Equilateral Triangle

Tetsuo Ida

Load Eos

In[]:=
<<EosLoader`
Eos3.7.2 (June 24,2023) running under Mathematica 13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023) on Fri 23 Jun 2023 16:06:57.

Equilateral Triangle 1

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EosSession["Equilateral Triangle 1"];

Construction


Proof

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ProofDocFormat["Proof","Subsection",1];
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ProofDocFormat["Goal","Subsubsection",1];
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Goal[SquaredDistance["A","B"]==SquaredDistance["B","G"]==SquaredDistance["G","A"]];
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Prove["Equilateral Triangle",ProofDocTrue]
Proof is successful.
Equilateral Triangle 1/Origami: Step 7
Out[]=
{Success,0.01248,
Equilateral Triangle.pdoc.nb
}
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EndSession[];

Equilateral Triangle 2

Construction

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EosSession["Equilateral Triangle 2"];
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NewOrigami[]
Equilateral Triangle 2/Origami: Step 1
Out[]=
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HO["A","B"]
Equilateral Triangle 2/Origami: Step 2
Out[]=
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HO["F","D"]
Equilateral Triangle 2/Origami: Step 3
Out[]=
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UnfoldAll[]//Column
Equilateral Triangle 2/Origami: Step 5
Out[]=
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HO["D","GH","F",Mark"AD",FoldLine1]
Equilateral Triangle 2/Origami: Step 6
Out[]=
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Unfold[]
Equilateral Triangle 2/Origami: Step 7
Out[]=
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HO["C","JI","F",Mark"CB",FoldLine2]
Equilateral Triangle 2/Origami: Step 8
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Unfold[]
Equilateral Triangle 2/Origami: Step 9
Out[]=
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HO["LK",Handle"A"]
Equilateral Triangle 2/Origami: Step 10
Out[]=

Equilateral Triangle 3

This constriction is simplest. I found this recipe in Fushimi’s book (Geometry of Origami, 1979)

Construction

Equilateral Triangle 4

Construction