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authorNorbert Preining <norbert@preining.info>2024-03-27 03:02:20 +0000
committerNorbert Preining <norbert@preining.info>2024-03-27 03:02:20 +0000
commit31fa8cd73bab8480d38dae3a89ca578f337d6bbd (patch)
treeba550e99e0cb15dbf5405369d536b12b051c5155 /macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
parent904f56f2c26edc7eb11d5a27579bccbeca29c618 (diff)
CTAN sync 202403270302
Diffstat (limited to 'macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex')
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex332
1 files changed, 243 insertions, 89 deletions
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
index 9261d6fbe7..f54a53f39e 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
@@ -1,6 +1,6 @@
\newpage
-\section{Classe \Iclass{triangle}} % (fold)
-\label{sec:classe_triangle}
+\section{Class \Iclass{triangle}} % (fold)
+\label{sec:class_triangle}
\subsection{Attributes of a triangle} % (fold)
\label{sub:attributes_of_a_triangle}
@@ -8,7 +8,7 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\begin{mybox}
Creation | T.ABC = triangle : new ( z.A , z.B , z.C ) |
\end{mybox}
-(See examples: \ref{sub:alternate}; \ref{sub:apollonius_circle}; \ref{sub:excircles} ). Multiple attributes are then created.
+(Refer to examples: \ref{sub:alternate}; \ref{sub:apollonius_circle}; \ref{sub:excircles} ). Multiple attributes are then created.
\bgroup
\catcode`_=12
@@ -44,7 +44,7 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\label{sub:triangle_attributes_angles}
\begin{minipage}{.6\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new(0,0)
z.B = point: new(5,0)
@@ -60,7 +60,7 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\tkzLabelAngle(C,B,A){$\wangle{beta}^\circ$}
\tkzLabelAngle(A,C,B){$\wangle{gamma}^\circ$}
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.4\textwidth}
\begin{tkzelements}
@@ -83,64 +83,64 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\subsubsection{Example: triangle attributes} % (fold)
\label{ssub:example_triangle_attributes}
\begin{minipage}{.5\textwidth}
- \begin{verbatim}
- \begin{tkzelements}
- z.a = point: new (0 , 0)
- z.b = point: new (4 , 0)
- z.c = point: new (0 , 3)
- T.abc = triangle : new (z.a,z.b,z.c)
- z.O = T.abc.circumcenter
- z.I = T.abc.incenter
- z.H = T.abc.orthocenter
- z.G = T.abc.centroid
- a = T.abc.a
- b = T.abc.b
- c = T.abc.c
- alpha = T.abc.alpha
- beta = T.abc.beta
- gamma = T.abc.gamma
- \end{tkzelements}
- \begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawPolygon(a,b,c)
- \tkzDrawPoints(a,b,c,O,G,I,H)
- \tkzLabelPoints(a,b,c,O,G,I)
- \tkzLabelPoints[above right](H)
- \tkzDrawCircles(O,a)
- \tkzLabelSegment[sloped](a,b){\tkzUseLua{c}}
- \tkzLabelSegment[sloped,above](b,c){\tkzUseLua{a}}
- \end{tikzpicture}
- \end{verbatim}
+\begin{Verbatim}
+\begin{tkzelements}
+ z.A = point: new (0 , 0)
+ z.B = point: new (4 , 0)
+ z.C = point: new (0 , 3)
+ T.ABC = triangle : new (z.A,z.B,z.C)
+ z.O = T.ABC.circumcenter
+ z.I = T.ABC.incenter
+ z.H = T.ABC.orthocenter
+ z.G = T.ABC.centroid
+ a = T.ABC.a
+ b = T.ABC.b
+ c = T.ABC.c
+ alpha = T.ABC.alpha
+ beta = T.ABC.beta
+ gamma = T.ABC.gamma
+\end{tkzelements}
+\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawPoints(A,B,C,O,G,I,H)
+ \tkzLabelPoints[below](A,B,O,G,I)
+ \tkzLabelPoints[above right](H,C)
+ \tkzDrawCircles(O,A)
+ \tkzLabelSegment[sloped](A,B){\tkzUseLua{c}}
+ \tkzLabelSegment[sloped,above](B,C){\tkzUseLua{a}}
+\end{tikzpicture}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
- scale = 1.2
- z.a = point: new (0 , 0)
- z.b = point: new (4 , 0)
- z.c = point: new (0 , 3)
- T.abc = triangle : new (z.a,z.b,z.c)
- z.O = T.abc.circumcenter
- z.I = T.abc.incenter
- z.H = T.abc.orthocenter
- z.G = T.abc.centroid
