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Diffstat (limited to 'macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex')
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1 files changed, 251 insertions, 229 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 9e79877299..5efb52381f 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 @@ -179,22 +179,23 @@ z.E = intersection (L.AI,L.LLC) \subsection{Apollonius circle} % (fold) \label{sub:apollonius_circle} -\begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} scale=.75 - z.A = point: new (0 , 0) - z.B = point: new (6 , 0) - z.M = point: new (5 , 3) + z.A = point: new (0 , 0) + z.B = point: new (6 , 0) + z.M = point: new (5 , 3) T.MAB = triangle : new (z.M,z.A,z.B) L.bis = T.MAB : bisector () - z.C = L.bis.pb + z.C = L.bis.pb L.bisext = T.MAB : bisector_ext () - z.D = intersection (T.MAB.bc, L.bisext) - L.CD = line: new (z.C,z.D) - z.O = L.CD.mid - L.AM = T.MAB.ab - z.E = z.M : symmetry (z.A) + z.D = intersection (T.MAB.bc, L.bisext) + L.CD = line: new (z.C,z.D) + z.O = L.CD.mid + L.AM = T.MAB.ab + z.E = z.M : symmetry (z.A) \end{tkzelements} + +\hspace*{\fill} \begin{tikzpicture} \tkzGetNodes \tkzDrawSegment[add=0 and 1](A,M) @@ -210,26 +211,24 @@ scale=.75 \tkzMarkAngles[mark=|](A,M,C C,M,B) \tkzMarkAngles[mark=||](B,M,D D,M,E) \end{tikzpicture} -\end{tkzexample} - +\hspace*{\fill} +\begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} scale=.75 - z.A = point: new (0 , 0) - z.B = point: new (6 , 0) - z.M = point: new (5 , 3) + z.A = point: new (0 , 0) + z.B = point: new (6 , 0) + z.M = point: new (5 , 3) T.MAB = triangle : new (z.M,z.A,z.B) L.bis = T.MAB : bisector () - z.C = L.bis.pb + z.C = L.bis.pb L.bisext = T.MAB : bisector_ext () - z.D = intersection (T.MAB.bc, L.bisext) - L.CD = line: new (z.C,z.D) - z.O = L.CD.mid - L.AM = T.MAB.ab - z.E = z.M : symmetry (z.A) + z.D = intersection (T.MAB.bc, L.bisext) + L.CD = line: new (z.C,z.D) + z.O = L.CD.mid + L.AM = T.MAB.ab + z.E = z.M : symmetry (z.A) \end{tkzelements} - -\hspace*{\fill} \begin{tikzpicture} \tkzGetNodes \tkzDrawSegment[add=0 and 1](A,M) @@ -245,7 +244,12 @@ scale=.75 \tkzMarkAngles[mark=|](A,M,C C,M,B) \tkzMarkAngles[mark=||](B,M,D D,M,E) \end{tikzpicture} -\hspace*{\fill} +\end{tkzexample} + +Remark : The circle can be obtained with: + +|C.AB = T.MAB.bc : apollonius (length(z.M,z.A)/length(z.M,z.B))| + %subsection apollonius_circle (end) @@ -428,8 +432,8 @@ Same result using the function |T.ABC.ab : apollonius (k) | z.w1,z.t1 = get_points ( C.AB ) C.AC = T.ABC.ca : apollonius (length(z.B,z.C)/length(z.B,z.A)) z.w2,z.t2 = get_points ( C.AC ) - C.AC = T.ABC.bc : apollonius (length(z.A,z.B)/length(z.A,z.C)) - z.w3,z.t3 = get_points ( C.AC ) + 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} @@ -733,19 +737,19 @@ Same result using the function |T.ABC.ab : apollonius (k) | z.c = C.center \end{tkzelements} - \hspace*{\fill} - \begin{tikzpicture} - \tkzGetNodes - \tkzDrawCircle(O,A) - \tkzDrawCircle[orange](c,z1) - \tkzDrawPoints[orange](O,A,z1,z2,c) - \tkzLabelPoints[right](O,A,z1,z2,c) - \end{tikzpicture} - \hspace*{\fill} +\hspace*{\fill} +\begin{tikzpicture} +\tkzGetNodes +\tkzDrawCircle(O,A) +\tkzDrawCircle[orange](c,z1) +\tkzDrawPoints[orange](O,A,z1,z2,c) +\tkzLabelPoints[right](O,A,z1,z2,c) +\end{tikzpicture} +\hspace*{\fill} % subsection orthogonal_circle_through (end) -\subsection{Devine ratio} % (fold) -\label{sub:devine_ratio} +\subsection{Divine ratio} % (fold) +\label{sub:divine_ratio} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} @@ -809,52 +813,53 @@ L.BG = line: new (z.B,z.G) z.L = intersection (L.AR,L.BG) \end{tkzelements} - \hspace*{\fill} - \begin{tikzpicture} - \tkzGetNodes - \tkzDrawPolygons(A,C,E,F A,B,G,H) - \tkzDrawCircles(O_1,C O_2,B O_0,B) - \tkzDrawSegments(H,C B,K A,L) - \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} - \hspace*{\fill} -% subsection devine_ratio (end) +\hspace*{\fill} +\begin{tikzpicture} +\tkzGetNodes +\tkzDrawPolygons(A,C,E,F A,B,G,H) +\tkzDrawCircles(O_1,C O_2,B O_0,B) +\tkzDrawSegments(H,C B,K A,L) +\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} +\hspace*{\fill} +% subsection divine_ratio (end) \subsection{Director circle} % (fold) \label{sub:director_circle} % modif C: point (0.25) instead of 2 \begin{minipage}[t]{.5\textwidth}\vspace{0pt}% - \begin{verbatim} - \begin{tkzelements} - scale = .5 - z.O = point: new (0 , 0) - z.F1 = point: new (4 , 0) - z.F2 = point: new (-4 , 0) - z.H = point: new (4*math.sqrt(2) , 0) - E = ellipse: foci (z.F2,z.F1,z.H) - a,b = E.Rx, E.Ry - z.A = E.covertex - T = triangle: new (z.H,z.O,z.A) - z.P = T: parallelogram () - C = circle: new (z.O,z.P) - z.L = C: point (0.25) - L.J,L.K = E: tangent_from (z.L) - z.J = L.J.pb - z.K = L.K.pb - \end{tkzelements} - \begin{tikzpicture} - \tkzGetNodes - \tkzDrawPoints(F1,F2,O) - \tkzDrawCircles[teal](O,P) - \tkzDrawPolygon(H,O,A,P) - \tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{b},0) - \tkzDrawSegments[orange](O,P O,L L,J L,K) - \tkzDrawPoints(F1,F2,O,H,A,P,L,J,K) - \tkzLabelPoints(F1,F2,O,H,A,P,L,J,K) - \tkzMarkRightAngles(A,P,H J,L,K) - \end{tikzpicture} - \end{verbatim} +\begin{verbatim} +\begin{tkzelements} + scale = .5 + z.O = point: new (0 , 0) + z.F1 = point: new (4 , 0) + z.F2 = point: new (-4 , 0) + z.H = point: new (4*math.sqrt(2) , 0) + E = ellipse: foci (z.F2,z.F1,z.H) + a,b = E.Rx, E.Ry + z.A = E.covertex + T = triangle: new (z.H,z.O,z.A) + z.P = T: parallelogram () + C = circle: new (z.O,z.P) + z.L = C: point (0.25) + L.J,L.K = E: tangent_from (z.L) + z.J = L.J.pb + z.K = L.K.pb +\end{tkzelements} +\begin{tikzpicture} + \tkzGetNodes + \tkzDrawPoints(F1,F2,O) + \tkzDrawCircles[teal](O,P) + \tkzDrawPolygon(H,O,A,P) + \tkzDrawEllipse[red](O,\tkzUseLua{a},\tkzUseLua{b},0) + \tkzDrawSegments[orange](O,P O,L L,J