JAMET

385 Reputation

4 Badges

6 years, 286 days

MaplePrimes Activity


These are replies submitted by JAMET

restart;
with(geometry);
with(plots);
_EnvHorizomtalName = 'x';
_EnvVerticalName = 'y';
_local(D);
line(delta, y = 1/3*x + 1, [x, y]);
line(deltap, y = (-1)/4*x - 2, [x, y]);
line(D, y = 3*x - 5, [x, y]);
point(S, -1, 0);
intersection(P, delta, D);
intersection(Pp, deltap, D);
intersection(N, delta, deltap);
projection(H, S, delta);
projection(K, S, deltap);
projection(M, S, D);
circle(c1, [H, K, M], 'centername' = O1);
coordinates(O1);
omega := FindAngle(delta, deltap);
line(SP, [S, P]);
line(SPp, [S, Pp]);
alpha := FindAngle(SP, SPp);
segment(sMH, M, H);
segment(sMK, M, K);
line(MH, [M, H]);
line(MK, [M, K]);
omega - alpha;
beta := FindAngle(MH, MK);
is(beta + omega - alpha = 0);
point(S1, 2*HorizontalCoord(O1) + 1, 2*VerticalCoord(O1));
coordinates(S1);
line(SS1, [S, S1]);
c := distance(S, S1)/2;
a := radius(c1);
b := sqrt(a^2 - c^2);
ell := x^2/a^2 + y^2/b^2 = 1;
ellip := implicitplot(ell, x = -2 .. 2, y = -2 .. 2, color = blue);
solve({Equation(SS1, [x, y])}, {y});
rotation(elli2, ellip, arccos(-3283/4253), 'clockwise', O1);
display(textplot([[coordinates(S)[], "S"], [coordinates(P)[], "P"], [coordinates(H)[], "H"], [coordinates(N)[], "N"], [coordinates(K)[], "K"], [coordinates(M)[], "M"], [coordinates(Pp)[], "P'"], [coordinates(S1)[], "S1"], [coordinates(O1)[], "O1"]], font = [times, bold, 16], align = [above, right]), draw([delta(color = green), deltap(color = blue), D(color = red), c1(color = black), MH(color = orange), MK(color = orange), SP(color = magenta), SPp(color = magenta), S(color = black, symbol = solidcircle, symbolsize = 18), H(color = black, symbol = solidcircle, symbolsize = 12), K(color = black, symbol = solidcircle, symbolsize = 12), M(color = black, symbol = solidcircle, symbolsize = 12), P(color = black, symbol = solidcircle, symbolsize = 12), S1(color = black, symbol = solidcircle, symbolsize = 12), O1(color = black, symbol = solidcircle, symbolsize = 12)]), ellip, scaling = constrained, axes = normal);
                         [-965  -3283]
                         [----, -----]
                         [5218  5218 ]

                                     /7 \
                      omega := arctan|--|
                                     \11/

                                     /276\
                      alpha := arctan|---|
                                     \61 /

                          /7 \         /276\
                    arctan|--| - arctan|---|
                          \11/         \61 /

                                    /2609\
                      beta := arctan|----|
                                    \2603/

                              true

                               S1

                         [1644  -3283]
                         [----, -----]
                         [2609  2609 ]

                              SS1

                    1             (1/2)        (1/2)
            c := -------- 28866098      6806881     
                 13613762                           

                   1             (1/2)         (1/2)
           a := -------- 34595401      13613762     
                13613762                            

                           2          (1/2)
                     b := ---- 2520294     
                          2609             

                       13613762  2   2609  2    
                ell := -------- x  + ---- y  = 1
                       34595401      3864       

                     /      3283   3283  \ 
                    { y = - ---- - ---- x }
                     \      4253   4253  / 

Error, (in geometry:-rotation) wrong type of arguments

NULL;I corrected the scale error of the previous program
I still haven’t understood my problem with display. Thank you very much.

restart;
with(geometry);
with(plots);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
cb := color = blue;
t3 := thickness = 3;
l3 := linestyle = 3;
xA := 3;
yA := 0;
xB := -3;
yB := 0;
c := 6;
point(A, xA, yA);
point(B, xB, yB);
R := 5;
alpha := arctan(3/4);
evalf(%*180/Pi);
                          36.86989765

xH := (xA + xB)/2;
yH := (yA + yB)/2;
point(H, xH, yH);
xO1 := 0;
yO1 := 4;
point(O1, xO1, yO1);
xO2 := 0;
yO2 := -4;
point(O2, xO2, yO2);
segment(sAB, A, B);
segment(sHO, H, O1);
segment(sAO, A, O1);
segment(sBO, B, O1);
                              sAB

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);
N := 80;
dt := (beta - alpha1)/(N - 1);
dr := draw({O1, O2, sAB, sHO, sAO(cb), sBO(cb)});
tex := textplot([[xA, yA - 0.5, "A"], [xB, yB - 0.5, "B"], [xO1, yO1 + 0.5, "O1"], [xO2, yO2 - 0.5, "O2"], [xH, yH - 0.5, "H"]]);
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 + Pi + alpha1) + xO2, R*sin(dt*t + Pi + alpha1) + yO2], 0.2, color = orange), t = 0 .. N);
point(m2, [R*cos(dt*t + Pi + alpha1) + xO2, R*sin(dt*t + Pi + alpha1) + yO2]);
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 + Pi + alpha1) + xO1, R*sin(dt*t + Pi + alpha1) + yO1], [xA, yA], [xB, yB]], color = aquamarine, linestyle = dash), t = 0 .. N);
triangle(ABM, [A, B, m2]);
AreCollinear: hint: could not determine if 24+30*sin(2/79*t*arctan(4/3)+1/79*t*Pi-arctan(4/3)) is zero
Error, (in geometry:-triangle) not enough information: the three points might be AreCollinear
for t to N do
    E[t] := display(dr, tex, AR1, AR2, M1[t], P1[t]);
    F[t] := display(dr, tex, AR1, AR2, M2[t], ABM);
end do;
Error, (in plots:-display) expecting plot structure but received: ABM
NULL;

display([seq(E[t], t = 1 .. N), seq(F[t], t = 1 .. N)], insequence = true, axes = none, scaling = constrained, view = [-10 .. 10, -10 .. 10]);
Error, (in plots:-display) expecting plot structures but received: [E[2], E[3], E[4], E[5], E[6], E[7], E[8], E[9], E[10], E[11], E[12], E[13], E[14], E[15], E[16], E[17], E[18], E[19], E[20], E[21], E[22], E[23], E[24], E[25], E[26], E[27], E[28], E[29], E[30], E[31], E[32], E[33], E[34], E[35], E[36], E[37], E[38], E[39], E[40], E[41], E[42], E[43], E[44], E[45], E[46], E[47], E[48], E[49], E[50], E[51], E[52], E[53], E[54], E[55], E[56], E[57], E[58], E[59], E[60], E[61], E[62], E[63], E[64], E[65], E[66], E[67], E[68], E[69], E[70], E[71], E[72], E[73], E[74], E[75], E[76], E[77], E[78], E[79], E[80], F[1], F[2], F[3], F[4], F[5], ...  F[71], F[72], F[73], F[74], F[75], F[76], F[77], F[78], F[79], F[80]]
NULL;
how to improve this program ? Thank you.

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
 

I don't understand this error. Thank you.

(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.

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