diff options
author | Norbert Preining <norbert@preining.info> | 2024-03-27 03:02:20 +0000 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2024-03-27 03:02:20 +0000 |
commit | 31fa8cd73bab8480d38dae3a89ca578f337d6bbd (patch) | |
tree | ba550e99e0cb15dbf5405369d536b12b051c5155 /macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex | |
parent | 904f56f2c26edc7eb11d5a27579bccbeca29c618 (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.tex | 332 |
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 |