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-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex1072
1 files changed, 563 insertions, 509 deletions
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
index 5efb52381f..1b35c27263 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
@@ -7,33 +7,33 @@
\label{sub:d_alembert_1}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
- \begin{verbatim}
- \begin{tkzelements}
- z.A = point : new (0,0)
- z.a = point : new (4,0)
- z.B = point : new (7,-1)
- z.b = point : new (5.5,-1)
- z.C = point : new (5,-4)
- z.c = point : new (4.25,-4)
- C.Aa = circle : new (z.A,z.a)
- C.Bb = circle : new (z.B,z.b)
- C.Cc = circle : new (z.C,z.c)
- z.I = C.Aa : external_similitude (C.Bb)
- z.J = C.Aa : external_similitude (C.Cc)
- z.K = C.Cc : external_similitude (C.Bb)
- z.Ip = C.Aa : internal_similitude (C.Bb)
- z.Jp = C.Aa : internal_similitude (C.Cc)
- z.Kp = C.Cc : internal_similitude (C.Bb)
- \end{tkzelements}
- \begin{tikzpicture}[rotate=-60]
- \tkzGetNodes
- \tkzDrawCircles(A,a B,b C,c)
- \tkzDrawPoints(A,B,C,I,J,K,I',J',K')
- \tkzDrawSegments[new](I,K A,I A,J B,I B,K C,J C,K)
- \tkzDrawSegments[purple](I,J' I',J I',K)
- \tkzLabelPoints(I,J,K,I',J',K')
- \end{tikzpicture}
- \end{verbatim}
+\begin{Verbatim}
+\begin{tkzelements}
+ z.A = point : new (0,0)
+ z.a = point : new (4,0)
+ z.B = point : new (7,-1)
+ z.b = point : new (5.5,-1)
+ z.C = point : new (5,-4)
+ z.c = point : new (4.25,-4)
+ C.Aa = circle : new (z.A,z.a)
+ C.Bb = circle : new (z.B,z.b)
+ C.Cc = circle : new (z.C,z.c)
+ z.I = C.Aa : external_similitude (C.Bb)
+ z.J = C.Aa : external_similitude (C.Cc)
+ z.K = C.Cc : external_similitude (C.Bb)
+ z.Ip = C.Aa : internal_similitude (C.Bb)
+ z.Jp = C.Aa : internal_similitude (C.Cc)
+ z.Kp = C.Cc : internal_similitude (C.Bb)
+\end{tkzelements}
+\begin{tikzpicture}[rotate=-60]
+ \tkzGetNodes
+ \tkzDrawCircles(A,a B,b C,c)
+ \tkzDrawPoints(A,B,C,I,J,K,I',J',K')
+ \tkzDrawSegments[new](I,K A,I A,J B,I B,K C,J C,K)
+ \tkzDrawSegments[purple](I,J' I',J I',K)
+ \tkzLabelPoints(I,J,K,I',J',K')
+\end{tikzpicture}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -70,28 +70,28 @@ z.Kp = C.Cc : internal_similitude (C.Bb)
\label{sub:d_alembert_2}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
- \begin{verbatim}
- \begin{tkzelements}
- scale = .75
- z.A = point : new (0,0)
- z.a = point : new (5,0)
- z.B = point : new (7,-1)
- z.b = point : new (3,-1)
- z.C = point : new (5,-4)
- z.c = point : new (2,-4)
- C.Aa = circle : new (z.A,z.a)
- C.Bb = circle : new (z.B,z.b)
- C.Cc = circle : new (z.C,z.c)
- z.i,z.j = get_points (C.Aa : radical_axis (C.Bb))
- z.k,z.l = get_points (C.Aa : radical_axis (C.Cc))
- z.m,z.n = get_points (C.Bb : radical_axis (C.Cc))
- \end{tkzelements}
- \begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawCircles(A,a B,b C,c)
- \tkzDrawLines[new](i,j k,l m,n)
- \end{tikzpicture}
- \end{verbatim}
+\begin{Verbatim}
+\begin{tkzelements}
+ scale = .75
+ z.A = point : new (0,0)
+ z.a = point : new (5,0)
+ z.B = point : new (7,-1)
+ z.b = point : new (3,-1)
+ z.C = point : new (5,-4)
+ z.c = point : new (2,-4)
+ C.Aa = circle : new (z.A,z.a)
+ C.Bb = circle : new (z.B,z.b)
+ C.Cc = circle : new (z.C,z.c)
+ z.i,z.j = get_points (C.Aa : radical_axis (C.Bb))
+ z.k,z.l = get_points (C.Aa : radical_axis (C.Cc))
+ z.m,z.n = get_points (C.Bb : radical_axis (C.Cc))
+\end{tkzelements}
+\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles(A,a B,b C,c)
+ \tkzDrawLines[new](i,j k,l m,n)
+\end{tikzpicture}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -122,7 +122,7 @@ z.Kp = C.Cc : internal_similitude (C.Bb)
\subsection{Alternate} % (fold)
\label{sub:alternate}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (6 , 0)
@@ -146,7 +146,7 @@ z.Kp = C.Cc : internal_similitude (C.Bb)
\tkzLabelPoints[above](C,D,E)
\tkzMarkSegments(A,C C,E)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\hspace*{\fill}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
@@ -195,25 +195,8 @@ scale=.75
z.E = z.M : symmetry (z.A)
\end{tkzelements}
-\hspace*{\fill}
-\begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawSegment[add=0 and 1](A,M)
- \tkzDrawSegments[purple](M,C M,D)
- \tkzDrawCircle[purple](O,C)
- \tkzDrawSegments(A,B B,M D,B)
- \tkzDrawPoints(A,B,M,C,D)
- \tkzLabelPoints[below right](A,B,C,D)
- \tkzLabelPoints[above](M)
- \tkzFillAngles[opacity=.4,cyan!20](A,M,B)
- \tkzFillAngles[opacity=.4,purple!20](B,M,E)
- \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
- \tkzMarkAngles[mark=|](A,M,C C,M,B)
- \tkzMarkAngles[mark=||](B,M,D D,M,E)
-\end{tikzpicture}
-\hspace*{\fill}
-
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
\begin{tkzelements}
scale=.75
z.A = point: new (0 , 0)
@@ -229,6 +212,31 @@ scale=.75
L.AM = T.MAB.ab
z.E = z.M : symmetry (z.A)
\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \hspace*{\fill}
+ \begin{tikzpicture}[scale=.8]
+ \tkzGetNodes
+ \tkzDrawSegment[add=0 and 1](A,M)
+ \tkzDrawSegments[purple](M,C M,D)
+ \tkzDrawCircle[purple](O,C)
+ \tkzDrawSegments(A,B B,M D,B)
+ \tkzDrawPoints(A,B,M,C,D)
+ \tkzLabelPoints[below right](A,B,C,D)
+ \tkzLabelPoints[above](M)
+ \tkzFillAngles[opacity=.4,cyan!20](A,M,B)
+ \tkzFillAngles[opacity=.4,purple!20](B,M,E)
+ \tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
+ \tkzMarkAngles[mark=|](A,M,C C,M,B)
+ \tkzMarkAngles[mark=||](B,M,D D,M,E)
+ \end{tikzpicture}
+ \hspace*{\fill}
+\end{minipage}
+
+
+
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawSegment[add=0 and 1](A,M)
@@ -244,7 +252,7 @@ scale=.75
\tkzMarkAngles[mark=|](A,M,C C,M,B)
\tkzMarkAngles[mark=||](B,M,D D,M,E)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
Remark : The circle can be obtained with:
@@ -256,7 +264,7 @@ Remark : The circle can be obtained with:
\subsection{Apollonius and circle circumscribed } % (fold)
\label{sub:apollonius_and_circle_circumscribed}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale =.75
z.A = point: new (0 , 0)
@@ -288,7 +296,7 @@ Remark : The circle can be obtained with:
\tkzLabelPoints[above](M)
\tkzMarkRightAngle[opacity=.4,fill=gray!20](C,M,D)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
@@ -331,7 +339,7 @@ Remark : The circle can be obtained with:
\label{sub:apollonius_circles}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (6 , 0)
@@ -361,6 +369,8 @@ Remark : The circle can be obtained with:
L.Bpt = line: new (z.Bp,z.T)
z.O3 = L.Bpt.mid
\end{tkzelements}
+\end{Verbatim}
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircles[blue!50!black](O1,C' O2,A' O3,B')
@@ -372,7 +382,7 @@ Remark : The circle can be obtained with:
\tkzDrawCircle[purple](O,A)
\tkzDrawLine(O1,O2)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
