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MATHEMATICS

Chris van Tienhoven

Menu nP - Objects  |      Menu nL - Objects   |       Menu nG - Objects

 
nL-n-Luc5g   nL-Par1/Per2-construction

nL-n-Luc5g is a Level-up construction which uses the 1st generation parallel n-Line Par1 and the 2nd generation perpendicular n-Line Per2 wrt some lower-level center to construct a Perspective / Homothetic Center. See nL-n-Luc5.

Examples are 5L-s-P9 and 5L-s-P10 and 5L-n-P12.

Also
• nL-n-Luc5g (X(2)) = QL-P12.Mid(QL-P2,QL-P20) (5:-1)
• nL-n-Luc5g (X(4)) = QL-P20.QL-P2 (2:-1).
 






Gegevens
Hits: 1980
Menu nP - Objects  |      Menu nL - Objects   |       Menu nG - Objects

EPG Menu

______________________________ References
____________________________________ N-POINT ITEMS
n-Point-General Information
nP-0 Menu n-Point Objects
nP-1 General Information
n = 3,4,5,6,7, etc. ---------------------------
n-Point Centers/Points
nP-n-P1: nP-MVP Centroid
nP-n-P2: nP-MVP Circumcenter
nP-n-P3: nP-MVP Orthocenter
nP-n-P4: nP-MVP Nine-point Center
nP-n-P5: nP-CC Moebius Center
n-Point Lines
nP-n-L1: nP-MVP-Eulerline
nP-n-L2: nP-LSD Line
n-Point Transformations
nP-n-Tf1: nP-CC Moebius Conjugate
nP-n-Tf2: nP-Linear Pole
n = even ---------------------------------------
e-Point Transformations
nP-e-Tf1: nP-Pedal Point
nP-e-Tf2: nP-AntiPedal Point
n = odd ----------------------------------------
o-Point Transformations
nP-o-Tf1: nP-Pedal Circle
nP-o-Tf2: nP-Pedal Circle Center
nP-o-Tf3: nP-AntiPedal Circle
nP-o-Tf4: nP-AntiPedal Circle Center
n = 2 exclusive ------------------------------
2-Point Specials
2P-s-iRg1 2P-Regular Lighthousen-Gons
n = 5 exclusive ------------------------------
5-Point Conics
5P-s-Co1: 5P-Circumscribed Conic
5-Point General Information
5P-1 Notes on the Pentangle
5-Point Centers/Points
5P-s-P2: 5P-Involutary Center
5P-s-P3: 5P-Quang Duong's Point
5P-s-P4: 5P-Keizer-Schmidt Center
5P-s-P5: 5P-Schmidt Point
5P-s-P6: 5P-Miquel Point
5P-s-2P1: 5P-Involutary Double Point
5-Point Lines
5P-s-L1: 5P-Schmidt Line
5-Point Transformations
5P-s-Tf1: 5P-Line of Involution Centers
5P-s-Tf2: 5P-Line of Invol. Conjugates
5P-s-Tf3: 5P-Orthopole
5P-s-Tf4: 5P-Orthopolar Line
5P-s-Tf5: 5P-Conical Pole
5P-s-Tf6: 5P-cb Conjugate
5P-s-Tf7: 5P-Schmidt Transformation
5P-s-Tf8: 5P-CSC Conjugate
n = 6 exclusive ------------------------------
6-Point Centers/Points
6P-s-P1: 6P-Schmidt Point
6P-s-P2: 6P-Cayley Bacharach Point Circular Cubic
6-Point Circles
6P-s-Ci1: 6P-CSC-Circle
6-Point Transformations
6P-s-Tf1: 6P-Schmidt Transformation
6P-s-Tf2: 7th point Tangent
n = 7 exclusive ------------------------------
7-Point Centers/Points
7P-s-P1: 7P-Schmidt Point/Focus Circular Cubic
7P-s-P2: CB-pivot of the 7P-Circular Cubic
7P-s-P3: 7P-s-Cu1 Tangential of 7P-s-P2
7-Point Cubics
7P-s-Cu1: 7P-Circular Cubic
7-Point Transformations
7P-s-Tf1: 7P-CB Conjugate
n = 8 exclusive ------------------------------
8-Point Centers/Points
8P-s-P1: 8P-Cayley-Bacharach Point
8-Point Transformations
8P-s-Tf1: 9th point Tangent
n = 9 exclusive ------------------------------
9-Point Cubics
9P-s-Cu1: 9P-Cubic
n = 14 exclusive ------------------------------
14-Point Quartics
14P-s-Cu1: 14P-Quartic
n-Point Level-up Constructions
nP-n-Luc1: nP-Mean Vector Point
