restart;
_EnvHorizomtalName = 'x';
_EnvVerticalName = 'y';
aProc := proc(t) local xA, yA, xB, yB, xH, yH, R, c, cb, O1, O2, xO1, yO1, xO2, yO2, AR1, AR2, M1, M2, P1, P2, N, dt, dr, alpha, alpha1, beta, l3, t3, tex, E, F; cb := color = blue; xA := 3; yA := 0; xB := -3; yB := 0; c := 6; alpha := artan(3/4); l3 := linestyle = 3; t3 := thickness = 3; N := 80; dt := (beta - alpha1)/(N - 1); geometry:-point(A, xA, yA); geometry:-point(B, xB, yB); R := 5; xH := 1/2*xA + 1/2*xB; yH := 1/2*yA + 1/2*yB; geometry:-point(H, xH, yH); xO1 := 0; yO1 := 4; geometry:-point(O1, xO1, yO1); xO2 := 0; yO2 := 4; geometry:-point(O2, xO2, yO2); geometry:-segment(sAB, A, B); geometry:-segment(sHO, H, O1); geometry:-segment(sAO, A, O1); geometry:-segment(sBO, B, O1); alpha1 := arctan((yO1 - yA)/(xO1 - xA)); beta := Pi + arctan((yO1 - yB)/(xO1 - xB)); AR1 := plottools[arc]([xO1, yO1], R, alpha1 .. beta, l3); AR2 := plottools[arc]([xO2, yO2], R, -beta .. -alpha1, l3); dr := geometry:-draw({sAB, sHO, sAO(cb), sBO(cb), O1, O2}); tex := texplot([[xA, yA - 0.5, "A"], [xB, yB - 0.5, "B"]]); M1 := seq(plottools[disk]([R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], 0.2, color = orange), t = 0 .. N); M2 := seq(plottools[disk]([R*cos(dt*t + alpha1 + Pi) + xO2, R*sin(dt*t + alpha1 + Pi) + yO2], 0.2, color = orange), t = 0 .. N); P1 := seq(plottools[polygon]([[R*cos(dt*t + alpha1) + xO1, R*sin(dt*t + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N); P2 := seq(plottools[polygon]([[R*cos(dt*t + alpha1 + Pi) + xO1, R*sin(dt*t + alpha1 + Pi) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N); for t to N do E[t] := plots:-display(dr, tex, AR1, AR2, M1[t], P1[t]); F[t] := plots:-display(dr, tex, AR1, AR2, M2[t], P2[t]); end do; plots:-display([seq(E[t], t = 1 .. N), seq(F[t], t = 1 .. N)], insequence = true, axes = none, scalming = constraioned, view = [-10 .. 10, -10 .. 10]); end proc;
nFig := 60;
plots:-display(seq(aProc(2*Pi*i/nFig), i = 0 .. nFig), insequence = true);
Error, (in aProc) illegal use of a formal parameter
 

(triangle ABM) the 3 vertices of a triangle are well placed except when the point M is on the bottom arc

the top of this angle rotates correctly, it is sufficient that these sides pass through A and B ?

FromLargestToSmallest(<27304197, 27304196, 38613965>)
Your procedure works very well. Best regards.

I am trying to say where these triples come from. With : 
R1:=matrix(3,3,[1,-2,2,2,-1,2,2,-2,3]):R2:=matrix(3,3,[1,2,2,2,1,2,2,2,3]):R3:=matrix(3,3,[-1,2,2-,2,-1,2,-2,-2,3]):
Do you understand ? Thank you very much.

Best regards,
I wish to write the following in this order (for instance)
<2275,3648,4275>,<975,448,1273>,<275,252,373>,<33,56,65>,<15,8,17>,<3,4,5> Is it possible ?

Thank you of your anwer. How to find the sequence of R[i ]to get (3,4,5) from any triplet?

Very good procedure, thank you

I misunderstood, I wanted all possible occurences to get 100 and not the first hundred numbers; Thank you.

proper procedure; Probleme with conguent(3); false
Have you look for the dimensions of the rectangular triangles ? Thank you;

restart;
with(LinearAlgebra);
with(geometry);
with(plots);
_EnvHorizontalName := 'x';

_EnvVerticalName := 'y';

xA := -7: yA := 0: xB := 5: yB := 9: xC := 9: yC := 1: 
xP:=3:yP:=5:
point(A, xA, yA);
point(B, xB, yB);
point(C, xC, yC);
point(P, xP, yP);
Mat := Matrix(3,3,[xA,xB,xC,yA,yB,yC,1,1,1]);