@@ -420,7 +430,7 @@ z.O3 = L.Bpt.mid
Same result using the function |T.ABC.ab : apollonius (k) |
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.A = point: new (0 , 0)
@@ -435,7 +445,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
C.BC = T.ABC.bc : apollonius (length(z.A,z.B)/length(z.A,z.C))
z.w3,z.t3 = get_points ( C.BC )
\end{tkzelements}
-\end{verbatim}
+\end{Verbatim}
% subsection apollonius_circles (end)
@@ -443,30 +453,30 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\label{sub:archimedes}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
- \begin{verbatim}
- \begin{tkzelements}
- z.O_1 = point: new (0, 0)
- z.O_2 = point: new (0, 1)
- z.A = point: new (0, 3)
- z.F = point: polar (3, math.pi/6)
- L = line: new (z.F,z.O_1)
- C = circle: new (z.O_1,z.A)
- z.E = intersection (L,C)
- T = triangle: new (z.F,z.E,z.O_2)
- z.x = T: parallelogram ()
- L = line: new (z.x,z.O_2)
- C = circle: new (z.O_2,z.A)
- z.C,z.D = intersection (L ,C)
- \end{tkzelements}
- \begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawCircles(O_1,A O_2,A)
- \tkzDrawSegments[new](O_1,A E,F C,D)
- \tkzDrawSegments[purple](A,E A,F)
- \tkzDrawPoints(A,O_1,O_2,E,F,C,D)
- \tkzLabelPoints(A,O_1,O_2,E,F,C,D)
- \end{tikzpicture}
- \end{verbatim}
+\begin{Verbatim}
+\begin{tkzelements}
+ z.O_1 = point: new (0, 0)
+ z.O_2 = point: new (0, 1)
+ z.A = point: new (0, 3)
+ z.F = point: polar (3, math.pi/6)
+ L = line: new (z.F,z.O_1)
+ C = circle: new (z.O_1,z.A)
+ z.E = intersection (L,C)
+ T = triangle: new (z.F,z.E,z.O_2)
+ z.x = T: parallelogram ()
+ L = line: new (z.x,z.O_2)
+ C = circle: new (z.O_2,z.A)
+ z.C,z.D = intersection (L ,C)
+\end{tkzelements}
+\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles(O_1,A O_2,A)
+ \tkzDrawSegments[new](O_1,A E,F C,D)
+ \tkzDrawSegments[purple](A,E A,F)
+ \tkzDrawPoints(A,O_1,O_2,E,F,C,D)
+ \tkzLabelPoints(A,O_1,O_2,E,F,C,D)
+\end{tikzpicture}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -497,7 +507,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\subsection{Bankoff circle} % (fold)
\label{sub:bankoff_circle}
-\begin{tkzexample}[small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (10 , 0)
@@ -537,6 +547,9 @@ Same result using the function |T.ABC.ab : apollonius (k) |
T.CP1P2 = triangle : new (z.C,z.P_1,z.P_2)
z.O_5 = T.CP1P2.circumcenter
\end{tkzelements}
+\end{Verbatim}
+
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawSemiCircles[teal](O_0,B)
@@ -558,7 +571,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\tkzLabelCircle[left](O_5,C)(140){$(\epsilon)$}
\end{scope}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
@@ -630,8 +643,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\subsection{Excircles} % (fold)
\label{sub:excircles}
-
-\begin{tkzexample}[small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = 0.7
z.A = point: new (0,0)
@@ -665,7 +677,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\tkzLabelPoints[new,right=6pt](T_a)
\tkzMarkRightAngles[fill=gray!15](J_a,T_a,B J_b,T_b,C J_c,T_c,A)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale=0.7
@@ -708,7 +720,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\subsection{Orthogonal circle through} % (fold)
\label{sub:orthogonal_circle_through}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.O = point: new (0,1)
z.A = point: new (1,0)
@@ -725,7 +737,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\tkzDrawPoints[new](O,A,z1,z2,c)
\tkzLabelPoints[right](O,A,z1,z2,c)
\end{tikzpicture}
-\end{tkzexample}%
+\end{Verbatim}
\begin{tkzelements}
z.O = point: new (0,1)
@@ -751,7 +763,7 @@ Same result using the function |T.ABC.ab : apollonius (k) |
\subsection{Divine ratio} % (fold)
\label{sub:divine_ratio}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (8 , 0)
@@ -785,7 +797,7 @@ z.L = intersection (L.AR,L.BG)
\tkzDrawPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
\tkzLabelPoints(A,B,C,K,E,F,G,H,O_0,O_1,O_2,R,S,T,L)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
@@ -829,7 +841,7 @@ z.L = intersection (L.AR,L.BG)
\label{sub:director_circle}
% modif C: point (0.25) instead of 2
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .5
z.O = point: new (0 , 0)
@@ -859,7 +871,7 @@ z.L = intersection (L.AR,L.BG)
\tkzLabelPoints[above](L)
\tkzMarkRightAngles(A,P,H J,L,K)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -900,7 +912,7 @@ z.K = L.K.pb
\subsection{Gold division} % (fold)
\label{sub:gold_division}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
z.B = point: new (2.5,0)
@@ -928,7 +940,7 @@ z.O = C.AB: antipode (z.B)
\tkzDrawPoints(A,B,C,E,I,J,G,O,K)
\tkzLabelPoints(A,B,C,E,I,J,G,O,K)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
@@ -965,7 +977,7 @@ z.O = C.AB: antipode (z.B)
\subsection{Ellipse} % (fold)
\label{sub:ellipse}
\begin{minipage}{.5\textwidth}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.C = point: new (3 , 2)
z.A = point: new (5 , 1)
@@ -985,7 +997,7 @@ z.O = C.AB: antipode (z.B)
\tkzDrawPoints(C,A,B,b)
\tkzLabelPoints(C,A,B)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1016,7 +1028,7 @@ slope = math.deg(E.slope)
\subsection{Ellipse with radii} % (fold)
\label{sub:ellipse_with_radii}
\begin{minipage}{.5\textwidth}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale=.5
z.C = point: new (0 , 4)
@@ -1033,7 +1045,7 @@ z.CoV = E : point (math.pi/2)
\tkzUseLua{b},\tkzUseLua{ang})
\tkzDrawPoints(C,V,CoV)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1059,7 +1071,7 @@ z.CoV = E : point (math.pi/2)
\subsection{Ellipse\_with\_foci} % (fold)
\label{sub:ellipse_with_foci}
\begin{minipage}{.5\textwidth}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
local e
e = .8
@@ -1086,7 +1098,7 @@ z.CoV = E : point (math.pi/2)
\tkzDrawEllipse[teal](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
\tkzDrawLines(K,F K,G)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1124,7 +1136,7 @@ z.G = L.tb.pb
\subsection{Euler relation} % (fold)
\label{sub:euler_relation}
\begin{minipage}{.5\textwidth}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.A = point: new (0 , 0)
@@ -1152,7 +1164,7 @@ z.G = L.tb.pb
\tkzLabelPoints(A,B,C,J,I,w,H,K,E,O)
\tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1190,7 +1202,7 @@ _,z.E = intersection (L.Ow, C.OA)
\subsection{External angle} % (fold)
\label{sub:external_angle}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.A = point: new (0 , 0)
@@ -1214,7 +1226,7 @@ _,z.E = intersection (L.Ow, C.OA)
\tkzLabelPoints[above](C)
\tkzLabelPoints(A,B,D)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -1249,7 +1261,7 @@ z.E = z.C: symmetry (z.B)
\subsection{Internal angle} % (fold)
