Test programs that run on Mathematica 13.1
Equal length of segments
Equal length of segments
Header
Header
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<<EosHeader`
Eos3.7 (November 15,2022) running under Mathematica 13.1.0 for Mac OS X ARM (64–bit) (June 16, 2022) on Wed 16 Nov 2022 08:57:24.
Construction
Construction
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EosSession["Equal test"];
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MarkOn[];
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NewOrigami[]
Equal test: Step 1
Out[]=
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HO["A","D"]
Equal test: Step 2
Out[]=
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Unfold[]
Equal test: Step 3
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Verification
Verification
In[]:=
Prove["Equal Test",GoalSquaredDistance["D","E"]==SquaredDistance["F","B"]]
::gbstart
::gbsuccess
Proof is successful.
Equal test: Step 3
Out[]=
In[]:=
EndSession[];
Regular Heptagon
Regular Heptagon
Load Eos
Load Eos
In[]:=
<<EosHeader`
Eos3.7 (November 15,2022) running under Mathematica 13.1.0 for Mac OS X ARM (64–bit) (June 16, 2022) on Wed 16 Nov 2022 08:55:14.
EosNotations
EosNotations
OrikotoNotations
OrikotoNotations
g3Notations
g3Notations
Construction
Construction
In[]:=
EosSession["Regular Heptagon"];
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MarkOff[];Inexact[];
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NewOrigami[]
Regular Heptagon: Step 1
Out[]=
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HO["A","D",Mark{{"AD","E"},{"BC","F"}}]
Regular Heptagon: Step 2
Out[]=
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Unfold[]
Regular Heptagon: Step 3
Out[]=
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HO["A","B",Mark{{"CD","G"},{"FE","H"}}]
Regular Heptagon: Step 4
Out[]=
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Unfold[]
Regular Heptagon: Step 5
Out[]=
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HO["E","H",Mark{{"EF","I"}}]
Regular Heptagon: Step 6
Out[]=
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Unfold[]
Regular Heptagon: Step 7
Out[]=
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HO["F","I",Mark{{"AB","J"},{"CD","K"}}]
Regular Heptagon: Step 8
Out[]=
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Unfold[]
Regular Heptagon: Step 9
Out[]=
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HO["A","E",Mark{{"KJ","L"}}]
Regular Heptagon: Step 10
Out[]=
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Unfold[]
Regular Heptagon: Step 11
Out[]=
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HO["I","GH","L","HF"]
Regular Heptagon: Step 11
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,
,
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HO["I","GH","L","HF",FoldLine3]
Regular Heptagon: Step 12
Out[]=
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DuplicatePoint[{"I""M"}]
Regular Heptagon: Step 12
Out[]=
〈M〉
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Unfold[]
Regular Heptagon: Step 13
Out[]=
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HO["HG","M",Mark{{"BC","N"}}]
Regular Heptagon: Step 14
Out[]=
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Unfold[]
Regular Heptagon: Step 15
Out[]=
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HO["G","MN","H"]
Regular Heptagon: Step 15
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,
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HO["G","MN","H",FoldLine1]
Regular Heptagon: Step 16
Out[]=
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DuplicatePoint[{"G""O"}]
Regular Heptagon: Step 16
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〈O〉
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Unfold[]
Regular Heptagon: Step 17
Out[]=
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HO["OH",Handle"G"]
Regular Heptagon: Step 18
Out[]=
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DuplicatePoint[{"G""P"}]
Regular Heptagon: Step 18
Out[]=
〈P〉
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Unfold[]
Regular Heptagon: Step 19
Out[]=
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HO["PH",Handle"O"]
Regular Heptagon: Step 20
Out[]=
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DuplicatePoint[{"O""Q"}]
Regular Heptagon: Step 20
Out[]=
〈Q〉
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Unfold[]
Regular Heptagon: Step 21
Out[]=
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HO["HG",Handle"B"]
Regular Heptagon: Step 22
Out[]=
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DuplicatePoint[{"O""R","P""S","Q""T"}]
Regular Heptagon: Step 22
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〈R,S,T〉
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Unfold[]
Regular Heptagon: Step 23
Out[]=
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ShowOrigami[MarkPoints{"A","B","C","D","H","G","O","P","Q","T","S","R"},More{Thickness[0.01],Hue[0.2],Line[{"G","R","S","T","Q","P","O","G"}]}]
Regular Heptagon: Step 23
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Verification
Verification
In[]:=
Goalα ToC["G","H"]–ToC["R","H"]0 ToC["G","H"]–ToC["S","H"]==0∧ ToC["G","H"]–ToC["T","H"]==0∧ToC["G","H"]–ToC["Q","H"]==0∧ToC["G","H"]–ToC["P","H"]==0∧ToC["G","H"]–ToC["O","H"]==0;
∀
α∈Complexes
2
α
3
α
4
α
5
α
6
α
In[]:=
Prove["Heptagon",TacticsSplit]
::gbstart
::gbsuccess
::gbstart
::gbsuccess
::gbstart
::gbsuccess
::gbstart
::gbsuccess
::gbstart
::gbsuccess
Proof is successful.
Regular Heptagon: Step 23
Out[]=
In[]:=
EndSession[];
Angle trisection
Angle trisection
Load Eos
Load Eos
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<<EosHeader`
g3 Version 2.1
Eos3.7 (November 15,2022) running under Mathematica 13.1.0 for Mac OS X ARM (64–bit) (June 16, 2022) on Wed 16 Nov 2022 08:02:31.
Construction
Construction
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EosSession["Angle trisector"];
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MarkOff[];
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NewOrigami[10]
Angle trisector: Step 1
Out[]=
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ProofDocFormat["Construction","Subsection",1];
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NewPoint["E"{7,10}]
Angle trisector: Step 1
Out[]=
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HO["AE",Handle"D"]
Angle trisector: Step 2
Out[]=
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Unfold[]
Angle trisector: Step 3
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HO["A","D",Mark{"AD","BC"}]
Angle trisector: Step 4
Out[]=
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Unfold[]
Angle trisector: Step 5
Out[]=
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HO["A","F",Mark{"AD","BC"}]
Angle trisector: Step 6
Out[]=
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Unfold[]
Angle trisector: Step 7
Out[]=
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HO["F","AE","A","HI"]
Angle trisector: Step 7
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,
,
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HO[FoldLine3]
Angle trisector: Step 8
Out[]=
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ProjectPoint[{"A","H"}]
Angle trisector: Step 8
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〈J,K〉
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Unfold[]
Angle trisector: Step 9
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HO["AJ",Handle"B",MarkFalse]
Angle trisector: Step 10
Out[]=
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Unfold[]
Angle trisector: Step 11
Out[]=
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HO["AK",Handle"B",MarkFalse]
Angle trisector: Step 12
Out[]=
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Unfold[]
Angle trisector: Step 13
Out[]=
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ShowOrigami[More{Thickness[0.01],Hue[0],Line[{"A","E"}],Line[{"A","K"}],Line[{"A","J"}],Line[{"A","B"}]}]
Angle trisector: Step 13
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Verification
Verification
In[]:=
Goal[Spread["E","A","K"]==Spread["K","A","J"]∧Spread["K","A","J"]==Spread["J","A","B"]];
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map={"A"{0,0},"B"{1,0},"C"{1,1},"D"{0,1},"E"{u,1}};
In[]:=
Prove["Angle trisection[Abe]",Mappingmap,TacticsSplit]
::gbstart
::gbsuccess
::gbstart
::gbsuccess
Proof is successful.
Angle trisector: Step 13
Out[]=
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EndSession[];
Yacht
Yacht