nL-n-L2: nL-MVP Eulerline
The nL-MVP Eulerline is the line connecting collinear points nL-n-P8, nL-n-P9, nL-n-P10, nL-n-P11.
For the allocation of the centroid, circumcenter, orthocenter and nine-point center on the nL-MVP Eulerline see nL-n-P8.
Next figure gives an example of nL-n-L2 in a 5-Line.
Correspondence with ETC/EQF:
When n=3, then nL-n-L2 = Triangle Eulerline X(3).X(4), with
• 3L-n-P8 = Centroid X(2)
• 3L-n-P9 = Circumcenter X(3)
• 3L-n-P10 = Orthocenter X(4)
• 3L-n-P11 = Nine-point Center X(5)
When n=3, then nL-n-L2 = Triangle Eulerline X(3).X(4), with
• 3L-n-P8 = Centroid X(2)
• 3L-n-P9 = Circumcenter X(3)
• 3L-n-P10 = Orthocenter X(4)
• 3L-n-P11 = Nine-point Center X(5)
When n=4, then nL-n-L2 = Quadrilateral Eulerline QL-P2.QL-P6, with
• 4L-n-P8 = Centroid-equivalent QL-P12 (4L-Centroid)
• 4L-n-P9 = Circumcenter-equivalent QL-P6 (Dimidium Point)
• 4L-n-P10 = Orthocenter-equivalent QL-P2 (Morley Point)
• 4L-n-P11 = Nine-point Center-equivalent Midpoint (QL-P2,QL-P6)
• 4L-n-P8 = Centroid-equivalent QL-P12 (4L-Centroid)
• 4L-n-P9 = Circumcenter-equivalent QL-P6 (Dimidium Point)
• 4L-n-P10 = Orthocenter-equivalent QL-P2 (Morley Point)
• 4L-n-P11 = Nine-point Center-equivalent Midpoint (QL-P2,QL-P6)