\label{sub:internal_angle}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .8
z.A = point: new (0 , 0)
@@ -1275,7 +1287,7 @@ z.E = z.C: symmetry (z.B)
\tkzLabelPoints[above](C,D,E)
\tkzMarkSegments(A,C C,E)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -1310,7 +1322,7 @@ z.E = intersection (L.LL,L.AD)
\subsection{Feuerbach theorem} % (fold)
\label{sub:nine_points}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = 1.5
z.A = point: new (0 , 0)
@@ -1350,7 +1362,7 @@ z.E = intersection (L.LL,L.AD)
\tkzDrawPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
\tkzLabelPoints(A,B,C,N,H,A',B',C',U,L,M,P,Q,F,I)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -1397,7 +1409,7 @@ z.F = intersection (L.LH,C.IH) -- feuerbach
\subsection{Gold ratio with segment} % (fold)
\label{sub:gold_ratio_with_segment}
\begin{minipage}{.5\textwidth}
- \begin{verbatim}
+ \begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (8 , 0)
@@ -1418,7 +1430,7 @@ z.F = intersection (L.LH,C.IH) -- feuerbach
\tkzDrawArc[delta=20](M,A)(K)
\tkzLabelPoints(A,B,C)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1450,7 +1462,7 @@ z.C = intersection (L.AK,L.AB)
\subsection{Gold Arbelos} % (fold)
\label{sub:gold_arbelos}
\begin{minipage}{.5\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .6
z.A = point: new (0 , 0)
@@ -1471,7 +1483,7 @@ z.C = intersection (L.AK,L.AB)
\tkzDrawPoints(A,C,B,O_1,O_2,O_0)
\tkzLabelPoints(A,C,B)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -1502,7 +1514,7 @@ z.O_0 = L.AB.mid
\subsection{Harmonic division v1} % (fold)
\label{sub:harmonic_division_v1}
\begin{minipage}[t]{.4\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale=.75
z.A = point: new (0 , 0)
@@ -1534,7 +1546,7 @@ z.C = intersection (L.XG,L.AB)
\tkzLabelPoints(A,B,G,E,F,C,D)
\tkzMarkSegments(F,B B,E)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.6\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -1576,7 +1588,7 @@ z.C = intersection (L.XG,L.AB)
\subsection{Harmonic division v2} % (fold)
\label{sub:harmonic_division_v2}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .5
z.A = point: new (0 , 0)
@@ -1601,7 +1613,7 @@ z.C = intersection (L.XG,L.AB)
\tkzDrawPoints(A,...,G,X)
\tkzLabelPoints(A,...,G,X)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -1636,7 +1648,7 @@ z.C = intersection (L.GX,L.AB)
\subsection{Menelaus} % (fold)
\label{sub:menelaus}
\begin{minipage}{.4\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (6 , 0)
@@ -1657,7 +1669,7 @@ z.C = intersection (L.GX,L.AB)
\tkzDrawPoints(P,Q,R,A,B,C)
\tkzLabelPoints(A,B,C,P,Q,R)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.6\textwidth}
\begin{tkzelements}
@@ -1689,7 +1701,7 @@ z.R = intersection (L.BC,L.PX)
\subsection{Radical axis v1} % (fold)
\label{sub:radical_axis_v1}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.X = point : new (0,0)
@@ -1718,7 +1730,7 @@ z.H = L.XY : projection (z.M)
\tkzDrawLines[red](A,M A',M X,Y E,F)
\tkzDrawLines[red,add=1 and 3](M,H)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = .75
@@ -1754,7 +1766,7 @@ z.H = L.XY : projection (z.M)
\subsection{Radical axis v2} % (fold)
\label{sub:radical_axis_v2}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = 1.25
z.O = point : new (-1,0)
@@ -1783,7 +1795,7 @@ _,z.Kp = get_points (L.MKp)
\tkzDrawPoints(O,O',T,M,T',K,K')
\tkzLabelPoints(O,O',T,T',K,K',M)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale =1.25
@@ -1820,7 +1832,7 @@ _,z.Kp = get_points (L.MKp)
\subsection{Radical axis v3} % (fold)
\label{sub:radical_axis_v3}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
z.B = point : new (4,0)
@@ -1845,7 +1857,7 @@ _,z.Kp = get_points (L.MKp)
\tkzLabelPoints(O,O',B,E,F,T,T')
\tkzDrawArc(M,T')(T)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
@@ -1877,7 +1889,7 @@ _,z.Tp = get_points (L)
\subsection{Radical axis v4} % (fold)
\label{sub:radical_axis_v4}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
z.B = point : new (5,0)
@@ -1903,7 +1915,7 @@ _,z.Tp = get_points (L)
\tkzLabelPoints[below right](O,O',E,F,M,T,T')
\tkzDrawArc(M,B)(T)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
@@ -1938,7 +1950,7 @@ _,z.Tp = get_points (L)
\subsection{Radical center} % (fold)
\label{sub:radical_center}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
z.x = point : new (1,0)
@@ -1965,7 +1977,7 @@ _,z.Tp = get_points (L)
\tkzDrawPoints(O,O',P,a,a',b,b',X,H)
\tkzLabelPoints[below right](O,O',P,H)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -2001,7 +2013,7 @@ z.H = L.OOp : projection (z.X)
\subsection{Radical circle} % (fold)
\label{sub:radical_circle}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .25
z.A = point: new (0,0)
@@ -2025,11 +2037,11 @@ z.H = L.OOp : projection (z.X)
\tkzDrawPoints(A,B,C)
\tkzLabelPoints(A,B,C)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
- scale = .25
+ scale = .5
z.A = point: new (0,0)
z.B = point: new (6,0)
z.C = point: new (0.8,4)
@@ -2053,79 +2065,23 @@ z.H = L.OOp : projection (z.X)
\tkzDrawPoints(A,B,C)
\tkzLabelPoints(A,B,C)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection radical_circle (end)
\subsection{Euler ellipse} % (fold)
\label{sub:hexagram}
-\begin{tkzexample}[latex=0cm,small,code only]
-\begin{tkzelements}
- z.A = point: new (0 , 0)
- z.B = point: new (5 , 1)
- L.AB = line : new (z.A,z.B)
- z.C = point: new (.8 , 3)
- T.ABC = triangle: new (z.A,z.B,z.C)
- z.N = T.ABC.eulercenter
- z.G = T.ABC.centroid
- z.O = T.ABC.circumcenter
- z.H = T.ABC.orthocenter
- z.Ma,z.Mb,z.Mc = get_points (T.ABC : medial ())
- z.Ha,z.Hb,z.Hc = get_points (T.ABC : orthic ())
- z.Ea,z.Eb,z.Ec = get_points (T.ABC: extouch())
- L.euler = T.ABC : euler_line ()
- C.circum = T.ABC : circum_circle ()
- C.euler = T.ABC : euler_circle ()
- z.I,z.J = intersection (L.euler,C.euler)
- E = ellipse: foci (z.H,z.O,z.I)
- a = E.Rx
- b = E.Ry
- ang = math.deg(E.slope)
- L.AH = line: new (z.A,z.H)
- L.BH = line: new (z.B,z.H)
- L.CH = line: new (z.C,z.H)
- z.X = intersection (L.AH,C.circum)
- _,z.Y = intersection (L.BH,C.circum)
- _,z.Z = intersection (L.CH,C.circum)
- L.BC = line: new (z.B,z.C)
- L.XO = line: new (z.X,z.O)
- L.YO = line: new (z.Y,z.O)
- L.ZO = line: new (z.Z,z.O)
- z.x = intersection (L.BC,L.XO)
- z.U = intersection (L.XO,E)
- _,z.V = intersection (L.YO,E)
- _,z.W = intersection (L.ZO,E)
- \end{tkzelements}
- \end{tkzexample}
-
-\begin{tkzexample}[latex=0cm,small,code only]
-\begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawPolygon(A,B,C)
- \tkzDrawCircles[red](N,Ma O,A)
- \tkzDrawSegments(A,X B,Y C,Z B,Hb C,Hc X,O Y,O Z,O)
- \tkzDrawPolygon[red](U,V,W)
- \tkzLabelPoints[red](U,V,W)
- \tkzLabelPoints(A,B,C,X,Y,Z)
- \tkzDrawLine[blue](I,J)
