?? pappus.m
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function pappus(L1,L2)% pappus(L1,L2): illustrate pappus' theorem.% L1: three colinear points% L2: three colinear points% Cross-connect the points and intersect coresponding lines.% The result is three colinear points.%% Note: points must be homogeneous with e3 as the special coordinate.%% Examples: % pappus({e3+e1,e3+2*e1+.1*e2,e3+5*e1+.4*e2},{e3+e2,e3+2*e1+2*e2,e3+4*e1+3*e2})% pappus({e3,e3+e1,e3+4*e1},{e3+e1+e2,e3+3*e1+2*e2,e3+7*e1+4*e2})P1 = L1{1};P2 = L1{2};P3 = L1{3};Q1 = L2{1};Q2 = L2{2};Q3 = L2{3};DrawPolyline(L1,'r');DrawPolyline(L2,'r');DrawPolyline({P1,Q2},'k');DrawPolyline({P1,Q3},'k');DrawPolyline({P2,Q1},'k');DrawPolyline({P2,Q3},'k');DrawPolyline({P3,Q1},'k');DrawPolyline({P3,Q2},'k');H1 = meet(join(P1,Q2),join(P2,Q1));A1 = H1/inner(H1,e3);H2 = meet(join(P2,Q3),join(P3,Q2));A2 = H2/inner(H2,e3);H3 = meet(join(P1,Q3),join(P3,Q1));A3 = H3/inner(H3,e3);DrawPolyline({A1,A2},'b')DrawHomogeneous(e3,H1,'n','g');DrawHomogeneous(e3,H2,'n','g');DrawHomogeneous(e3,H3,'n','g');GAview([0,90]);?? 快捷鍵說明
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