nL-n-L1: nL-Morley’s Eulerline

Since Morley described the equivalents of a circumcenter (nL-n-P3), an orthocenter (nL-n-P4) and a Nine-point-center (nL-n-P5) in a general n-Line which also happen to be collinear it is evident that the connecting line of these points will be Morley’s Eulerline here coded nL-n-L1.

For the allocation of the centroid, circumcenter, orthocenter and nine-point center on the nL-Morley’s Eulerline see nL-n-P2.

Next figure gives an example of nL-n-L1 in a 5-Line.

Correspondence with ETC/EQF

• When n=3, then nL-n-L1 = Triangle Eulerline X(3).X(4), with
  • 3L-n-P2 = Centroid X(2)
  • 3L-n-P3 = Circumcenter X(3)
  • 3L-n-P4 = Orthocenter X(4)
  • 3L-n-P5 = Nine-point Center X(5)
• When n=4, then nL-n-L1 = Quadrilateral Eulerline QL-P2.QL-P4, with
  • 4L-n-P2 = Centroid-equivalent QL-P22
  • 4L-n-P3 = Circumcenter-equivalent QL-P4
  • 4L-n-P4 = Orthocenter-equivalent QL-P2
  • 4L-n-P5 = Nine-point Center-equivalent QL-P30

Properties

• nL-n-P2, nL-n-P3, nL-n-P4, nL-n-P5 lie on nL-n-L1.

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