- \tkzLabelPoints[blue,right](O,N,G,H,I,J)
- \tkzDrawPoints(I,J,U,V,W)
- \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
- \tkzDrawEllipse[blue](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
-\end{tikzpicture}
-\end{tkzexample}
-
\begin{tkzelements}
-scale = 2
-E = {}
+ scale =1.3
z.A = point: new (0 , 0)
z.B = point: new (5 , 1)
L.AB = line : new (z.A,z.B)
z.C = point: new (.8 , 3)
T.ABC = triangle: new (z.A,z.B,z.C)
-z.N = T.ABC.eulercenter
-z.G = T.ABC.centroid
-z.O = T.ABC.circumcenter
-z.H = T.ABC.orthocenter
+z.N = T.ABC.eulercenter
+z.G = T.ABC.centroid
+z.O = T.ABC.circumcenter
+z.H = T.ABC.orthocenter
z.Ma,z.Mb,z.Mc = get_points (T.ABC : medial ())
z.Ha,z.Hb,z.Hc = get_points (T.ABC : orthic ())
z.Ea,z.Eb,z.Ec = get_points (T.ABC: extouch())
@@ -2133,7 +2089,7 @@ L.euler = T.ABC : euler_line ()
C.circum = T.ABC : circum_circle ()
C.euler = T.ABC : euler_circle ()
z.I,z.J = intersection (L.euler,C.euler)
- E = ellipse: foci (z.H,z.O,z.I)
+E = ellipse: foci (z.H,z.O,z.I)
a = E.Rx
b = E.Ry
ang = math.deg(E.slope)
@@ -2153,6 +2109,51 @@ _,z.V = intersection (L.YO,E)
_,z.W = intersection (L.ZO,E)
\end{tkzelements}
+\begin{minipage}{.4\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+ scale = 1.3
+ z.A = point: new (0 , 0)
+ z.B = point: new (5 , 1)
+ L.AB = line : new (z.A,z.B)
+ z.C = point: new (.8 , 3)
+ T.ABC = triangle: new (z.A,z.B,z.C)
+ z.N = T.ABC.eulercenter
+ z.G = T.ABC.centroid
+ z.O = T.ABC.circumcenter
+ z.H = T.ABC.orthocenter
+ z.Ma,z.Mb,
+ z.Mc = get_points (T.ABC : medial ())
+ z.Ha,z.Hb,
+ z.Hc = get_points (T.ABC : orthic ())
+ z.Ea,z.Eb,
+ z.Ec = get_points (T.ABC: extouch())
+ L.euler = T.ABC : euler_line ()
+ C.circum = T.ABC : circum_circle ()
+ C.euler = T.ABC : euler_circle ()
+ z.I,z.J = intersection (L.euler,C.euler)
+ E = ellipse: foci (z.H,z.O,z.I)
+ a = E.Rx
+ b = E.Ry
+ ang = math.deg(E.slope)
+ L.AH = line: new (z.A,z.H)
+ L.BH = line: new (z.B,z.H)
+ L.CH = line: new (z.C,z.H)
+ z.X = intersection (L.AH,C.circum)
+ _,z.Y = intersection (L.BH,C.circum)
+ _,z.Z = intersection (L.CH,C.circum)
+ L.BC = line: new (z.B,z.C)
+ L.XO = line: new (z.X,z.O)
+ L.YO = line: new (z.Y,z.O)
+ L.ZO = line: new (z.Z,z.O)
+ z.x = intersection (L.BC,L.XO)
+ z.U = intersection (L.XO,E)
+ _,z.V = intersection (L.YO,E)
+ _,z.W = intersection (L.ZO,E)
+\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
\hspace*{\fill}
\begin{tikzpicture}
\tkzGetNodes
@@ -2169,80 +2170,32 @@ _,z.W = intersection (L.ZO,E)
\tkzDrawEllipse[blue](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
\end{tikzpicture}
\hspace*{\fill}
-% subsection hexagram (end)
-
-\subsection{Gold Arbelos properties} % (fold)
-\label{sub:gold_arbelos_properties}
+\end{minipage}
-\begin{tkzexample}[latex=0cm,small,code only]
-\begin{tkzelements}
- z.A = point : new(0,0)
- z.B = point : new(10,0)
- z.C = gold_segment_ (z.A,z.B)
- L.AB = line:new (z.A,z.B)
- z.O_1 = L.AB.mid
- L.AC = line:new (z.A,z.C)
- z.O_2 = L.AC.mid
- L.CB = line:new (z.C,z.B)
- z.O_3 = L.CB.mid
- C1 = circle:new (z.O_1,z.B)
- C2 = circle:new (z.O_2,z.C)
- C3 = circle:new (z.O_3,z.B)
- z.Q = C2.north
- z.P = C3.north
- L1 = line:new (z.O_2,z.O_3)
- z.M_0 = L1:harmonic_ext (z.C)
- L2 = line:new (z.O_1,z.O_2)
- z.M_1 = L2:harmonic_int (z.A)
- L3 = line:new (z.O_1,z.O_3)
- z.M_2 = L3:harmonic_int (z.B)
- Lbq = line:new (z.B,z.Q)
- Lap = line:new (z.A,z.P)
- z.S = intersection (Lbq,Lap)
- z.x = z.C: north ()
- L = line : new (z.C,z.x)
- z.D,_ = intersection (L,C1)
- L.CD = line :new (z.C,z.D)
- z.O_7 = L.CD.mid
- C.DC = circle: new (z.D,z.C)
- z.U,z.V = intersection (C.DC,C1)
- L.UV = line :new (z.U,z.V)
- z.R ,z.S = L.UV : projection (z.O_2,z.O_3)
- L.O1D = line : new (z.O_1,z.D)
- z.W = intersection (L.UV,L.O1D)
- z.O = C.DC : inversion (z.W)
-\end{tkzelements}
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
- \tkzDrawCircles[teal](O_1,B)
- \tkzDrawSemiCircles[thin,teal](O_2,C O_3,B)
- \tkzDrawArc[purple,delta=0](D,V)(U)
- \tkzDrawCircle[new](O_7,C)
- \tkzDrawSegments[thin,purple](A,D D,B C,R C,S C,D U,V)
- \tkzDrawSegments[thin,red](O,D A,O O,B)
- \tkzDrawPoints(A,B,C,D,O_7) %,
- \tkzDrawPoints(O_1,O_2,O_3,U,V,R,S,W,O)
- \tkzDrawSegments[cyan](O_3,S O_2,R)
- \tkzDrawSegments[very thin](A,B)
- \tkzDrawSegments[cyan,thin](C,U U,D)
- \tkzMarkRightAngles[size=.2,fill=gray!40,opacity=.4](D,C,A A,D,B
- D,S,C D,W,V O_3,S,U O_2,R,U)
- \tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_1
- C,D,B D,C,R B,C,S A,R,O_2)
- \tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D
- D,B,C R,C,A O_3,S,B)
- \tkzLabelPoints[below](C,O_2,O_3,O_1)
- \tkzLabelPoints[above](D)
- \tkzLabelPoints[below](O)
- \tkzLabelPoints[below left](A)
- \tkzLabelPoints[above left](R)
- \tkzLabelPoints[above right](S)
- \tkzLabelPoints[left](V)
- \tkzLabelPoints[below right](B,U,W,O_7)
+ \tkzDrawPolygon(A,B,C)
+ \tkzDrawCircles[red](N,Ma O,A)
+ \tkzDrawSegments(A,X B,Y C,Z B,Hb C,Hc X,O Y,O Z,O)
+ \tkzDrawPolygon[red](U,V,W)
+ \tkzLabelPoints[red](U,V,W)
+ \tkzLabelPoints(A,B,C,X,Y,Z)
+ \tkzDrawLine[blue](I,J)
+ \tkzLabelPoints[blue,right](O,N,G,H,I,J)
+ \tkzDrawPoints(I,J,U,V,W)
+ \tkzDrawPoints(A,B,C,N,G,H,O,X,Y,Z,Ma,Mb,Mc,Ha,Hb,Hc)
+ \tkzDrawEllipse[blue](N,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang})
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
+
+% subsection hexagram (end)
+
+\subsection{Gold Arbelos properties} % (fold)
+\label{sub:gold_arbelos_properties}
\begin{tkzelements}
+scale = .7
z.A = point : new(0,0)
z.B = point : new(10,0)
z.C = gold_segment_ (z.A,z.B)
@@ -2280,6 +2233,48 @@ z.W = intersection (L.UV,L.O1D)
z.O = C.DC : inversion (z.W)
\end{tkzelements}
+\begin{minipage}{.4\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+ z.A = point : new(0,0)
+ z.B = point : new(10,0)
+ z.C = gold_segment_ (z.A,z.B)
+ L.AB = line:new (z.A,z.B)
+ z.O_1 = L.AB.mid
+ L.AC = line:new (z.A,z.C)
+ z.O_2 = L.AC.mid
+ L.CB = line:new (z.C,z.B)
+ z.O_3 = L.CB.mid
+ C1 = circle:new (z.O_1,z.B)
+ C2 = circle:new (z.O_2,z.C)
+ C3 = circle:new (z.O_3,z.B)
+ z.Q = C2.north
+ z.P = C3.north
+ L1 = line:new (z.O_2,z.O_3)
+ z.M_0 = L1:harmonic_ext (z.C)
+ L2 = line:new (z.O_1,z.O_2)
+ z.M_1 = L2:harmonic_int (z.A)
+ L3 = line:new (z.O_1,z.O_3)
+ z.M_2 = L3:harmonic_int (z.B)
+ Lbq = line:new (z.B,z.Q)
+ Lap = line:new (z.A,z.P)
+ z.S = intersection (Lbq,Lap)
+ z.x = z.C: north ()
+ L = line : new (z.C,z.x)
+ z.D,_ = intersection (L,C1)
+ L.CD = line :new (z.C,z.D)
+ z.O_7 = L.CD.mid
+ C.DC = circle: new (z.D,z.C)
+ z.U,z.V = intersection (C.DC,C1)
+ L.UV = line :new (z.U,z.V)
+ z.R ,z.S = L.UV : projection (z.O_2,z.O_3)
+ L.O1D = line : new (z.O_1,z.D)
+ z.W = intersection (L.UV,L.O1D)
+ z.O = C.DC : inversion (z.W)
