Question I need help STAT

Questions
1

I need help with this really hard question and I can’t seem to construct it properly. Can someone help me out with this one?

2

This looks like blatant homework, doesn’t it? Had you typed

Remove[taF]
taF[{n_Integer, p_List}, \[Alpha]_, \[Beta]_] := 
 Block[{e1 = {1, 0}, e2 = {4/10, 0}, p1, p2},
   p1 = RotationTransform[n \[Alpha]][e1];
   p2 = RotationTransform[n \[Beta]][e2];
   {n + 1, {Last[p] + p1, Last[p] + p1 + p2}}
   ] /; Length[p] == 2

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 62 \[Degree], 60 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 180]]], 1]]], Frame -> True]

you had have the joy of having solved it on your own.

comm578358_1.PNG
comm578358_1.PNG870×425 35 KB

Had your teacher switched the angles, it had looked a bit more interesting

comm578358_2.PNG
comm578358_2.PNG882×406 26.9 KB

Inputs to probe

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 60 \[Degree], 90 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 180]]], 1]]], Frame -> True]

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 60 \[Degree], 30 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 180]]], 1]]], Frame -> True]

they give archaic looking pictograms. Experiment a bit, check for errors. Another one

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 30 \[Degree], 19 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 180]]], 1]]], Frame -> True]

is filigree and the last one:

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 62 \[Degree], 31 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 180]]], 1]]], Frame -> True]

comm578358_3.PNG
comm578358_3.PNG874×421 25.7 KB

3

This

Graphics[Line[Join[{{0, 0}}, Flatten[Last[Transpose[
      NestList[taF[#, 22.5 \[Degree], 122.5 \[Degree]] &, {1, {{1, 0}, {7/5, 0}}}, 177]]], 1]]]]

gives

comm578358_4.PNG
comm578358_4.PNG889×866 30.3 KB

the angles appear in From Close to Perfect: A Triangle Problem by Ed Pegg Jr. As a replacement - not so blatant - homework you could try to replace the current implementation by an application of AnglePath only.

4

As a replacement - not so blatant - homework you could try …

    Remove[taF]
    taF[\[Alpha]_, \[Beta]_, n_?Positive, len1_: 1, len2_: 2/5] := 
     Graphics[Line[
       Join[{{0, 0}}, AnglePath[{len1 + len2, 0}, 
         Transpose[{Flatten[ConstantArray[{len1, len2}, n], 1], 
           Join[{\[Alpha]}, Differences[Flatten[Table[{o \[Alpha], o \[Beta]}, {o, 1, n}], 1]]]}]]]]]

compare it with yesterday’s implementation

10595comm578358_5.PNG
10595comm578358_5.PNG662×513 28.2 KB

5

I can’t thank you enough haha XD
I really appreciate this !