nL-n-P1: nL-Centric Focus
A Triangle (3-Line) has a circumcircle. Morley in Ref-49 calls this circle a Centercircle.
In a Quadrilateral (4-Line) there are 4 Component 3-Lines whose 3L-Centercircle centers are concyclic on the 4L-Centercircle.
In a Quadrilateral (4-Line) there are 4 Component 3-Lines whose 3L-Centercircle centers are concyclic on the 4L-Centercircle.
Moreover the 4 3L-Centercircles have a common point, the 4L-Centric Focus.
In a Pentalateral (5-Line) there are 5 Component 4-Lines whose 4L-Centercircle centers are concyclic on the 5L-Centercircle.
In a Pentalateral (5-Line) there are 5 Component 4-Lines whose 4L-Centercircle centers are concyclic on the 5L-Centercircle.
Again the 5 4L-Centercircles have a common point, the 5L-Centric Focus.
Etc.
Goormaghtigh (Ref-55) named this point the Centric Focus because in a 4-Line this point is the Focus of the inscribed parabola (QL-Co1).
Etc.
Goormaghtigh (Ref-55) named this point the Centric Focus because in a 4-Line this point is the Focus of the inscribed parabola (QL-Co1).
In a 4-Line it also is the node of Morley’s Mono Cardioid (QL-Qu1).
Moreover nL-n-P1 is the node of the generalized Mono Cardioid nL-n-Cv1, also called the nL-Mono EnnaCardioid described by Morley in Ref-47.
Moreover nL-n-P1 is the node of the generalized Mono Cardioid nL-n-Cv1, also called the nL-Mono EnnaCardioid described by Morley in Ref-47.
This nL-Mono EnnaCardioid is a curve circumscribing all (n-1)L-Centercircles.
Properties:
• 5L-n-P1 is collinear with 5L-o-P2 and 5L-n-P3.
• 5L-n-P1 is a point on 5L-o-Ci1 and the inversion of 5L-o-P2 wrt 5L-n-Ci1 (Ref-34, QFG#722, October 6, 2014, Eckart Schmidt).
• 5L-n-P1 is a node of the Mono EnnaCardioid nL-n-Cv1, circumscribing n (n-1)L-EnnaCardioids (n-1)L-n-iCv1. See Ref-37, Morley's paper: Extensions of Clifford’s Chain Theorem.
• 5L-n-P1 is collinear with 5L-o-P2 and 5L-n-P3.
• 5L-n-P1 is a point on 5L-o-Ci1 and the inversion of 5L-o-P2 wrt 5L-n-Ci1 (Ref-34, QFG#722, October 6, 2014, Eckart Schmidt).
• 5L-n-P1 is a node of the Mono EnnaCardioid nL-n-Cv1, circumscribing n (n-1)L-EnnaCardioids (n-1)L-n-iCv1. See Ref-37, Morley's paper: Extensions of Clifford’s Chain Theorem.