+\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
\hspace*{\fill}
\begin{tikzpicture}
\tkzGetNodes
@@ -2310,11 +2305,43 @@ z.O = C.DC : inversion (z.W)
\tkzLabelPoints[below right](B,U,W,O_7)
\end{tikzpicture}
\hspace*{\fill}
+\end{minipage}
+
+\begin{Verbatim}
+\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles[teal](O_1,B)
+ \tkzDrawSemiCircles[thin,teal](O_2,C O_3,B)
+ \tkzDrawArc[purple,delta=0](D,V)(U)
+ \tkzDrawCircle[new](O_7,C)
+ \tkzDrawSegments[thin,purple](A,D D,B C,R C,S C,D U,V)
+ \tkzDrawSegments[thin,red](O,D A,O O,B)
+ \tkzDrawPoints(A,B,C,D,O_7) %,
+ \tkzDrawPoints(O_1,O_2,O_3,U,V,R,S,W,O)
+ \tkzDrawSegments[cyan](O_3,S O_2,R)
+ \tkzDrawSegments[very thin](A,B)
+ \tkzDrawSegments[cyan,thin](C,U U,D)
+ \tkzMarkRightAngles[size=.2,fill=gray!40,opacity=.4](D,C,A A,D,B
+ D,S,C D,W,V O_3,S,U O_2,R,U)
+ \tkzFillAngles[cyan!40,opacity=.4](B,A,D A,D,O_1
+ C,D,B D,C,R B,C,S A,R,O_2)
+ \tkzFillAngles[green!40,opacity=.4](S,C,D W,R,D
+ D,B,C R,C,A O_3,S,B)
+ \tkzLabelPoints[below](C,O_2,O_3,O_1)
+ \tkzLabelPoints[above](D)
+ \tkzLabelPoints[below](O)
+ \tkzLabelPoints[below left](A)
+ \tkzLabelPoints[above left](R)
+ \tkzLabelPoints[above right](S)
+ \tkzLabelPoints[left](V)
+ \tkzLabelPoints[below right](B,U,W,O_7)
+\end{tikzpicture}
+\end{Verbatim}
% subsection gold_arbelos_properties (end)
\subsection{Apollonius circle v1 with inversion} % (fold)
\label{sub:apollonius_circle_v1_with_inversion}
-\begin{tkzexample}[code only,small]
+\begin{Verbatim}
\begin{tkzelements}
scale = .7
z.A = point: new (0,0)
@@ -2350,7 +2377,7 @@ z.O = C.DC : inversion (z.W)
\tkzDrawPoints[teal](S)
\tkzLabelPoints(A,B,C,O,S,N)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = .5
@@ -2394,7 +2421,7 @@ z.O = C.DC : inversion (z.W)
\subsection{Apollonius circle v2} % (fold)
\label{sub:apollonius_circle_v2}
- \begin{tkzexample}[small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .5
z.A = point: new (0,0)
@@ -2434,7 +2461,7 @@ z.O = C.DC : inversion (z.W)
\tkzDrawPoints[red](N,O,L,S,o,t)
\tkzLabelPoints[right,font=\tiny](A,B,C,Ja,Jb,Jc,O,N,L,S,Ma,o)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale =.5
@@ -2484,7 +2511,7 @@ z.t = intersection (L.ox,L.MaS) -- through
\subsection{Orthogonal circles v1} % (fold)
\label{sub:orthogonal_circles_v1}
-\begin{tkzexample}[small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .6
z.C_1 = point: new (0,0)
@@ -2509,7 +2536,7 @@ z.t = intersection (L.ox,L.MaS) -- through
\tkzLabelCircle[left=10pt](C_1,T)(180){Circle 1}
\tkzLabelCircle[right=10pt](C_2,T)(180){Circle 2}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = .6
@@ -2542,7 +2569,7 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\subsection{Orthogonal circles v2} % (fold)
\label{sub:orthogonal_circles_v2}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.O = point: new (2,2)
@@ -2575,7 +2602,7 @@ z.M = L.OOp.mid
\tkzLabelPoint[below](T'){$T'$}
\tkzLabelPoint[above left](O'){$O'$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = .75
@@ -2617,7 +2644,7 @@ z.M = L.OOp.mid
\subsection{Orthogonal circle to two circles} % (fold)
\label{sub:orthogonal_circle_to_two_circles}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (-1,0)
z.B = point : new (0,2)
@@ -2645,7 +2672,7 @@ z.M = L.OOp.mid
\tkzDrawPoints(O,O',T,M,T',K,K')
\tkzLabelPoints(O,O',T,T',M,K,K')
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = 1.25
@@ -2761,7 +2788,7 @@ z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
\end{tikzpicture}
\hspace*{\fill}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (10 , 0)
@@ -2808,9 +2835,9 @@ z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
z.Ap = z.M_1: symmetry (z.A)
z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
\end{tkzelements}
-\end{tkzexample}
+\end{Verbatim}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawCircle[thin,fill=green!10](O_4,P_0)
@@ -2839,14 +2866,14 @@ z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
\tkzLabelCircle[left,font=\scriptsize](O_4,P_2)(60){$(\delta)$}
\tkzLabelCircle[above left,font=\scriptsize](O_5,C)(40){$(\epsilon)$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
% subsection midcircles (end)
\subsection{Pencil v1} % (fold)
\label{sub:pencil_v1}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .75
z.A = point : new (0,2)
@@ -2873,7 +2900,7 @@ z.H_4,z.F,z.E,z.H_0 = L.AB : projection (z.O_4,z.G,z.H,z.P_0)
\tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,x,y)
\tkzLabelLine[pos=1.25,right]( M_0,M_1){$(\Delta)$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale=.75
@@ -2908,7 +2935,7 @@ z.O = L.BA.mid
\subsection{Pencil v2} % (fold)
\label{sub:pencil_v2}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale=.75
z.A = point : new (0,0)
@@ -2937,7 +2964,7 @@ z.O = L.BA.mid
\tkzLabelPoints[below right](A,B,C_0,C_1,M_0,M_1,M_2)
\tkzLabelLine[pos=2,right]( M_0,M_1){$(\Delta)$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale=.75
@@ -2975,7 +3002,7 @@ z.O = L.BA.mid
\subsection{Power v1} % (fold)
\label{sub:power_v1}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
z.A = point : new (2,-2)
@@ -2994,7 +3021,7 @@ z.O = L.BA.mid
\tkzLabelPoints(O,A,A',M,B)
\tkzDrawSegments[-Triangle](M,A M,A')
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3024,7 +3051,7 @@ z.B = intersection (L.AM, C.OA)
\subsection{Power v2} % (fold)
\label{sub:power_v2}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.O = point : new (0,0)
z.A = point : new (2,2)
@@ -3047,7 +3074,7 @@ z.B = intersection (L.AM, C.OA)
\tkzLabelPoints[below left](A',B)
\tkzDrawSegments(M,A M,A')
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3079,7 +3106,7 @@ z.U,z.V = intersection (L.mM,C.OA)
\subsection{Reim v1} % (fold)
\label{sub:reim_v1}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
z.E = point: new (-2,2)
@@ -3110,7 +3137,7 @@ z.U,z.V = intersection (L.mM,C.OA)
\tkzMarkAngles[size=.5](F,C,H G,D,E)
\tkzFillAngles[red!40,opacity=.4,size=.5](F,C,H G,D,E)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
@@ -3149,7 +3176,7 @@ z.U,z.V = intersection (L.mM,C.OA)
\subsection{Reim v2} % (fold)
\label{sub:reim_v2}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = .6
z.A = point: new (0,0)
@@ -3175,10 +3202,10 @@ z.U,z.V = intersection (L.mM,C.OA)
\tkzLabelCircle[below=4pt,font=\scriptsize](A,C)(90){$(\alpha)$}
\tkzLabelCircle[left=4pt,font=\scriptsize](B,C)(-90){$(\beta)$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
-scale = .6
+scale = .4
z.A = point: new (0,0)
z.B = point: new (10,0)
z.C = point: new (4,0)
@@ -3209,7 +3236,7 @@ z.n,z.np = get_points (C.BC: tangent_at (z.N))
\subsection{Reim v3} % (fold)
\label{sub:reim_v3}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
