Is there a way to add 'dimensions' on to multiple graphic objects?

[paul2cleary (Paul Cleary)]

I have tried adding text as such into the graphic part of the code in all possible places but can’t get any lable to appear in the graphic. I have included the code in its entirety rather than a snippet. I would like to see the dimentions of the 4 triangles included on the graphic if possible.

Clear[x,y,q,p];

list=Reap[Do[p=Solve[x^2+y^2==q^2&&x>0&&y>0&&x<y,{x,y},Integers];

p={x,y}/.p;

k=Total@Flatten[p];

If[k>0,Sow[Partition[Riffle[Flatten[p],q,{3,-1,3}],3]]],{q,5,1000}]];

list=Flatten[list[[2]],2];lst=SortBy[list,{#[[1]],#[[2]]}&];ml=Max[lst[[All,1]]];

flist=Reap[Do[g=Select[lst,#[[1]]==y&];

		Do[If[Length[g]>=2,j=Select[lst,#[[1]]==g[[q,2]]&]];

		k=Select[lst,#[[1]]==g[[w,2]]&];If[Length[j]<1||Length[k]<1,Continue[]];

		j1=Flatten[j];k1=Flatten[k];

		m=Take[j1,{2,-1,3}];

		m1=Take[k1,{2,-1,3}];

		m2=FromDigits[Intersection[m,m1]];

		r=Select[j,#[[2]]==m2&];

		t=Select[k,#[[2]]==m2&];If[Length[r]>0,Sow[{g[[q]],g[[w]],r,t}]],

		{q,1,Length[g]},{w,q+1,Length[g]}],

	{y,15,ml}]];

nflist={};flist=Partition[Flatten[flist[[2]]],12];simt=Reap[Do[If[flist[[q,2]]/flist[[q,1]]==flist[[q,11]]/flist[[q,10]],Sow[flist[[q]]],AppendTo[nflist,flist[[q]]]],{q,1,Length[flist]}]];

simt=Flatten[simt[[2]],1];

Do[AppendTo[simt[[q]],simt[[q,3]]+simt[[q,6]]+simt[[q,9]]+simt[[q,12]]],{q,1,Length[simt]}];Do[AppendTo[nflist[[q]],nflist[[q,3]]+nflist[[q,6]]+nflist[[q,9]]+nflist[[q,12]]],{q,1,Length[nflist]}];

nflist=SortBy[nflist,#[[13]]&];simt=SortBy[simt,#[[13]]&];

Print["Number of non similar triangles is ",Length[nflist]];

Print["Number of simmilar triangles is ",Length[simt]];

Do[Print[Partition[nflist[[q]],3,3,1,{}]];

t1={{0,0},{nflist[[q,1]],0},{0,nflist[[q,2]]}};

t2={{0,0},{nflist[[q,1]],0},{0,-nflist[[q,6]]}};

t3={{0,0},{-nflist[[q,8]],0},{0,-nflist[[q,6]]}};

t4={{0,0},{-nflist[[q,8]],0},{0,nflist[[q,2]]}};

Print[Graphics[{EdgeForm[Black],Red,Polygon[{t1}]

,EdgeForm[Black],Yellow,Polygon[{t2}],EdgeForm[Black],Cyan,Polygon[{t3}],EdgeForm[Black],Green,Polygon[{t4}]}]];Print[],{q,1,Length[nflist]}];Print[];Print[];

Print["Similar from here"];

Do[Print[Partition[simt[[q]],3,3,1,{}]];

t1={{0,0},{simt[[q,1]],0},{0,simt[[q,2]]}};

t2={{0,0},{simt[[q,1]],0},{0,-simt[[q,6]]}};

t3={{0,0},{-simt[[q,8]],0},{0,-simt[[q,6]]}};

t4={{0,0},{-simt[[q,8]],0},{0,simt[[q,2]]}};

Print[Graphics[{EdgeForm[Black],Red,Polygon[{t1}]

,EdgeForm[Black],Yellow,Polygon[{t2}],EdgeForm[Black],Red,Polygon[{t3}],EdgeForm[Black],Yellow,Polygon[{t4}]}]];Print[],{q,1,Length[simt]}];Print[];

The figures in the braces are the dimensions I would like inserting into the graphic.

