint{C}
\tkzDefPointBy[rotation= center A angle -\tkzang ](B)
\tkzGetPoint{D}
- \tkzCompass[length=1](A,C)
- \tkzCompass[delta=10](B,C) \tkzDrawPoints(A,B,C,D)
- \tkzLabelPoints(B,C,D) \tkzLabelPoints[above left](A)
+ \tkzCompass[orange,length=1](A,C)
+ \tkzCompass[orange,delta=10](B,C)
+ \tkzDrawPoints(A,B,C,D)
+ \tkzLabelPoints(B,C,D)
+ \tkzLabelPoints[above left](A)
\tkzDrawSegments[style=dashed,color=orange](A,C A,D)
\end{tikzpicture}
\end{tkzexample}
+\subsubsection{Example of the use of \tkzcname{tkzFindSlopeAngle}}
+Here is another version of the construction of a mediator
+
+\begin{tkzexample}[latex=6cm,small]
+\begin{tikzpicture}
+ \tkzInit
+ \tkzDefPoint(0,0){A}
+ \tkzDefPoint(3,2){B}
+ \tkzDefLine[mediator](A,B)
+ \tkzGetPoints{I}{J}
+ \tkzCalcLength[cm](A,B)
+ \tkzGetLength{dAB}
+ \tkzFindSlopeAngle(A,B)
+ \tkzGetAngle{tkzangle}
+ \begin{scope}[rotate=\tkzangle]
+ \tikzset{arc/.style={color=gray,delta=10}}
+ \tkzDrawArc[orange,R,arc](B,3/4*\dAB)(120,240)
+ \tkzDrawArc[orange,R,arc](A,3/4*\dAB)(-45,60)
+ \tkzDrawLine(I,J)
+ \tkzDrawSegment(A,B)
+ \end{scope}
+ \tkzDrawPoints(A,B,I,J)
+ \tkzLabelPoints(A,B)
+ \tkzLabelPoints[right](I,J)
+\end{tikzpicture}
+\end{tkzexample}
\endinput
-% \tkzGetAngle
-% \tkzNormalizeAngle
-% \tkzFindSlopeAngle
-% \tkzFindAngle
+