z.B = point: new (8,0)
@@ -3247,10 +3274,10 @@ z.n,z.np = get_points (C.BC: tangent_at (z.N))
\tkzLabelCircle[left=4pt,font=\scriptsize](y,B)(60){$(\beta)$}
\tkzLabelCircle[below=4pt,font=\scriptsize](z,C)(60){$(\gamma)$}
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
- scale = 1.25
+ scale = .75
z.A = point: new (0,0)
z.B = point: new (8,0)
z.C = point: new (2,6)
@@ -3294,7 +3321,7 @@ z.n,z.np = get_points (C.BC: tangent_at (z.N))
\subsection{Tangent and circle} % (fold)
\label{sub:tangent_and_circle}
\begin{minipage}{.5\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (1,0)
z.B = point: new (2,2)
@@ -3315,7 +3342,7 @@ z.n,z.np = get_points (C.BC: tangent_at (z.N))
\tkzDrawLines(E,i E,j k,l)
\tkzLabelPoints[right,font=\small](A,B,E,S,M)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -3345,7 +3372,7 @@ z.k,z.l = get_points (C.AB: tangent_at (z.B))
\subsection{Homothety} % (fold)
\label{sub:homothety}
\begin{minipage}{.5\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (0,0)
z.B = point: new (1,2)
@@ -3359,7 +3386,7 @@ z.k,z.l = get_points (C.AB: tangent_at (z.B))
\tkzDrawCircles(A,B C,D)
\tkzDrawLines(E,C E,D)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -3382,7 +3409,7 @@ z.C,z.D = z.E : homothety(2,z.A,z.B)
\subsection{Tangent and chord} % (fold)
\label{sub:tangent_and_chord}
\begin{minipage}{.5\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = .8
z.A = point: new (0 , 0)
@@ -3409,7 +3436,7 @@ z.C,z.D = z.E : homothety(2,z.A,z.B)
\tkzFillAngles[teal!20,opacity=.3](A,D,B b2,B,A)
\tkzLabelPoints(A,B,C,D,H,O)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -3447,7 +3474,7 @@ z.H = L.AB: projection (z.O)
\subsection{Three chords} % (fold)
\label{sub:three_chords}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
z.O = point: new (0 , 0)
z.B = point: new (0 , 2)
@@ -3477,25 +3504,8 @@ z.Ap = intersection (L.GB,C.xB)
z.Ep,_ = intersection (L.GE,C.xF)
z.Cp,_ = intersection (L.GD,C.xD)
\end{tkzelements}
-\begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawCircles(O,B)
- \tkzDrawCircles[cyan](P,B)
- \tkzDrawCircles[red](w,E)
- \tkzDrawCircles[new](x,F)
- \tkzDrawSegments(A,G E,G C,G)
- \tkzDrawPolygons[new](A,E,C A',E',C')
- \tkzDrawPoints(A,...,G,A',E',C',O,P)
- \begin{scope}[font=\scriptsize]
- \tkzLabelPoints(A,...,F)
- \tkzLabelPoints[above left](G,A',E',C')
- \tkzLabelCircle[left](O,B)(30){$(\beta)$}
- \tkzLabelCircle[below](P,A)(40){$(\gamma)$}
- \tkzLabelCircle[right](w,C)(90){$(\alpha)$}
- \tkzLabelCircle[left](x,B)(-230){$((\delta))$}
- \end{scope}
-\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
+
\begin{tkzelements}
z.O = point: new (0 , 0)
@@ -3527,8 +3537,31 @@ z.Ep,_ = intersection (L.GE,C.xF)
z.Cp,_ = intersection (L.GD,C.xD)
\end{tkzelements}
+\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
+\begin{Verbatim}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles(O,B)
+ \tkzDrawCircles[cyan](P,B)
+ \tkzDrawCircles[red](w,E)
+ \tkzDrawCircles[new](x,F)
+ \tkzDrawSegments(A,G E,G C,G)
+ \tkzDrawPolygons[new](A,E,C A',E',C')
+ \tkzDrawPoints(A,...,G,A',E',C',O,P)
+ \begin{scope}[font=\scriptsize]
+ \tkzLabelPoints(A,...,F)
+ \tkzLabelPoints[above left](G,A',E',C')
+ \tkzLabelCircle[left](O,B)(30){$(\beta)$}
+ \tkzLabelCircle[below](P,A)(40){$(\gamma)$}
+ \tkzLabelCircle[right](w,C)(90){$(\alpha)$}
+ \tkzLabelCircle[left](x,B)(-230){$((\delta))$}
+ \end{scope}
+ \end{tikzpicture}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\hspace*{\fill}
-\begin{tikzpicture}
+\begin{tikzpicture}[scale=.75]
\tkzGetNodes
\tkzDrawCircles(O,B)
\tkzDrawCircles[cyan](P,B)
@@ -3547,13 +3580,14 @@ z.Cp,_ = intersection (L.GD,C.xD)
\end{scope}
\end{tikzpicture}
\hspace*{\fill}
+\end{minipage}
% subsection three_chords (end)
\subsection{Three tangents} % (fold)
\label{sub:three_tangents}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (-1 , 0)
z.C = point: new (4 , -1.5)
@@ -3583,7 +3617,7 @@ z.Cp,_ = intersection (L.GD,C.xD)
\tkzLabelPoints[above right](E,F)
\tkzLabelPoints[below](C)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3624,7 +3658,7 @@ z.I = intersection (L.TA,L.TC)
\subsection{Midarc} % (fold)
\label{sub:midarc}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (-1,0)
z.B = point: new (2,4)
@@ -3639,7 +3673,7 @@ z.I = intersection (L.TA,L.TC)
\tkzDrawPoints(A,...,D)
\tkzLabelPoints(A,...,D)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3658,6 +3692,7 @@ z.D = C.AB: midarc (z.B,z.C)
\tkzDrawPoints(A,...,D)
\tkzLabelPoints(A,...,D)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection midarc (end)
@@ -3665,7 +3700,7 @@ z.D = C.AB: midarc (z.B,z.C)
\label{sub:lemoine_line_without_macro}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
scale = 1.6
z.A = point: new (1,0)
@@ -3697,7 +3732,7 @@ z.D = C.AB: midarc (z.B,z.C)
\tkzDrawLines[red](Ar,Al Br,Q Cr,Cl)
\tkzDrawSegments(A,R C,P C,Q)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3740,7 +3775,7 @@ z.R = intersection (L.tC,L.AB)
\label{sub:first_lemoine_circle}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point: new (1,1)
z.B = point: new (5,1)
@@ -3758,7 +3793,7 @@ z.R = intersection (L.tC,L.AB)
\tkzLabelPoints(A,B,C,o,w,O,L)
\tkzDrawCircles(o,w O,A)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3771,20 +3806,21 @@ z.o,z.w = get_points (T : first_lemoine_circle ())
z.L = T : lemoine_point ()
\end{tkzelements}
\hspace*{\fill}
-\begin{tikzpicture}
+\begin{tikzpicture}[scale = 1.25]
\tkzGetNodes
\tkzDrawPolygons(A,B,C)
\tkzDrawPoints(A,B,C,o,w,O,L)
\tkzLabelPoints(A,B,C,o,w,O,L)
\tkzDrawCircles(o,w O,A)
\end{tikzpicture}
+\hspace*{\fill}
\end{minipage}
% subsection first_lemoine_circle (end)
\subsection{First and second Lemoine circles} % (fold)
\label{sub:first_and_second_lemoine_circles}
-\begin{tkzexample}[latex=0cm,small,code only]
+\begin{Verbatim}
\begin{tkzelements}
scale = 2
z.a = point: new (0,0)
@@ -3820,7 +3856,7 @@ z.L = T : lemoine_point ()
\tkzDrawCircles(L,x o,p O,a)
\tkzDrawSegments(L,O x1,x4 x2,x5 x3,x6)
\end{tikzpicture}
-\end{tkzexample}
+\end{Verbatim}
\begin{tkzelements}
scale = 2
@@ -3848,7 +3884,7 @@ L.y2y3 = line : new (z.y2,z.y3)
\end{tkzelements}
\hspace*{\fill}
-\begin{tikzpicture}
+\begin{tikzpicture}[scale = .75]
\tkzGetNodes
\tkzDrawPolygons(a,b,c y1,y2,y3,y4,y5,y6)
\tkzDrawPoints(x1,x2,x3,x4,x5,x6,L)
@@ -3865,34 +3901,6 @@ L.y2y3 = line : new (z.y2,z.y3)
\subsection{Inversion} % (fold)
\label{sub:inversion}
-\begin{tkzexample}[latex=0cm,small,code only]
- \begin{tkzelements}
- z.A = point: new (-1,0)
- z.B = point: new (2,2)
- z.C = point: new (2,4)
- z.E = point: new (1,6)
- C.AC = circle: new (z.A,z.C)
- L.Tt1,L.Tt2 = C.AC: tangent_from (z.E)
- z.t1 = L.Tt1.pb
- z.t2 = L.Tt2.pb