Paul.

[sghuisman (Sander Huisman)]

Hi Paul,

You can use Text[“The text here”,{x,y}] to insert text in your graphics. Your code looks really complicated, what is your input? What is that you are planning to do?

[Vitaliyk (Vitaliy Kaurov)]

Here is a simple effort to implement Sander’s suggestion. As you can see length of the side is attached as a label to the side center and follows all transformations.

Manipulate[Graphics3D[{{Opacity[.35], EdgeForm[Opacity[.35]], 
    Cuboid[-d {1, 1, 1}, d {1, 1, 1}]}, {Red, PointSize[Large], 
    Point[-{d, d, 0}]}, Text[Style[2 d, 17], -{d, d, 0}]}, 
    SphericalRegion -> True, RotationAction -> "Clip", PlotRange -> 2.3, Axes -> True
  ], {{d, 5/3}, 1/2, 2, 1/10, Appearance -> "Labeled"}]

[paul2cleary (Paul Cleary)]

Thanks for your reply Sander, I played with your idea and got it to work to an extent, it just didn’t have everything to display all I needed. Regarding the input, it is self contained. The program first calculates all Pythagorean Triangles with a hypotenuse less than 1000. this bit {q, 5, 1000}. The remainder upto the graphic section looks for 4 PT’s that share 2 sides each, such that the right angled corners can be plotted at a point. It also sorts out similar and non similar triangles.

Thanks also to Vitaliy, I was able to pick out the required bits from your code and include them into mine with success. What took a litte time to sort out were the order of plotting points so that previous points were not overdrawn by the next triangle, and also finding a scaling factor such that all looked equal regardless of the size of triangles. I have included a cut down version that only plots the first non similar triangles.