"v := <x, y, 1>;

  1/Mat;

  Mcb := MatrixVectorMultiply(1/Mat, v);

  Mbc := MatrixVectorMultiply(Mat, Mcb);

  Triangle(Tr, [A, B, C]);

  line(AP, [A, P]);

  line(BP, [B, P]);

  line(CP, [C, P]);

  line(AB, [A, B]);

  line(BC, [B, C]);

  line(CA, [C, A]);

  alpha := FindAngle(BP, CP);

  beta := FindAngle(CP, AP);

  eta := FindAngle(BP, AP);

  Aa := FindAngle(AB, CA);

  Bb := FindAngle(BC, AB);

  Cc := FindAngle(BC, CA);

  t3 := thickness = 3;

  Mcb := <1/(cot(Aa) - cot(alpha)), 1/(cot(Bb) - cot(beta)), 

   1/(cot(Cc) - cot(eta))>;

  Mbc := MatrixVectorMultiply(Mat, Mcb);

  L3 := linestyle = 1;

  cbl := color = blue;

  dr := draw([AB, BC, CA, AP(cbl, L3), BP(cbl, L3), CP(cbl, L3)]);

  tp := textplot([[coordinates(A)[], "A"], [coordinates(B)[], 

   "B"], [coordinates(C)[], "C"], [coordinates(P)[], "P"]], 

   align = {above, right});

  display*[textplot*([[coordinates(A)[], "A"], [coordinates(B)[]\

  , "B"], [coordinates(C)[], "C"]], align = {"above", 

   'right'}), draw*([AP(color = black), BP(color = green), 

   CP(color = green), Tr(color = blue, filled = true, 

   transparency = 0.9)], axes = none)];"

Can you tell me why this program is not running ? Thank you.

                     "with(geometry);

                       with(LinearAlgebra);

                       with(plots);"

                  "_EnvHorizontalName := 'x'"

                   "_EnvVerticalName := 'y'"

xA := 1: yA := 0: xB := 0: yB := 0: xC := 0: yC := 1:
Mat := Matrix(3,3,[xA,xB,xC,yA,yB,yC,1,1,1]);
                        "v := <x, y, 1>"

            "Mcb := MatrixVectorMultiply(1/Mat, v)"

            "Mbc := MatrixVectorMultiply(Mat, Mcb)"

   "xA := 4;

     yA := 10;

     xB := 0;

     yB := -2;

     xC := 13;

     yC := 0;

     xP := 5;

     yP := 4;

     Mat := Matrix(3, 3, [xA, xB, xC, yA, yB, yC, 1, 1, 1]);"

            "Mcb := MatrixVectorMultiply(1/Mat, v)"

            "Mbc := MatrixVectorMultiply(Mat, Mcb)"

                  "point(A, xA, yA);

                    point(B, xB, yB);

                    point(C, xC, yC);

                    point(P, xP, yP);

                    triangle(Tr, [A, B, C]);"

                      "line(AP, [A, P]);

                        line(BP, [B, P]);

                        line(CP, [C, P]);"

                  "alpha := FindAngle(BP, CP)"

                  "beta := FindAngle(CP, AP)"

                   "eta := FindAngle(BP, AP)"

                      "line(AB, [A, B]);

                        line(BC, [B, C]);

                        line(CA, [C, A]);"

                             "NULL"

                   "Aa := FindAngle(AB, CA)"

                   "Bb := FindAngle(BC, AB)"

                   "Cc := FindAngle(BC, CA)"

  "Mcb := <1/(cot(Aa) - cot(alpha)), 1/(cot(Bb) - cot(beta)), 

     1/(cot(Cc) - cot(eta))>"

            "Mbc := MatrixVectorMultiply(Mat, Mcb)"

                    "t3 := thickness = 3;

                      L3 := linestyle = 1;

                      cbl := color = blue;"

"dr := draw([Tr(t3), AP(cbl, L3), BP(cbl, L3), CP(cbl, L3)]), 

   textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], 

   [coordinates(C)[], "C"], [coordinates(P)[], "P"]], align = 

   {above, right})"

  "display({dr}, title = "Conversion", scaling = constrained, 

     axes = none, view = [-1 .. 14, -1 .. 11])"

Do you want to tell me why the program is not running ? Thank you very much.

How do you get these results? Thank you.

I want to write the equivalent of this statement with LinearAlgebra. Best regards.

the program following the previous
eta:=(x,y,z)->evalm(Mat&*[x,y,z]);        
eta(9/25,144/325,64/325); I should fond [4,18/5,1]. How to manufacture this adjutemen. Thank you.