- L.AE = line: new (z.A,z.E)
- z.H = L.AE : projection (z.t1)
- z.Bp,
- z.Ep,
- z.Cp = C.AC: inversion ( z.B, z.E, z.C )
-\end{tkzelements}
-
-\begin{tikzpicture}
- \tkzGetNodes
- \tkzDrawPoints(A,B,C)
- \tkzDrawCircles(A,C A,B)
- \tkzDrawLines(A,B' E,t1 E,t2 t1,t2 A,E)
- \tkzDrawPoints(A,B,C,E,t1,t2,H,B',E')
- \tkzLabelPoints(A,B,C,E,t1,t2,B',E')
- \tkzLabelPoints[above](C')
-\end{tikzpicture}
-\end{tkzexample}
-
\begin{tkzelements}
scale = .75
z.A = point: new (-1,0)
@@ -3910,7 +3918,26 @@ z.Ep,
z.Cp = C.AC: inversion ( z.B, z.E, z.C )
\end{tkzelements}
-\hspace*{\fill}
+
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+ \begin{tkzelements}
+ z.A = point: new (-1,0)
+ z.B = point: new (2,2)
+ z.C = point: new (2,4)
+ z.E = point: new (1,6)
+ C.AC = circle: new (z.A,z.C)
+ L.Tt1,
+ L.Tt2 = C.AC: tangent_from (z.E)
+ z.t1 = L.Tt1.pb
+ z.t2 = L.Tt2.pb
+ L.AE = line: new (z.A,z.E)
+ z.H = L.AE : projection (z.t1)
+ z.Bp,
+ z.Ep,
+ z.Cp = C.AC: inversion ( z.B, z.E, z.C )
+\end{tkzelements}
+
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPoints(A,B,C)
@@ -3920,14 +3947,26 @@ z.Cp = C.AC: inversion ( z.B, z.E, z.C )
\tkzLabelPoints(A,B,C,E,t1,t2,B',E')
\tkzLabelPoints[above](C')
\end{tikzpicture}
-\hspace*{\fill}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \begin{tikzpicture}[scale=.75]
+ \tkzGetNodes
+ \tkzDrawPoints(A,B,C)
+ \tkzDrawCircles(A,C A,B)
+ \tkzDrawLines(A,B' E,t1 E,t2 t1,t2 A,E)
+ \tkzDrawPoints(A,B,C,E,t1,t2,H,B',E')
+ \tkzLabelPoints(A,B,C,E,t1,t2,B',E')
+ \tkzLabelPoints[above](C')
+ \end{tikzpicture}
+\end{minipage}
% subsection inversion (end)
\subsection{Gergonne point} % (fold)
\label{sub:gergonne_point}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.a = point: new(1,0)
z.b = point: new(6,2)
@@ -3945,7 +3984,7 @@ z.ta,z.tb,z.tc = get_points (T : intouch ())
\tkzDrawSegments (a,ta b,tb c,tc)
\tkzDrawCircle(i,ta)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}\vspace{0pt}%
\begin{tkzelements}
@@ -3975,7 +4014,7 @@ z.ta,z.tb,z.tc = get_points (T : intouch ())
\begin{minipage}{.5\textwidth}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.a = point: new (0,0)
z.b = point: new (5,0)
@@ -3999,7 +4038,7 @@ z.ta,z.tb,z.tc = get_points (T : intouch ())
\tkzDrawSegments(x_0,x_1 y_0,y_1 z_0,z_1)
\tkzDrawCircle(L,x_0)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\end{minipage}
\begin{minipage}{.5\textwidth}
\begin{tkzelements}
@@ -4032,7 +4071,7 @@ z.z_0,z.z_1 = get_points (L.anti)
\subsection{Soddy circle without function} % (fold)
\label{sub:soddy}
-\begin{verbatim}
+\begin{Verbatim}
\begin{tkzelements}
z.A = point : new ( 0 , 0 )
z.B = point : new ( 5 , 0 )
@@ -4077,7 +4116,7 @@ z.Xip,z.Yip,z.Zip = C.ins : inversion (z.Xi,z.Yi,z.Zi)
\tkzDrawLines(X',Ha Y',Hb Z',Hc)
\tkzDrawLines(X',E Y',F Z',G)
\end{tikzpicture}
-\end{verbatim}
+\end{Verbatim}
\begin{tkzelements}
z.A = point : new ( 0 , 0 )
@@ -4128,7 +4167,6 @@ z.Xip,z.Yip,z.Zip = C.ins : inversion (z.Xi,z.Yi,z.Zi)
\subsection{Soddy circle with function} % (fold)
\label{sub:soddy_circle_with_function}
-\begin{verbatim}
\begin{tkzelements}
z.A = point : new ( 0 , 0 )
z.B = point : new ( 5 , 0 )
@@ -4145,9 +4183,33 @@ C.soddy_ext = C.ins : inversion (C.soddy_int)
z.w = C.soddy_ext.center
z.t = C.soddy_ext.through
z.Xip,z.Yip,z.Zip = C.ins : inversion (z.xi,z.yi,z.zi)
- \end{tkzelements}
+\end{tkzelements}
-\begin{tikzpicture}
+\begin{minipage}{.5\textwidth}
+ \begin{Verbatim}
+ \begin{tkzelements}
+ z.A = point : new ( 0 , 0 )
+ z.B = point : new ( 5 , 0 )
+ z.C = point : new (4 , 4 )
+ T.ABC = triangle : new ( z.A,z.B,z.C )
+ z.I = T.ABC.incenter
+ z.E,z.F,z.G = T.ABC : projection (z.I)
+ T.orthic = T.ABC : orthic ()
+ z.Ha,z.Hb,z.Hc = get_points (T.orthic)
+ C.ins = circle : new (z.I,z.E)
+ z.s,z.xi,z.yi,
+ z.zi = T.ABC : soddy_center ()
+ C.soddy_int = circle : new (z.s,z.xi)
+ C.soddy_ext = C.ins : inversion (C.soddy_int)
+ z.w = C.soddy_ext.center
+ z.t = C.soddy_ext.through
+ z.Xip,z.Yip,
+ z.Zip = C.ins : inversion (z.xi,z.yi,z.zi)
+ \end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+\begin{tikzpicture}[scale=.6]
\tkzGetNodes
\tkzDrawPolygon(A,B,C)
\tkzDrawCircles(A,G B,E C,F I,E s,xi w,t)
@@ -4156,28 +4218,10 @@ z.Xip,z.Yip,z.Zip = C.ins : inversion (z.xi,z.yi,z.zi)
\tkzDrawPoints(A,B,C,E,F,G,Ha,Hb,Hc,xi,yi,zi,I)
\tkzDrawPoints(Xi',Yi',Zi')
\tkzLabelPoints(A,B,C,E,F,G)
-\tkzDrawCircles(A,G B,E C,F I,E w,s)
\end{tikzpicture}
-\end{verbatim}
-
-\begin{tkzelements}
-z.A = point : new ( 0 , 0 )
-z.B = point : new ( 5 , 0 )
-z.C = point : new (4 , 4 )
-T.ABC = triangle : new ( z.A,z.B,z.C )
-z.I = T.ABC.incenter
-z.E,z.F,z.G = T.ABC : projection (z.I)
-T.orthic = T.ABC : orthic ()
-z.Ha,z.Hb,z.Hc = get_points (T.orthic)
-C.ins = circle : new (z.I,z.E)
-z.s,z.xi,z.yi,z.zi = T.ABC : soddy_center ()
-C.soddy_int = circle : new (z.s,z.xi)
-C.soddy_ext = C.ins : inversion (C.soddy_int)
-z.w = C.soddy_ext.center
-z.t = C.soddy_ext.through
-z.Xip,z.Yip,z.Zip = C.ins : inversion (z.xi,z.yi,z.zi)
- \end{tkzelements}
+\end{minipage}
+\begin{Verbatim}
\begin{tikzpicture}
\tkzGetNodes
\tkzDrawPolygon(A,B,C)
@@ -4187,8 +4231,9 @@ z.Xip,z.Yip,z.Zip = C.ins : inversion (z.xi,z.yi,z.zi)
\tkzDrawPoints(A,B,C,E,F,G,Ha,Hb,Hc,xi,yi,zi,I)
\tkzDrawPoints(Xi',Yi',Zi')
\tkzLabelPoints(A,B,C,E,F,G)
-\tkzDrawCircles(A,G B,E C,F I,E w,s)
\end{tikzpicture}
+\end{Verbatim}
+
% subsection soddy_circle_with_function (end)
@@ -4244,8 +4289,8 @@ Les cercles de centre $J_i$ et de diamètre $S_iT_i$ ont pour images les cercles
\tkzLabelPoint(H'){$H'_\i$}}
\end{tikzpicture}
-\begin{verbatim}
\begin{tkzelements}
+ scale =.75
xC,nc = 10,16
xB = xC/tkzphi
xD = (xC*xC)/xB
@@ -4273,49 +4318,39 @@ Les cercles de centre $J_i$ et de diamètre $S_iT_i$ ont pour images les cercles
end
\end{tkzelements}
-\def\nc{\tkzUseLua{nc}}
-
-\begin{tikzpicture}[ultra thin]
- \tkzGetNodes
- \tkzDrawCircle[fill=teal!20](i,C)
- \tkzDrawCircle[fill=PineGreen!60](j,B)
- \foreach \i in {-\nc,...,0,...,\nc} {
- \tkzDrawCircle[fill=teal]({I\i},{S\i'})
- }
-\end{tikzpicture}
-
-\end{verbatim}
-
+\begin{Verbatim}
\begin{tkzelements}
- xC,nc = 10,16
- xB = xC/tkzphi
- xD = (xC*xC)/xB
- xJ = (xC+xD)/2
- r = xD-xJ
- z.A = point : new ( 0 , 0 )
- z.B = point : new ( xB , 0)
- z.C = point : new ( xC , 0)
- L.AC = line : new (z.A,z.C)
- z.i = L.AC.mid
- L.AB = line:new (z.A,z.B)
- z.j = L.AB.mid
- z.D = point : new ( xD , 0)
- C.AC = circle: new (z.A,z.C)
- for i = -nc,nc do
- z["J"..i] = point: new (xJ,2*r*i)
- z["H"..i] = point: new (xJ,2*r*i-r)
- z["J"..i.."p"], z["H"..i.."p"] = C.AC : inversion (z["J"..i],z["H"..i])
- L.AJ = line : new (z.A,z["J"..i])
- C.JH = circle: new ( z["J"..i] , z["H"..i])
- z["S"..i], z["T"..i] = intersection (L.AJ,C.JH)
