Euler Line
Euler Line
Load Eos
Load Eos
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<<EosLoader.m
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 15:59:21.
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.
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EosSession["Euler line"];
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NewOrigami[10]
Euler line/Origami: Step 1
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NewPoint["E"{7,8}]
Euler line/Origami: Step 1
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HO["A","E",Mark{{"AD","F1"},{"AB","F2"}}]!
Euler line/Origami: Step 3
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HO["B","E",Mark{{"F1F2","O"}}]!
Euler line/Origami: Step 5
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circle={Green,Thickness[0.01],GraphicsCircle["O","OE"]};triangle={Red,Thickness[0.01],Line[{"A","B","E","A"}]};
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ShowOrigami[More{triangle,circle}]
Euler line/Origami: Step 5
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O is the circumcenter.
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HO["BE"]!
Euler line/Origami: Step 7
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HO["BE","A",Mark{{"BE","J"}}]!
Euler line/Origami: Step 9
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HO["AE"]!
Euler line/Origami: Step 11
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HO["AE","B",Mark{{"AJ","H"}}]!
Euler line/Origami: Step 13
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HO["A","E",Mark{{"AE","K"}}]!
Euler line/Origami: Step 15
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HO["B","E",Mark{{"BE","L"}}]!
Euler line/Origami: Step 17
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HO["AL"]!
Euler line/Origami: Step 19
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