Euler Line
Euler Line
Load Eos
Load Eos
In[]:=
<<EosLoader`
Eos3.7.1.1 (March 21,2023) running under Mathematica 13.2.0 for Mac OS X ARM (64-bit) (November 18, 2022) on Thu 30 Mar 2023 14:35:18.
Euler line
Euler line
Three centers are collinear
Three centers are collinear
For any triangle ΔABE, the circumcenter, the centroid and the orthocenter are collinear.
The line determined by the three points is called Euler line.
In[]:=
EosSession["Euler line"];
In[]:=
NewOrigami[10]
Euler line: Step 1
Out[]=
In[]:=
NewPoint["E"{7,8}]
Euler line: Step 1
Out[]=
In[]:=
HO["A","E",Mark{{"AD","F1"},{"AB","F2"}}]!
Euler line: Step 3
Out[]=
In[]:=
HO["B","E",Mark{{"F1F2","O"}}]!
Euler line: Step 5
Out[]=
In[]:=
circle={Green,Thickness[0.01],GraphicsCircle["O","OE"]};triangle={Red,Thickness[0.01],Line[{"A","B","E","A"}]};
In[]:=
ShowOrigami[More{triangle,circle}]
Euler line: Step 5
Out[]=
O is the circumcenter.
In[]:=
HO["BE"]!
Euler line: Step 7
Out[]=
In[]:=
HO["BE","A",Mark{{"BE","J"}}]!
Euler line: Step 9
Out[]=
In[]:=
HO["AE"]!
Euler line: Step 11
Out[]=
In[]:=
HO["AE","B",Mark{{"AJ","H"}}]!
Euler line: Step 13
Out[]=
In[]:=
HO["A","E",Mark{{"AE","K"}}]!
Euler line: Step 15
Out[]=
In[]:=
HO["B","E",Mark{{"BE","L"}}]!
Euler line: Step 17
Out[]=
In[]:=
HO["AL"]!
Euler line: Step 19
Out[]=