- a = T.abc.a
- b = T.abc.b
- c = T.abc.c
- alpha = T.abc.alpha
- beta = T.abc.beta
- gamma = T.abc.gamma
-\end{tkzelements}
+ z.A = point: new (0 , 0)
+ z.B = point: new (4 , 0)
+ z.C = point: new (0 , 3)
+ T.ABC = triangle : new (z.A,z.B,z.C)
+ z.O = T.ABC.circumcenter
+ z.I = T.ABC.incenter
+ z.H = T.ABC.orthocenter
+ z.G = T.ABC.centroid
+ a = T.ABC.a
+ b = T.ABC.b
+ c = T.ABC.c
+ alpha = T.ABC.alpha
+ beta = T.ABC.beta
+ gamma = T.ABC.gamma
+\end{tkzelements}
\hspace*{\fill}
\begin{tikzpicture}
-\tkzGetNodes
-\tkzDrawPolygon(a,b,c)
-\tkzDrawPoints(a,b,c,O,G,I,H)
-\tkzLabelPoints(a,b,c,O,G,I)
-\tkzLabelPoints[above right](H)
-\tkzDrawCircles(O,a)
-\tkzLabelSegment[sloped](a,b){\tkzUseLua{c}}
-\tkzLabelSegment[sloped,above](b,c){\tkzUseLua{a}}
+ \tkzGetNodes
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawPoints(A,B,C,O,G,I,H)
+ \tkzLabelPoints[below](A,B,O,G,I)
+ \tkzLabelPoints[above right](H,C)
+ \tkzDrawCircles(O,A)
+ \tkzLabelSegment[sloped](A,B){\tkzUseLua{c}}
+ \tkzLabelSegment[sloped,above](B,C){\tkzUseLua{a}}
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsubsection example_triangle_attributes (end)
@@ -200,7 +200,7 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\Imeth{triangle}{first\_lemoine\_circle ()} & The center is the midpoint between Lemoine point and the circumcenter.\footnote{
Through the Lemoine point draw lines parallel to the triangle's sides. The points where the parallel lines intersect the sides of ABC
then lie on a circle known as the first Lemoine circle. } \\
-\Imeth{triangle}{second\_lemoine\_circle ()} & see example \ref{sub:antiparallel_through_lemoine_point}\\
+\Imeth{triangle}{second\_lemoine\_circle ()} & Refer to example \ref{sub:antiparallel_through_lemoine_point}\\
\Imeth{triangle}{spieker\_circle ()} & The incircle of the medial triangle\\
\bottomrule
@@ -210,7 +210,7 @@ Through the Lemoine point draw lines parallel to the triangle's sides. The point
Remark: If you don't need to use the triangle object several times, you can obtain a bisector or a altitude with the next functions
-|bisector (z.A,z.B,z.C)| and |altitude (z.A,z.B,z.C)| See (\ref{misc})
+|bisector (z.A,z.B,z.C)| and |altitude (z.A,z.B,z.C)| Refer to (\ref{misc})
\clearpage\newpage
\bgroup
@@ -238,7 +238,11 @@ Remark: If you don't need to use the triangle object several times, you can obta
\Imeth{triangle}{symmedian ()} & Triangle formed with the intersection points of the symmedians. \\
\Imeth{triangle}{euler ()} & Triangle formed with the euler points \\
\midrule
-\midrule
+ \textbf{Ellipses} &\\
+\Imeth{triangle}{steiner\_inellipse ()} & Refer to ex. (\ref{ssub:steiner_inellipse_and_circumellipse})\\
+\Imeth{triangle}{steiner\_circumellipse ()} & Refer to ex. (\ref{ssub:steiner_inellipse_and_circumellipse})\\
+\Imeth{triangle}{euler\_ellipse ()} & Refer to ex. (\ref{sub:euler_ellipse})\\
+ \midrule
\textbf{Miscellaneous} &\\
\midrule
\Imeth{triangle}{area ()} & $ \mathcal{A}$| = T.ABC: area ()|\\
@@ -256,7 +260,7 @@ Remark: If you don't need to use the triangle object several times, you can obta
\label{ssub:euler_line}
\begin{minipage}{.5\textwidth}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (6 , 0)
@@ -281,7 +285,7 @@ Remark: If you don't need to use the triangle object several times, you can obta
\tkzLabelPoints(A,B,C,I,J,K,P,Q,R,H)
\tkzLabelPoints[below](N,O,G)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -310,36 +314,186 @@ Remark: If you don't need to use the triangle object several times, you can obta
\tkzLabelPoints[below](N,O,G,H)
\end{tikzpicture}
\end{minipage}
-
-%\caption{Euler line}
% subsubsection euler_line (end)
+\subsection{Euler ellipse} % (fold)
+\label{sub:euler_ellipse}
+Example of obtaining the Euler circle as well as the Euler ellipse.
