nL-n-P2: nL-Morley’s Centroid
In accordance to the Encyclopedia of Triangle Centers (Ref-12) the 2nd center is a centroid.
Morley describes in Ref-49 an nL-Circumcenter (nL-n-P3), an nL-Orthocenter (nL-n-P4) and an nL-n-Nine-point Center (nL-n-P5) but he doesn’t describe a Centroid of the n-Line.
Eckart Schmidt describes in [34], QFG#880 an nL-Centroid related to Morley’s nL-Circumcenter (nL-n-P3) and nL-Orthocenter (nL-n-P4) as nL-n-P2 = Ratiopoint nL-n-P3.nL-n-P4 (n-2 : 2). For explanation of Ratiopoint see nL-1.
This centroid is also the Homothetic Center of the Reference n-Line and the n-Line formed by the lines through nL-n-P5 parallel to Li. See Level-up Construction nL-n-Luc5a.
Because it is derived from Morley’s Centers it is called Morley’s Centroid.
Correspondence with ETC/EQF
- When n=3, then nL-n-P2 = X(2).
- When n=4, then nL-n-P2 = QL-P22.
Properties
- nL-n-P2 is also the Homothetic Center of the Reference n-Line and the n-Line formed by the lines through the n (n-1)L-versions of nL-n-P2 parallel to the omitted Line.
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