function r=morley(T)% morley(T) - illustrate Morley's theorem%  T - a triple of homogeneous (in e3) vertices%  r - an array with angles of Morley's triangle (should be 60,60,60)%% Examples: morley({e3,e3+2*e1+.5*e2,e3+e1+2*e2})%           morley({e3,e3+5*e1+.1*e2,e3+2.5*e1+e2})%           morley({e3,e3+1.8*e1+1.8*e2,e3+e1+2*e2})P1 = T{1};P2 = T{2};P3 = T{3};DrawPolyline({P1,P2,P3,P1},'k');GAview([0,90]);i = e1^e2;R1 = (P3-P1)*(P2-P1);R13 = gexp(sLog(R1)/3);R2 = (P1-P2)*(P3-P2);R23 = gexp(sLog(R2)/3);R3 = (P2-P3)*(P1-P3);R33 = gexp(sLog(R3)/3);L12 = P1^(R13*(P2-P1));L13 = P1^((P3-P1)*R13);L23 = P2^(R23*(P3-P2));L21 = P2^((P1-P2)*R23);L31 = P3^(R33*(P1-P3));L32 = P3^((P2-P3)*R33);H1 = meet(L12,L21);C1 = H1/inner(H1,e3);DrawHomogeneous(e3,H1,'n','y')H2 = meet(L23,L32);C2 = H2/inner(H2,e3);DrawHomogeneous(e3,H2,'n','y')H3 = meet(L31,L13);C3 = H3/inner(H3,e3);DrawHomogeneous(e3,H3,'n','y')DrawPolyline({P1,C1,P2},'g')DrawPolyline({P2,C2,P3},'g')DrawPolyline({P3,C3,P1},'g')DrawPolyline({C1,C2,C3,C1},'r')r = [inner(C2-C1,C3-C1)/norm(C3-C1)/norm(C2-C1), inner(C3-C2,C1-C2)/norm(C1-C2)/norm(C3-C2), inner(C1-C3,C2-C3)/norm(C2-C3)/norm(C1-C2)];r = acos(r)*180/pi;