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Diffstat (limited to 'macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex')
-rw-r--r-- | macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex | 1072 |
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)
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