- z["S"..i.."p"], z["T"..i.."p"] = C.AC : inversion (z["S"..i],z["T"..i])
- L.SpTp = line:new ( z["S"..i.."p"], z["T"..i.."p"])
- z["I"..i] = L.SpTp.mid
- end
+ xC,nc = 10,16
+ xB = xC/tkzphi
+ xD = (xC*xC)/xB
+ xJ = (xC+xD)/2
+ r = xD-xJ
+ z.A = point : new ( 0 , 0 )
+ z.B = point : new ( xB , 0)
+ z.C = point : new ( xC , 0)
+ L.AC = line : new (z.A,z.C)
+ z.i = L.AC.mid
+ L.AB = line:new (z.A,z.B)
+ z.j = L.AB.mid
+ z.D = point : new ( xD , 0)
+ C.AC = circle: new (z.A,z.C)
+ for i = -nc,nc do
+ z["J"..i] = point: new (xJ,2*r*i)
+ z["H"..i] = point: new (xJ,2*r*i-r)
+ z["J"..i.."p"], z["H"..i.."p"] = C.AC : inversion (z["J"..i],z["H"..i])
+ L.AJ = line : new (z.A,z["J"..i])
+ C.JH = circle: new ( z["J"..i] , z["H"..i])
+ z["S"..i], z["T"..i] = intersection (L.AJ,C.JH)
+ z["S"..i.."p"], z["T"..i.."p"] = C.AC : inversion (z["S"..i],z["T"..i])
+ L.SpTp = line:new ( z["S"..i.."p"], z["T"..i.."p"])
+ z["I"..i] = L.SpTp.mid
+ end
\end{tkzelements}
+\end{Verbatim}
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
\def\nc{\tkzUseLua{nc}}
-
\begin{tikzpicture}[ultra thin]
\tkzGetNodes
\tkzDrawCircle[fill=teal!20](i,C)
@@ -4324,14 +4359,26 @@ Les cercles de centre $J_i$ et de diamètre $S_iT_i$ ont pour images les cercles
\tkzDrawCircle[fill=teal]({I\i},{S\i'})
}
\end{tikzpicture}
-
-
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+ \def\nc{\tkzUseLua{nc}}
+
+ \begin{tikzpicture}[ultra thin]
+ \tkzGetNodes
+ \tkzDrawCircle[fill=teal!20](i,C)
+ \tkzDrawCircle[fill=PineGreen!60](j,B)
+ \foreach \i in {-\nc,...,0,...,\nc} {
+ \tkzDrawCircle[fill=teal]({I\i},{S\i'})
+ }
+ \end{tikzpicture}
+ \vfill
+\end{minipage}
% subsubsection pappus_chain (end)
\subsection{Three Circles} % (fold)
\label{sub:three_circles}
-\begin{verbatim}
\begin{tkzelements}
function threecircles(c1,r1,c2,r2,c3,h1,h3,h2)
local xk = math.sqrt (r1*r2)
@@ -4348,15 +4395,8 @@ end
threecircles("A",4,"B",3,"C","E","G","F")
\end{tkzelements}
-\begin{tikzpicture}
-\tkzGetNodes
-\tkzDrawSegment[color = red](E,F)
-\tkzDrawCircle[orange,fill=orange!20](A,E)
-\tkzDrawCircle[purple,fill=purple!20](B,F)
-\tkzDrawCircle[teal,fill=teal!20](C,G)
-\end{tikzpicture}
-\end{verbatim}
-
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
\begin{tkzelements}
function threecircles(c1,r1,c2,r2,c3,h1,h3,h2)
local xk = math.sqrt (r1*r2)
@@ -4374,19 +4414,28 @@ end
\end{tkzelements}
\begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawSegment[color = red](E,F)
+ \tkzDrawCircle[orange,fill=orange!20](A,E)
+ \tkzDrawCircle[purple,fill=purple!20](B,F)
+ \tkzDrawCircle[teal,fill=teal!20](C,G)
+\end{tikzpicture}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+\begin{tikzpicture}[scale=.5]
\tkzGetNodes
\tkzDrawSegment[color = red](E,F)
\tkzDrawCircle[orange,fill=orange!20](A,E)
\tkzDrawCircle[purple,fill=purple!20](B,F)
\tkzDrawCircle[teal,fill=teal!20](C,G)
\end{tikzpicture}
-
+\end{minipage}
% subsection three_circles (end)
\subsection{pentagons in a golden arbelos} % (fold)
\label{sub:golden_arbelos}
-\begin{verbatim}
\begin{tkzelements}
z.A = point: new (0 , 0)
z.B = point: new (10 , 0)
@@ -4407,7 +4456,7 @@ z.L = T.golden.pc
L.O0L = line:new(z.O_0,z.L)
z.D = intersection (L.O0L,C.O0B)
L.DB = line:new(z.D,z.B)
-z.Z = intersection (L.DB,C.O2B)
+_,z.Z = intersection (L.DB,C.O2B)
L.DA = line:new(z.D,z.A)
z.I = intersection (L.DA,C.O1C)
L.O2Z = line:new(z.O_2,z.Z)
@@ -4423,10 +4472,49 @@ kk = tkzphi
z.D_1,z.E_1,z.F_1,z.G_1 = z.B : homothety (k, z.D,z.E,z.F,z.G)
z.D_2,z.E_2,z.F_2,z.G_2 = z.M_0 : homothety (kk,z.D_1,z.E_1,z.F_1,z.G_1)
\end{tkzelements}
-\end{verbatim}
-\begin{verbatim}
-\begin{tikzpicture}[scale=.8]
+\begin{minipage}{.5\textwidth}
+\begin{Verbatim}
+\begin{tkzelements}
+ z.A = point: new (0 , 0)
+ z.B = point: new (10 , 0)
+ L.AB = line: new ( z.A, z.B)
+ z.C = L.AB : gold_ratio ()
+ L.AC = line: new ( z.A, z.C)
+ L.CB = line: new ( z.C, z.B)
+ z.O_0 = L.AB.mid
+ z.O_1 = L.AC.mid
+ z.O_2 = L.CB.mid
+ C.O0B = circle: new ( z.O_0, z.B)
+ C.O1C = circle: new ( z.O_1, z.C)
+ C.O2B = circle: new ( z.O_2, z.B)
+ z.M_0 = C.O1C : external_similitude (C.O2B)
+ L.O0C = line:new(z.O_0,z.C)
+ T.golden = L.O0C : golden ()
+ z.L = T.golden.pc
+ L.O0L = line:new(z.O_0,z.L)
+ z.D = intersection (L.O0L,C.O0B)
+ L.DB = line:new(z.D,z.B)
+ z.Z = intersection (L.DB,C.O2B)
+ L.DA = line:new(z.D,z.A)
+ z.I = intersection (L.DA,C.O1C)
+ L.O2Z = line:new(z.O_2,z.Z)
+ z.H = intersection (L.O2Z,C.O0B)
+ C.BD = circle:new (z.B,z.D)
+ C.DB = circle:new (z.D,z.B)
+ _,z.G = intersection (C.BD,C.O0B)
+ z.E = intersection (C.DB,C.O0B)
+ C.GB = circle:new (z.G,z.B)
+ _,z.F = intersection (C.GB,C.O0B)
+ k = 1/tkzphi^2
+ kk = tkzphi
+ z.D_1,z.E_1,z.F_1,z.G_1 = z.B : homothety (k, z.D,z.E,z.F,z.G)
+ z.D_2,z.E_2,z.F_2,z.G_2 = z.M_0 : homothety (kk,z.D_1,z.E_1,z.F_1,z.G_1)
+\end{tkzelements}
+\end{Verbatim}
+\end{minipage}
+\begin{minipage}{.5\textwidth}
+\begin{tikzpicture}[scale=.7]
\tkzGetNodes
\tkzDrawPolygon[red](O_2,O_0,I,D,H)
\tkzDrawPolygon[blue](B,D_1,E_1,F_1,G_1)
@@ -4451,46 +4539,9 @@ z.D_2,z.E_2,z.F_2,z.G_2 = z.M_0 : homothety (kk,z.D_1,z.E_1,z.F_1,z.G_1)
\tkzLabelPoints(D_1,G_1)
\tkzLabelPoints(D_2,G_2)
\end{tikzpicture}
-\vspace{\fill}
-\end{verbatim}
+\end{minipage}
-\begin{tkzelements}
-z.A = point: new (0 , 0)
-z.B = point: new (10 , 0)
-L.AB = line: new ( z.A, z.B)
-z.C = L.AB : gold_ratio ()
-L.AC = line: new ( z.A, z.C)
-L.CB = line: new ( z.C, z.B)
-z.O_0 = L.AB.mid
-z.O_1 = L.AC.mid
-z.O_2 = L.CB.mid
-C.O0B = circle: new ( z.O_0, z.B)
-C.O1C = circle: new ( z.O_1, z.C)
-C.O2B = circle: new ( z.O_2, z.B)
-z.M_0 = C.O1C : external_similitude (C.O2B)
-L.O0C = line:new(z.O_0,z.C)
-T.golden = L.O0C : golden ()
-z.L = T.golden.pc
-L.O0L = line:new(z.O_0,z.L)
-z.D = intersection (L.O0L,C.O0B)
-L.DB = line:new(z.D,z.B)
-_,z.Z = intersection (L.DB,C.O2B)
-L.DA = line:new(z.D,z.A)
-z.I = intersection (L.DA,C.O1C)
-L.O2Z = line:new(z.O_2,z.Z)
-_,z.H = intersection (L.O2Z,C.O0B)
-C.BD = circle:new (z.B,z.D)
-C.DB = circle:new (z.D,z.B)
-_,z.G = intersection (C.BD,C.O0B)
-z.E = intersection (C.DB,C.O0B)
-C.GB = circle:new (z.G,z.B)
-_,z.F = intersection (C.GB,C.O0B)
-k = 1/tkzphi^2
-kk = tkzphi
-z.D_1,z.E_1,z.F_1,z.G_1 = z.B : homothety (k, z.D,z.E,z.F,z.G)
-z.D_2,z.E_2,z.F_2,z.G_2 = z.M_0 : homothety (kk,z.D_1,z.E_1,z.F_1,z.G_1)
-\end{tkzelements}
-\vspace{\fill}
+\begin{Verbatim}
\begin{tikzpicture}[scale=.8]
\tkzGetNodes
\tkzDrawPolygon[red](O_2,O_0,I,D,H)
@@ -4516,5 +4567,8 @@ z.D_2,z.E_2,z.F_2,z.G_2 = z.M_0 : homothety (kk,z.D_1,z.E_1,z.F_1,z.G_1)
\tkzLabelPoints(D_1,G_1)
\tkzLabelPoints(D_2,G_2)
\end{tikzpicture}
-\vspace{\fill}
+\end{Verbatim}
+
+
+
% subsection golden_arbelos (end) \ No newline at end of file