L,K) + \tkzDrawPoints(F1,F2,O,H,A,P,L,J,K) + \tkzLabelPoints(F1,F2,O,H,A,P,L,J,K) + \tkzLabelPoints[above](L) + \tkzMarkRightAngles(A,P,H J,L,K) +\end{tikzpicture} +\end{verbatim} \end{minipage} \begin{minipage}[t]{.5\textwidth}\vspace{0pt}% \begin{tkzelements} @@ -885,6 +890,7 @@ z.K = L.K.pb \tkzDrawSegments[orange](O,P O,L L,J L,K) \tkzDrawPoints(F1,F2,O,H,A,P,L,J,K) \tkzLabelPoints(F1,F2,O,H,A,P,L,J,K) +\tkzLabelPoints[above](L) \tkzMarkRightAngles(A,P,H J,L,K) \end{tikzpicture} \end{minipage} @@ -942,8 +948,8 @@ z.C = intersection (L.EG,L.AB) z.O = C.AB: antipode (z.B) \end{tkzelements} - \hspace*{\fill} - \begin{tikzpicture} +\hspace*{\fill} +\begin{tikzpicture} \tkzGetNodes \tkzDrawArc[delta=5](O,B)(G) \tkzDrawCircles(A,B B,A) @@ -952,13 +958,13 @@ z.O = C.AB: antipode (z.B) \tkzMarkSegments[mark=s||](A,E B,E O,A) \tkzDrawPoints(A,B,C,E,I,J,G,O,K) \tkzLabelPoints(A,B,C,E,I,J,G,O,K) - \end{tikzpicture} - \hspace*{\fill} +\end{tikzpicture} + \hspace*{\fill} % subsection gold_division (end) \subsection{Ellipse} % (fold) \label{sub:ellipse} - +\begin{minipage}{.5\textwidth} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} z.C = point: new (3 , 2) @@ -971,7 +977,6 @@ z.O = C.AB: antipode (z.B) a = E.Rx b = E.Ry slope = math.deg(E.slope) - \end{tkzelements} \begin{tikzpicture} \tkzGetNodes @@ -981,7 +986,8 @@ z.O = C.AB: antipode (z.B) \tkzLabelPoints(C,A,B) \end{tikzpicture} \end{tkzexample} - +\end{minipage} +\begin{minipage}{.5\textwidth} \begin{tkzelements} z.C = point: new (3 , 2) z.A = point: new (5 , 1) @@ -1004,53 +1010,55 @@ slope = math.deg(E.slope) \tkzLabelPoints(C,A,B) \end{tikzpicture} \hspace*{\fill} +\end{minipage} % subsection ellipse (end) \subsection{Ellipse with radii} % (fold) \label{sub:ellipse_with_radii} - +\begin{minipage}{.5\textwidth} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} -z.C = point: new (0 , 4) -z.B = point: new (4 , 0) -z.D = point: new (2 , 6) -b = math.sqrt(8) -a = math.sqrt(32) -ang = math.deg(math.pi/4) -E = ellipse: radii (z.C,a,b,math.pi/4) -z.V = E : point (0) -z.CoV = E : point (0.25) -\end{tkzelements} -\begin{tikzpicture} +scale=.5 +z.C = point: new (0 , 4) +b = value(math.sqrt(8)) +a = value(math.sqrt(32)) +ang = math.deg(math.pi/4) +E = ellipse: radii (z.C,a,b,math.pi/4) +z.V = E : point (0) +z.CoV = E : point (math.pi/2) +\end{tkzelements} +\begin{tikzpicture}[gridded] \tkzGetNodes -\tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang}) +\tkzDrawEllipse[blue](C,\tkzUseLua{a}, + \tkzUseLua{b},\tkzUseLua{ang}) \tkzDrawPoints(C,V,CoV) \end{tikzpicture} \end{tkzexample} - +\end{minipage} +\begin{minipage}{.5\textwidth} \begin{tkzelements} +scale=.5 z.C = point: new (0 , 4) -z.B = point: new (4 , 0) -z.D = point: new (2 , 6) -b = math.sqrt(8) -a = math.sqrt(32) +b = value(math.sqrt(8)) +a = value(math.sqrt(32)) ang = math.deg(math.pi/4) -E = ellipse: radii (z.C,a,b,math.pi/4) +E = ellipse: radii (z.C,a,b,math.pi/4) z.V = E : point (0) -z.CoV = E : point (0.25) -\end{tkzelements} +z.CoV = E : point (math.pi/2) +\end{tkzelements} \hspace*{\fill} -\begin{tikzpicture} +\begin{tikzpicture}[gridded] \tkzGetNodes \tkzDrawEllipse[blue](C,\tkzUseLua{a},\tkzUseLua{b},\tkzUseLua{ang}) \tkzDrawPoints(C,V,CoV) \end{tikzpicture} +\end{minipage} % subsection ellipse_with_radii (end) \subsection{Ellipse\_with\_foci} % (fold) \label{sub:ellipse_with_foci} - +\begin{minipage}{.5\textwidth} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} local e @@ -1079,7 +1087,8 @@ z.CoV = E : point (0.25) \tkzDrawLines(K,F K,G) \end{tikzpicture} \end{tkzexample} - +\end{minipage} +\begin{minipage}{.5\textwidth} \begin{tkzelements} local e e = .8 @@ -1109,27 +1118,28 @@ z.G = L.tb.pb \tkzDrawLines(K,F K,G) \end{tikzpicture} \hspace*{\fill} + \end{minipage} % subsection ellipse_with_foci (end) \subsection{Euler relation} % (fold) \label{sub:euler_relation} - +\begin{minipage}{.5\textwidth} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} - scale = .75 - 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.J,z.K = get_points(T.ABC: ex_circle (2)) - z.X ,z.Y,z.K = T.ABC : projection (z.J) - z.I,z.H = get_points(T.ABC : in_circle()) - z.O = T.ABC.circumcenter - C.OA = circle : new (z.O,z.A) - T.IBA = triangle: new (z.I,z.B,z.A) - z.w = T.IBA.circumcenter - L.Ow = line : new (z.O,z.w) - _,z.E = intersection (L.Ow, C.OA) + scale = .75 + 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.J,z.K = get_points(T.ABC: ex_circle (2)) + z.X,z.Y,z.K= T.ABC : projection (z.J) + z.I,z.H = get_points(T.ABC : in_circle()) + z.O = T.ABC.circumcenter + C.OA = circle : new (z.O,z.A) + T.IBA = triangle: new (z.I,z.B,z.A) + z.w = T.IBA.circumcenter + L.Ow = line : new (z.O,z.w) + _,z.E = intersection (L.Ow, C.OA) \end{tkzelements} \begin{tikzpicture} \tkzGetNodes @@ -1143,7 +1153,8 @@ z.G = L.tb.pb \tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J) \end{tikzpicture} \end{tkzexample} - +\end{minipage} +\begin{minipage}{.5\textwidth} \begin{tkzelements} z.A = point: new (0 , 0) z.B = point: new (5 , 0) @@ -1173,6 +1184,7 @@ _,z.E = intersection (L.Ow, C.OA) \tkzMarkRightAngles[fill=gray!20,opacity=.4](C,H,I A,K,J) \end{tikzpicture} \hspace*{\fill} +\end{minipage} % subsection euler_relation (end) \subsection{External angle} % (fold) @@ -1180,33 +1192,33 @@ _,z.E = intersection (L.Ow, C.OA) \begin{minipage}[t]{.5\textwidth}\vspace{0pt}% \begin{verbatim} \begin{tkzelements} - scale =.8 - z.A = point: new (0 , 0) - z.B = point: new (5 , 0) - z.C = point: new (-2 , 4) - T.ABC = triangle: new (z.A,z.B,z.C) - T.ext = T.ABC: excentral () - z.O = T.ABC.circumcenter - z.D = intersection (T.ext.ab,T.ABC.ab) - z.E = z.C: symmetry (z.B) + scale = .75 + z.A = point: new (0 , 0) + z.B = point: new (5 , 0) + z.C = point: new (-2 , 4) + T.ABC = triangle: new (z.A,z.B,z.C) + T.ext = T.ABC: excentral () + z.O = T.ABC.circumcenter + z.D = intersection (T.ext.ab,T.ABC.ab) + z.E = z.C: symmetry (z.B) \end{tkzelements} \begin{tikzpicture} - \tkzGetNodes - \tkzDrawPolygon(A,B,C) - \tkzDrawLine[purple,add=0 and .5](B,C) - \tkzDrawSegment[purple](A,D) - \tkzDrawSegment[orange](C,D) - \tkzFillAngles[purple!30,opacity=.2](D,C,A E,C,D) - \tkzMarkAngles[mark=|](D,C,A E,C,D) - \tkzDrawPoints(A,...,D) - \tkzLabelPoints[above](C) - \tkzLabelPoints(A,B,D) + \tkzGetNodes + \tkzDrawPolygon(A,B,C) + \tkzDrawLine[purple,add=0 and .5](B,C) + \tkzDrawSegment[purple](A,D) + \tkzDrawSegment[orange](C,D) + \tkzFillAngles[purple!30,opacity=.2](D,C,A E,C,D) + \tkzMarkAngles[mark=|](D,C,A E,C,D) + \tkzDrawPoints(A,...,D) + \tkzLabelPoints[above](C) + \tkzLabelPoints(A,B,D) \end{tikzpicture} \end{verbatim} \end{minipage} \begin{minipage}[t]{.5\textwidth}\vspace{0pt}% \begin{tkzelements} -scale = .8 +scale = .75 z.A = point: new (0 , 0) z.B = point: new (5 , 0) z.C = point: new (-2 , 4) @@ -1230,6 +1242,7 @@ z.E = z.C: symmetry (z.B) \tkzLabelPoints[above](C) \tkzLabelPoints(A,B,D) \end{tikzpicture} +\hspace*{\fill} \end{minipage} % subsection external_angle (end) @@ -1488,7 +1501,7 @@ z.O_0 = L.AB.mid \subsection{Harmonic division v1} % (fold) \label{sub:harmonic_division_v1} -\begin{minipage}[t]{.5\textwidth}\vspace{0pt}% +\begin{minipage}[t]{.4\textwidth}\vspace{0pt}% \begin{verbatim} \begin{tkzelements} scale=.75 @@ -1523,7 +1536,7 @@ z.C = intersection (L.XG,L.AB) \end{tikzpicture} \end{verbatim} \end{minipage} -\begin{minipage}[t]{.5\textwidth}\vspace{0pt}% +\begin{minipage}[t]{.6\textwidth}\vspace{0pt}% \begin{tkzelements} scale=.75 z.A = point: new (0 , 0) @@ -1556,6 +1569,7 @@ z.C = intersection (L.XG,L.AB) \tkzLabelPoints(A,B,G,E,F,C,D) \tkzMarkSegments(F,B B,E) \end{tikzpicture} +\hspace*{\fill} \end{minipage} % subsection harmonic_division_v1 (end) @@ -1621,7 +1635,7 @@ z.C = intersection (L.GX,L.AB) \subsection{Menelaus} % (fold) \label{sub:menelaus} -\begin{minipage}{.5\textwidth} +\begin{minipage}{.4\textwidth} \begin{verbatim} \begin{tkzelements} z.A = point: new (0 , 0) @@ -1645,7 +1659,7 @@ z.C = intersection (L.GX,L.AB) \end{tikzpicture} \end{verbatim} \end{minipage} -\begin{minipage}{.5\textwidth} +\begin{minipage}{.6\textwidth} \begin{tkzelements} z.A = point: new (0 , 0) z.B = point: new (6 , 0) @@ -1668,6 +1682,7 @@ z.R = intersection (L.BC,L.PX) \tkzDrawPoints(P,Q,R,A,B,C) \tkzLabelPoints(A,B,C,P,Q,R) \end{tikzpicture} +\hspace*{\fill} \end{minipage} % subsection menelaus (end) @@ -2041,7 +2056,7 @@ z.H = L.OOp : projection (z.X) \end{minipage} % subsection radical_circle (end) -\subsection{Hexagram} % (fold) +\subsection{Euler ellipse} % (fold) \label{sub:hexagram} \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} @@ -2080,6 +2095,9 @@ z.H = L.OOp : projection (z.X) _,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) @@ -2419,7 +2437,7 @@ z.O = C.DC : inversion (z.W) \end{tkzexample} \begin{tkzelements} -scale =.3 +scale =.5 z.A = point: new (0,0) z.B = point: new (6,0) z.C = point: new (0.8,4) @@ -2665,6 +2683,84 @@ z.Kp = L.Kp.pb \subsection{Midcircles} % (fold) \label{sub:midcircles} +\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.O2C = circle : new (z.O_2,z.B) +z.Q = C.O1C : midarc (z.C,z.A) +z.P = C.O2C : midarc (z.B,z.C) +L.O1O2 = line : new (z.O_1,z.O_2) +L.O0O1 = line : new (z.O_0,z.O_1) +L.O0O2 = line : new (z.O_0,z.O_2) +z.M_0 = L.O1O2 : harmonic_ext (z.C) +z.M_1 = L.O0O1 : harmonic_int (z.A) +z.M_2 = L.O0O2 : harmonic_int (z.B) +L.BQ = line : new (z.B,z.Q) +L.AP = line : new (z.A,z.P) +z.S = intersection (L.BQ,L.AP) +L.CS = line : new (z.C,z.S) +C.M1A = circle : new (z.M_1,z.A) +C.M2B = circle : new (z.M_2,z.B) +z.P_0 = intersection (L.CS,C.O0B) +z.P_1 = intersection (C.M2B,C.O1C) +z.P_2 = intersection (C.M1A,C.O2C) +T.P012 = triangle : new (z.P_0,z.P_1,z.P_2) +z.O_4 = T.P012.circumcenter +T.CP12 = triangle : new (z.C,z.P_1,z.P_2) +z.O_5 = T.CP12.circumcenter +z.BN = z.B : north () +L.BBN = line : new (z.B,z.BN) +L.M1P2 = line : new (z.M_1,z.P_2) +z.J = intersection (L.BBN,L.M1P2) +L.AP0 = line : new (z.A,z.P_0) +L.BP0 = line : new (z.B,z.P_0) +C.O4P0 = circle : new (z.O_4,z.P_0) +_,z.G = intersection (L.AP0,C.O4P0) +z.H = intersection (L.BP0,C.O4P0) +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} + +\hspace*{\fill} +\begin{tikzpicture} +\tkzGetNodes +\tkzDrawCircle[thin,fill=green!10](O_4,P_0) +\tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C) +\tkzDrawSemiCircles[teal](O_0,B) +\tkzDrawSemiCircles[thin,teal,fill=teal!20,opacity=.5](O_1,C O_2,B) +\tkzDrawSemiCircles[color = orange](M_2,B) +\tkzDrawSemiCircles[color = orange](M_1,A') +\tkzDrawArc[purple,delta=0](M_0,P_0)(C) +\tkzDrawSegments[very thin](A,B A,P B,Q) +\tkzDrawSegments[color=cyan](O_0,P_0 B,J G,J G,O_0 H,O_2) +\tkzDrawSegments[ultra thin,purple](M_1,P_0 M_2,P_0 M_1,M_0 M_0,P_1 M_0,P_0 M_1,J) +\tkzDrawPoints(A,B,C,P_0,P_2,P_1,M_0,M_1,M_2,J,P,Q,S) +\tkzDrawPoints(O_0,O_1,O_2,O_4,O_5,G,H) +\tkzMarkRightAngle[size=.2,fill=gray!20,opacity=.4](O_0,P_0,M_0) +\tkzLabelPoints[below](A,B,C,M_0,M_1,M_2,O_1,O_2,O_0) +\tkzLabelPoints[above](P_0,O_5,O_4) +\tkzLabelPoints[above](P_1,J) +\tkzLabelPoints[above](P_2,P,Q,S) +\tkzLabelPoints[above right](H,E) +\tkzLabelPoints[above left](F,G) +\tkzLabelPoints[below right](H_0) +\tkzLabelCircle[below=4pt,font=\scriptsize](O_1,C)(80){$(\beta)$} +\tkzLabelCircle[below=4pt,font=\scriptsize](O_2,B)(80){$(\gamma)$} +\tkzLabelCircle[below=4pt,font=\scriptsize](O_0,B)(110){$(\alpha)$} +\tkzLabelCircle[left,font=\scriptsize](O_4,P_2)(60){$(\delta)$} +\tkzLabelCircle[above left,font=\scriptsize](O_5,C)(40){$(\epsilon)$} +\end{tikzpicture} +\hspace*{\fill} + \begin{tkzexample}[latex=0cm,small,code only] \begin{tkzelements} z.A = point: new (0 , 0) @@ -2712,7 +2808,9 @@ z.Kp = L.Kp.pb 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} +\begin{tkzexample}[latex=0cm,small,code