nP-n-P2

nP-n-P2 nP-MVP-Circumcenter

nP-n-P2 is the nL-Mean Vector Point of X(3), the Triangle Circumcenter.

In this method central points from ETC are successively constructed in higher level n-Point figures starting with n=3, then n=4 using the results of n=3, then n=5 using the results of n=4, etc.

See nP-n-Luc1 for a detailed description.

Infovisual nP-n-P2-infovisual-cvt-01.png

Correspondence with ETC/EQF

In a 3-Point:

3P-n-P1 = 3P-MVP Centroid = X(2)
3P-n-P2 = 3P-MVP Circumcenter = X(3)
3P-n-P3 = 3P-MVP Orthocenter = X(4)
3P-n-P4 = 3P-MVP Nine-point center = X(5)

In a 4-Point we find:

4P-n-P1 = 4P-MVP Centroid = QA-P1 (QA-Centroid)
4P-n-P2 = 4P-MVP Circumcenter = QA-P32 (Centroid Circumcenter Quadrangle)
4P-n-P3 = 4P-MVP Orthocenter = QA-P33 (Centroid Orthocenter Quadrangle)
4P-n-P4 = 4P-MVP Nine-point center = Midpoint (QA-P32,QA-P33)

Properties

nP-n-P1, nP-n-P2, nP-n-P3 and nP-n-P4 are collinear on nP-n-L1. Their mutual distance ratios correspond with the mutual distance ratios from triangle centers X(2), X(3), X(4) and X(5).
When the vertices of the n-Point are cocyclic, then nP-n-P2 will be the center of the circle through these vertices.

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