Clear[x, y, q, p]; list = 
 Reap[Do[p = 
    Solve[x^2 + y^2 == q^2 && x > 0 && y > 0 && x < y, {x, y}, 
     Integers]; p = {x, y} /. p; k = Total@Flatten[p];
   If[k > 0, 
    Sow[Partition[Riffle[Flatten[p], q, {3, -1, 3}], 3]]], {q, 5, 
    1000}]]; list = Flatten[list[[2]], 2]; lst = 
 SortBy[list, {#[[1]], #[[2]]} &]; ml = Max[lst[[All, 1]]]; flist = 
 Reap[Do[g = Select[lst, #[[1]] == y &];
   Do[If[Length[g] >= 2, j = Select[lst, #[[1]] == g[[q, 2]] &]];
    k = Select[lst, #[[1]] == g[[w, 2]] &];
    If[Length[j] < 1 || Length[k] < 1, Continue[]]; j1 = Flatten[j];
    k1 = Flatten[k]; m = Take[j1, {2, -1, 3}];
    m1 = Take[k1, {2, -1, 3}]; m2 = FromDigits[Intersection[m, m1]];
    r = Select[j, #[[2]] == m2 &]; t = Select[k, #[[2]] == m2 &];
    If[Length[r] > 0, Sow[{g[[q]], g[[w]], r, t}]], {q, 1, 
     Length[g]}, {w, q + 1, Length[g]}], {y, 15, 
    ml}]]; nflist = {}; flist = 
 Partition[Flatten[flist[[2]]], 12]; simt = 
 Reap[Do[If[
    flist[[q, 2]]/flist[[q, 1]] == flist[[q, 11]]/flist[[q, 10]], 
    Sow[flist[[q]]], AppendTo[nflist, flist[[q]]]], {q, 1, 
    Length[flist]}]]; simt = Flatten[simt[[2]], 1]; Do[
 AppendTo[simt[[q]], 
  simt[[q, 3]] + simt[[q, 6]] + simt[[q, 9]] + simt[[q, 12]]], {q, 1, 
  Length[simt]}]; Do[
 AppendTo[nflist[[q]], 
  nflist[[q, 3]] + nflist[[q, 6]] + nflist[[q, 9]] + 
   nflist[[q, 12]]], {q, 1, Length[nflist]}]; nflist = 
 SortBy[nflist, #[[13]] &]; simt = 
 SortBy[simt, #[[13]] &]; Print["Number of non similar triangles is ",
  Length[nflist]]; Do[
 Print[Grid[Partition[nflist[[q]], 3, 3, 1, {}], Alignment -> Left, 
   Frame -> All, Spacings -> {1, 1}]]; dp = nflist[[q, 8]]/25;
 Print[Graphics[{EdgeForm[Black], Red, 
    Polygon[{{0, 0}, {nflist[[q, 1]], 0}, {0, 
       nflist[[q, 2]]}}], {Blue, PointSize[Medium], 
     Point[{nflist[[q, 1]]/2, 0}]}, {Blue, PointSize[Large], 
     Point[{0, nflist[[q, 2]]/2}]}, {Blue, PointSize[Medium], 
     Point[{nflist[[q, 1]]/2, nflist[[q, 2]]/2}]}, 
    Text[Style[nflist[[q, 3]], Black, 17], {nflist[[q, 1]]/2 + dp, 
      nflist[[q, 2]]/2}], EdgeForm[Black], Yellow, 
    Polygon[{{0, 0}, {nflist[[q, 1]], 
       0}, {0, -nflist[[q, 5]]}}], {Blue, PointSize[Medium], 
     Point[{nflist[[q, 1]]/2, 0}]}, 
    Text[Style[nflist[[q, 1]], Black, 
      17], {nflist[[q, 1]]/2, -dp}], {Blue, PointSize[Medium], 
     Point[{0, -(nflist[[q, 5]]/2)}]}, {Blue, PointSize[Medium], 
     Point[{nflist[[q, 1]]/2, -(nflist[[q, 5]]/2)}]}, 
    Text[Style[nflist[[q, 6]], Black, 
      17], {nflist[[q, 1]]/2 + dp, -(nflist[[q, 5]]/2)}], 
    EdgeForm[Black], Cyan, 
    Polygon[{{0, 0}, {-nflist[[q, 8]], 
       0}, {0, -nflist[[q, 5]]}}], {Blue, PointSize[Medium], 
     Point[{0, -(nflist[[q, 5]]/2)}]}, 
    Text[Style[nflist[[q, 5]], Black, 
      17], {-dp, -(nflist[[q, 5]]/2)}], {Blue, PointSize[Medium], 
     Point[{-(nflist[[q, 8]]/2), 0}]}, 
    Text[Style[nflist[[q, 8]], Black, 
      17], {-(nflist[[q, 8]]/2), -dp}], {Blue, PointSize[Medium], 
     Point[{-(nflist[[q, 8]]/2), -(nflist[[q, 5]]/2)}]}, 
    Text[Style[nflist[[q, 12]], Black, 
      17], {-(nflist[[q, 8]]/2), -(nflist[[q, 5]]/2) - dp}], 
    EdgeForm[Black], Green, 
    Polygon[{{0, 0}, {-nflist[[q, 8]], 0}, {0, 
       nflist[[q, 2]]}}], {Blue, PointSize[Medium], 
     Point[{0, nflist[[q, 2]]/2}]}, 
    Text[Style[nflist[[q, 2]], Black, 17], {-dp, 
      nflist[[q, 2]]/2}], {Blue, PointSize[Medium], 
     Point[{-(nflist[[q, 8]]/2), 0}]}, 
    Text[Style[nflist[[q, 8]], Black, 
      17], {-(nflist[[q, 8]]/2), -dp}], {Blue, PointSize[Medium], 
     Point[{-(nflist[[q, 8]]/2), nflist[[q, 2]]/2}]}, 
    Text[Style[nflist[[q, 9]], Black, 17], {-(nflist[[q, 8]]/2), 
      nflist[[q, 2]]/2 + dp}]}, ImageSize -> {700, 700}]];
 Print[], {q, 1, Length[nflist]}]

Thanks again for your quick replies and sorry i was late in replying.

Paul.