only] \begin{tikzpicture} \tkzGetNodes \tkzDrawCircle[thin,fill=green!10](O_4,P_0) @@ -2743,83 +2841,7 @@ z.Kp = L.Kp.pb \end{tikzpicture} \end{tkzexample} -\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.O2C = circle : new (z.O_2,z.B) -z.Q = C.O1C : midarc (z.C,z.A) -z.P = C.O2C : midarc (z.B,z.C) -L.O1O2 = line : new (z.O_1,z.O_2) -L.O0O1 = line : new (z.O_0,z.O_1) -L.O0O2 = line : new (z.O_0,z.O_2) -z.M_0 = L.O1O2 : harmonic_ext (z.C) -z.M_1 = L.O0O1 : harmonic_int (z.A) -z.M_2 = L.O0O2 : harmonic_int (z.B) -L.BQ = line : new (z.B,z.Q) -L.AP = line : new (z.A,z.P) -z.S = intersection (L.BQ,L.AP) -L.CS = line : new (z.C,z.S) -C.M1A = circle : new (z.M_1,z.A) -C.M2B = circle : new (z.M_2,z.B) -z.P_0 = intersection (L.CS,C.O0B) -z.P_1 = intersection (C.M2B,C.O1C) -z.P_2 = intersection (C.M1A,C.O2C) -T.P012 = triangle : new (z.P_0,z.P_1,z.P_2) -z.O_4 = T.P012.circumcenter -T.CP12 = triangle : new (z.C,z.P_1,z.P_2) -z.O_5 = T.CP12.circumcenter -z.BN = z.B : north () -L.BBN = line : new (z.B,z.BN) -L.M1P2 = line : new (z.M_1,z.P_2) -z.J = intersection (L.BBN,L.M1P2) -L.AP0 = line : new (z.A,z.P_0) -L.BP0 = line : new (z.B,z.P_0) -C.O4P0 = circle : new (z.O_4,z.P_0) -_,z.G = intersection (L.AP0,C.O4P0) -z.H = intersection (L.BP0,C.O4P0) -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} -\hspace*{\fill} -\begin{tikzpicture} -\tkzGetNodes -\tkzDrawCircle[thin,fill=green!10](O_4,P_0) -\tkzDrawCircle[purple,fill=purple!10,opacity=.5](O_5,C) -\tkzDrawSemiCircles[teal](O_0,B) -\tkzDrawSemiCircles[thin,teal,fill=teal!20,opacity=.5](O_1,C O_2,B) -\tkzDrawSemiCircles[color = orange](M_2,B) -\tkzDrawSemiCircles[color = orange](M_1,A') -\tkzDrawArc[purple,delta=0](M_0,P_0)(C) -\tkzDrawSegments[very thin](A,B A,P B,Q) -\tkzDrawSegments[color=cyan](O_0,P_0 B,J G,J G,O_0 H,O_2) -\tkzDrawSegments[ultra thin,purple](M_1,P_0 M_2,P_0 M_1,M_0 M_0,P_1 M_0,P_0 M_1,J) -\tkzDrawPoints(A,B,C,P_0,P_2,P_1,M_0,M_1,M_2,J,P,Q,S) -\tkzDrawPoints(O_0,O_1,O_2,O_4,O_5,G,H) -\tkzMarkRightAngle[size=.2,fill=gray!20,opacity=.4](O_0,P_0,M_0) -\tkzLabelPoints[below](A,B,C,M_0,M_1,M_2,O_1,O_2,O_0) -\tkzLabelPoints[above](P_0,O_5,O_4) -\tkzLabelPoints[above](P_1,J) -\tkzLabelPoints[above](P_2,P,Q,S) -\tkzLabelPoints[above right](H,E) -\tkzLabelPoints[above left](F,G) -\tkzLabelPoints[below right](H_0) -\tkzLabelCircle[below=4pt,font=\scriptsize](O_1,C)(80){$(\beta)$} -\tkzLabelCircle[below=4pt,font=\scriptsize](O_2,B)(80){$(\gamma)$} -\tkzLabelCircle[below=4pt,font=\scriptsize](O_0,B)(110){$(\alpha)$} -\tkzLabelCircle[left,font=\scriptsize](O_4,P_2)(60){$(\delta)$} -\tkzLabelCircle[above left,font=\scriptsize](O_5,C)(40){$(\epsilon)$} -\end{tikzpicture} -\hspace*{\fill} % subsection midcircles (end) \subsection{Pencil v1} % (fold) @@ -4452,11 +4474,11 @@ 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) -z.H = intersection (L.O2Z,C.O0B) +_,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) |