Computational exploration of Barycentric coordinate system

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I manually created my own version of the Wikipedia math article for barycentric coordinates, which are related to triangle geometry including trilinear coordinates.
I made some edits with distance functions in barycentric coordinates and added geometric scenes.
I wonder if there are higher dimensional versions of the centroid, orthocenter, Gergonne point, circumcenter, etc.
I typed out the Wikipedia article for the Euler line and adding it as an attachment to this post. I have almost finished typing out the article for triangle center.

Open in Wolfram Cloud ↗

Barycentric Coordinates Wikipedia Community Post.nb (798 KB)
Euler Line.nb (41.7 KB)
Triangle Centers Wikipedia Article after Deletion.nb (76.2 KB)

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2

Great summary. Thanks for creating and sharing. Did you also see my WFR function: https://resources.wolframcloud.com/FunctionRepository/resources/BarycentricCoordinates/ which implements the conversion?

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Yes I used this. I like the barycentric coordinates Manipulate in the documentation.

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