+
+\begin{tkzelements}
+z.A = point: new (2,3.8)
+z.B = point: new (0 ,0)
+z.C = point: new (6.2 ,0)
+L.AB = line : new ( z.A , z.B )
+T.ABC = triangle: new (z.A,z.B,z.C)
+z.K = midpoint (z.B,z.C)
+E.euler = T.ABC : euler_ellipse ()
+z.N = T.ABC.eulercenter
+C.euler = circle : new (z.N,z.K)
+ang = math.deg(E.euler.slope)
+z.O = T.ABC.circumcenter
+z.G = T.ABC.centroid
+z.H = T.ABC.orthocenter
+\end{tkzelements}
+
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+z.A = point: new (2,3.8)
+z.B = point: new (0 ,0)
+z.C = point: new (6.2 ,0)
+L.AB = line : new ( z.A , z.B )
+T.ABC = triangle: new (z.A,z.B,z.C)
+z.K = midpoint (z.B,z.C)
+E.euler = T.ABC : euler_ellipse ()
+z.N = T.ABC.eulercenter
+C.euler = circle : new (z.N,z.K)
+ang = math.deg(E.euler.slope)
+z.O = T.ABC.circumcenter
+z.G = T.ABC.centroid
+z.H = T.ABC.orthocenter
+\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircle(N,K)
+\tkzDrawEllipse[teal](N,\tkzUseLua{E.euler.Rx},
+ \tkzUseLua{E.euler.Ry},\tkzUseLua{ang})
+\tkzDrawLine(O,H)
+\tkzDrawPoints(A,B,C,N,O,H,G)
+\tkzLabelPoints[below left](B,C,N,O,H,G)
+\tkzLabelPoints[above](A)
+\end{tikzpicture}
+\end{minipage}
+
+\begin{Verbatim}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircle(N,K)
+\tkzDrawEllipse[teal](N,\tkzUseLua{E.euler.Rx},
+ \tkzUseLua{E.euler.Ry},\tkzUseLua{ang})
+\tkzDrawLine(O,H)
+\tkzDrawPoints(A,B,C,N,O,H,G)
+\tkzLabelPoints[below left](B,C,N,O,H,G)
+\tkzLabelPoints[above](A)
+\end{tikzpicture}
+\end{Verbatim}
+% subsection euler_ellipse (end)
+
+\subsubsection{Steiner inellipse and circumellipse} % (fold)
+\label{ssub:steiner_inellipse_and_circumellipse}
+In this example, the inner and outer Steiner ellipses, referred to as the "inellipse" and "circumellipse" (Mathworld.com), respectively, along with the orthoptic circle, are depicted.. The triangle must be acutangle.
