disp('>> %	PAPPUS'' THEOREM');     %	PAPPUS' THEOREM     GAfigure; clc; %/     disp('>> %	PAPPUS'' THEOREM');     %	PAPPUS' THEOREM     disp('>> %');     %     disp('>> % 	We use Pappus merely as an example doing geometry.');     % 	We use Pappus merely as an example doing geometry.     disp('>> %');     %     disp('>> %	Pappus'' theorem (actually from projective geometry):');     %	Pappus' theorem (actually from projective geometry):     disp('>> %	-- Specify two pairs of collinear points');     %	-- Specify two pairs of collinear points     disp('>> % 	-- Cross-connect the points and intersect corresponding lines.');     % 	-- Cross-connect the points and intersect corresponding lines.     disp('>> % 	-> The result is three collinear points.');     % 	-> The result is three collinear points.     disp('>> %');     %     disp('>> % Two points and a factor to determine collinear point:');     % Two points and a factor to determine collinear point:     global P1 P2 P3 Q1 Q2 Q3 H1 H2 H3 A1 A2 A3; %/     clf;	%/     e = e3;	%/     P1 = e - e1; %/     P2 = e  + e2/4; %/     mu = 1.5; %/     P3 = (1-mu)*P1 + mu*P2; %/     Q1 = e - 3*e1/4 -e2; %/     Q2 = e + e1/6 - 1.1*e2; %/     nu = 1.5; %/     Q3 = (1-nu)*Q1 + nu*Q2; %/     maxx = max([inner(e1,P1),inner(e1,P2),inner(e1,P3), inner(e1,Q1),inner(e1,Q2),inner(e1,Q3)]); %/     minx = min([inner(e1,P1),inner(e1,P2),inner(e1,P3), inner(e1,Q1),inner(e1,Q2),inner(e1,Q3)]); %/     maxy = max([inner(e2,P1),inner(e2,P2),inner(e2,P3), inner(e2,Q1),inner(e2,Q2),inner(e2,Q3)]); %/     miny = min([inner(e2,P1),inner(e2,P2),inner(e2,P3), inner(e2,Q1),inner(e2,Q2),inner(e2,Q3)]); %/     disp('>> ');          GAmouse = 1; %/     disp('>> % 	First line');     % 	First line     DrawHomogeneous(e,P1,'n','r'); GAtext(1.1*P1,'P_1','r'); %/     DrawHomogeneous(e,P2,'n','r'); GAtext(1.1*P2,'P_2','r'); %/     DrawHomogeneous(e,P3,'n','r'); GAtext(1.1*P3,'P_3','r'); %/     DrawPolyline({P1,P2,P3},'r'); %/     axis off; %/     GAview([0 90]); %/     axis([minx maxx miny maxy 0 1]);  %/     disp('>> % 	Next: second line');     % 	Next: second line     GAprompt; %/     DrawHomogeneous(e,Q1,'n','m'); GAtext(1.1*Q1,'Q_1','m'); %/     DrawHomogeneous(e,Q2,'n','m'); GAtext(1.1*Q2,'Q_2','m'); %/     DrawHomogeneous(e,Q3,'n','m'); GAtext(1.1*Q3,'Q_3','m'); %/     DrawPolyline({Q1,Q2,Q3},'m'); %/     axis([minx maxx miny maxy 0 1]);  %/     disp('>> % 	Next: intersect the connection lines');     % 	Next: intersect the connection lines     GAprompt; %/     DrawPolyline({P1,Q2},'k'); %/     DrawPolyline({P2,Q1},'k'); %/     disp('>> H1 = meet(join(P1,Q2),join(P2,Q1));');     H1 = meet(join(P1,Q2),join(P2,Q1));     disp('>> A1 = H1/inner(H1,e3);');     A1 = H1/inner(H1,e3);     DrawHomogeneous(e3,A1,'n','g'); GAtext(1.1*A1,'A_1','b'); %/     axis([minx maxx miny maxy 0 1]);  %/     GAprompt; %/     DrawPolyline({P3,Q2},'k'); %/     DrawPolyline({P2,Q3},'k'); %/     H2 = meet(join(P2,Q3),join(P3,Q2)); %/     A2 = H2/inner(H2,e3); %/     DrawHomogeneous(e3,A2,'n','g'); GAtext(1.1*A2,'A_2','b'); %/     axis([minx maxx miny maxy 0 1]);  %/     GAprompt; %/     DrawPolyline({P1,Q3},'k'); %/     DrawPolyline({P3,Q1},'k'); %/     H3 = meet(join(P1,Q3),join(P3,Q1)); %/     A3 = H3/inner(H3,e3); %/     DrawHomogeneous(e3,A3,'n','g'); GAtext(1.1*A3,'A_3','b'); %/     axis([minx maxx miny maxy 0 1]);  %/     GAprompt; %/     DrawPolyline({A1,A2},'b') %/     axis([minx maxx miny maxy 0 1]);  %/     disp('>> % 	Next: check whether A1, A2, A3 are on a line:');     % 	Next: check whether A1, A2, A3 are on a line:     GAprompt; %/     error = grade( A1^A2^A3/I3, 0); %/     title(['A_1 \wedge A_2 \wedge A_3 = ' num2str(error) ' * I_3'],'Color','b'); %/     GAmouse =0; %/