+
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+ scale = .5
+ z.A = point: new (1 , 4)
+ z.B = point: new (11 , 1)
+ z.C = point: new (5 , 12)
+ T.ABC = triangle: new(z.A,z.B,z.C)
+ E = T.ABC: steiner_inellipse ()
+ z.G = E.center
+ ang = math.deg(E.slope)
+ z.F = E.Fa
+ z.E = E.Fb
+ C = E: orthoptic_circle ()
+ z.w = C.center
+ z.o = C.through
+ EE = T.ABC : steiner_circumellipse ()
+ z.M = C : point (0)
+ L.T1,L.T2= E : tangent_from (z.M)
+ z.T1 = L.T1.pb
+ z.T2 = L.T2.pb
+\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}\begin{tkzelements}
+ scale = .5
+z.A = point: new (1 , 4)
+z.B = point: new (11 , 1)
+z.C = point: new (5 , 12)
+T.ABC = triangle: new(z.A,z.B,z.C)
+E = T.ABC: steiner_inellipse ()
+z.G = E.center
+ang = math.deg(E.slope)
+z.F = E.Fa
+z.E = E.Fb
+C = E: orthoptic_circle ()
+z.w = C.center
+z.o = C.through
+EE = T.ABC : steiner_circumellipse ()
+z.M = C : point (0)
+L.T1,L.T2= E : tangent_from (z.M)
+z.T1 = L.T1.pb
+z.T2 = L.T2.pb
+\end{tkzelements}
+
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircles(w,o)
+\tkzDrawEllipse[teal](G,\tkzUseLua{E.Rx},
+ \tkzUseLua{E.Ry},\tkzUseLua{ang})
+\tkzDrawEllipse[red](G,\tkzUseLua{EE.Rx},
+ \tkzUseLua{EE.Ry},\tkzUseLua{ang})
+\tkzDrawLines(F,E M,T1 M,T2) %
+\tkzDrawPoints(A,B,C,F,E,G,M,T1,T2)
+\tkzLabelPoints[above](C,M,T1)
+\tkzLabelPoints[right](T2,B)
+\tkzLabelPoints[below left](A,F,E,G)
+\end{tikzpicture}
+\end{minipage}
+
+\begin{Verbatim}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawPolygon(A,B,C)
+\tkzDrawCircles(w,o)
+\tkzDrawEllipse[teal](G,\tkzUseLua{E.Rx},
+ \tkzUseLua{E.Ry},\tkzUseLua{ang})
+\tkzDrawEllipse[red](G,\tkzUseLua{EE.Rx},
+ \tkzUseLua{EE.Ry},\tkzUseLua{ang})
+\tkzDrawLines(F,E M,T1 M,T2) %
+\tkzDrawPoints(A,B,C,F,E,G,M,T1,T2)
+\tkzLabelPoints[above](C,M,T1)
+\tkzLabelPoints[right](T2,B)
+\tkzLabelPoints[below left](A,F,E,G)
+\end{tikzpicture}
+\end{Verbatim}
+% subsubsection steiner_inellipse_and_circumellipse (end)
+
+
\subsection{Harmonic division and bisector} % (fold)
\label{sub:harmonic_division_and_bisector}
\begin{minipage}{.4\textwidth}
- \begin{verbatim}
- \begin{tkzelements}
- scale = .4
- z.A = point: new (0 , 0)
- z.B = point: new (6 , 0)
- z.M = point: new (5 , 4)
- T.AMB = triangle : new (z.A,z.M,z.B)
- L.AB = T.AMB.ca
- L.bis = T.AMB : bisector (1)
- z.C = L.bis.pb
- L.bisext = T.AMB : bisector_ext (1)
- z.D = intersection (L.bisext,L.AB)
- L.CD = line: new (z.C,z.D)
- z.O = L.CD.mid
- L.AM = line: new (z.A,z.M)
- L.LL = L.AM : ll_from (z.B)
- L.MC = line: new (z.M,z.C)
- L.MD = line: new (z.M,z.D)
- z.E = intersection (L.LL,L.MC)
- z.F = intersection (L.LL,L.MD)
- \end{tkzelements}
- \end{verbatim}
+\begin{Verbatim}
+\begin{tkzelements}
+ scale = .4
+ z.A = point: new (0 , 0)
+ z.B = point: new (6 , 0)
+ z.M = point: new (5 , 4)
+ T.AMB = triangle : new (z.A,z.M,z.B)
+ L.AB = T.AMB.ca
+ L.bis = T.AMB : bisector (1)
+ z.C = L.bis.pb
+ L.bisext = T.AMB : bisector_ext (1)
+ z.D = intersection (L.bisext,L.AB)
+ L.CD = line: new (z.C,z.D)
+ z.O = L.CD.mid
+ L.AM = line: new (z.A,z.M)
+ L.LL = L.AM : ll_from (z.B)
+ L.MC = line: new (z.M,z.C)
+ L.MD = line: new (z.M,z.D)
+ z.E = intersection (L.LL,L.MC)
+ z.F = intersection (L.LL,L.MD)
+\end{tkzelements}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
\begin{tkzelements}
@@ -379,7 +533,7 @@ Remark: If you don't need to use the triangle object several times, you can obta
\end{tikzpicture}
\end{minipage}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPolygon(A,B,M)
@@ -394,11 +548,11 @@ Remark: If you don't need to use the triangle object several times, you can obta
\tkzMarkAngles[mark=|,size=.5](B,M,F M,F,B)
\tkzMarkSegments(B,E B,M B,F)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
% subsection harmonic_division_and_bisector (end)
% subsection methods_of_the_class_triangle (end)
-% section classe_triangle (end)
+% section class_triangle (end)
\endinput