____________________________________ N-LINE ITEMS
n-Line General Information
nL-0: Menu n-Line Objects
nL-1: General Information
n = 3,4,5,6,7, etc. ---------------------------
n-Line Points
nL-n-P1: nL-Centric Focus
nL-n-P2: nL-Morley's Centroid
nL-n-P3: nL-Morley’s Circumcenter
nL-n-P4: nL-Morley's 2nd Orthocenter
nL-n-P5: nL-Morley's 2nd Circle Center
nL-n-P6: nL-LSD Point
nL-n-P7: nL-Hervey Point
nL-n-P8: nL-MVP Centroid
nL-n-P9: nL-MVP Circumcenter
nL-n-P10: nL-MVP Orthocenter
nL-n-P11: nL-MVP Nine-point Center
nL-n-P12: nL-QL-P4 Par1/Par2 HC
nL-n-P13: nL-QL-P28 Par1/Par2 HC
nL-n-P14: nL-QL-P29 Par1/Par2 HC
nL-n-pi: Morley's intermediate recursive pi pts
nL-n-gi: Morley's intermediate recursive gi pts
n-Line Lines
nL-n-L1: nL-Morley’s Eulerline
nL-n-L2: nL-MVP-Eulerline
nL-n-iL1: nL-Morley Axes
n-Line Circles
nL-n-Ci1: nL-Center Circle
nL-n-Ci2: nL-Second Circle
n-Line Curves
nL-n-Cv1: nL-Morley’s Mono EnnaCardioid
nL-n-Cv2: nL-Morley’s Limacon
nL-n-(i)Cv1: nL-Morley’s Multiple EnnaCardioids
n-Line Transformations
nL-n-Tf1: nL-Orthopole
nL-n-Tf2: nL-Orthopolar
nL-n-Tf3: nL-2nd generation Orthopole
nL-n-Tf4: nL-2nd generation Orthopolar
nL-n-Tf5: nL-Linear Polar
n = even ---------------------------------------
e-Line Points
nL-e-P1: nL-Morley's EnnaDeltoid Center
nL-e-P2: nL-Clifford's Point
e-Line Lines
nL-e-L1: nL-Morley's Ortho Directrix
nL-e-L2: nL-Morley's Alternate Line of Orthocenters
e-Line Curves
nL-e-Cv1: nL-Morley's Inscribed EnnaDeltoid
n = odd ----------------------------------------
o-Line Points
nL-o-P1: nL-Morley's 1st Orthocenter
nL-o-P2: nL-Clifford's Circle Center
o-Line Lines
nL-o-2L1: nL-Orthogonal Ortho Axes
nL-o-L1: nL-Line of Inscribed EnnaDeltoid Centers
nL-o-L2: nL-Morley's Line of Orthocenters
o-Line Circles
nL-o-Ci1: nL-Clifford's Circle
n = 5 exclusive ------------------------------
5-Line General Information
5L-1: Notes on the Pentalateral
5-Line Points
5L-s-P1: 5L-Inscribed Conic Center
5L-s-P2: 5L-X(186)-Hofstadter Point
5L-s-P3: 5L-X(265)-Hofstadter Point
5L-s-P4: 5L-Center of Anticenter Circle
5L-s-P5: 5L-OH Division Point
5L-s-P6: 5L-QL-P3 Par1/Par2-HC
5L-s-P7: 5L-QL-P20 Par1/Par2-HC
5L-s-P8: 5L-QL-P27 Ref/Par1/Par2-HC
5L-s-P9: 5L-QL-P28 Par1/Per2-HC
5L-s-P10: 5L-QL-P29 Par1/Per2-HC
5L-s-P11: 5L-Schmidt Point
5-Line Lines
5L-s-L1: 5L-Newton Line
5L-s-L2: 5L-Isoconjugate Line
5L-s-L3: 5L-PAP Miquel Points Line
5-Line Conics
5L-s-Co1: 5L-Inscribed Conic
5-Line Transformations
5L-s-Tf1: 5L-Schmidt Transformation
5L-s-Tf2: 5L-Inscribed Conical Pole
5L-s-Tf3: 5L-Inscribed Conical Polar
n = 6 exclusive -------------------------------
6-Line Points
6L-s-P1: 6L-Conical Center
6L-s-P2: 6L-Conical Ref-Par2 HC
6L-s-P3: 6L-Conical Ref-Per2 HC
6L-s-P4: 6L-Conical Par2-Per2 HC
6-Line Conics
6L-s-Co1: 6L-Conical Center Conic
6-Line Transformations
6L-s-Tf1: 6L-Schmidt Transformation
n = 7 exclusive ------------------------------
7-Line Points
7L-s-3P1: 7L-Conical Triplet Points
7-Line Circles
7L-s-Ci1: 7L-Conical Triplet Circle
n = 8 exclusive ------------------------------
8-Line Points
8L-s-P1: 8L-Conical Center
8-Line Lines
8L-s-L1: 8L-Keizer-Schmidt Line
n-Line Level-up Constructions
nL-n-Luc-1: General Information
nL-n-Luc1: nL-Common Point of Perpendiculars On Omitted Line
nL-n-Luc2: nL-Common Point of Perpendicular Bisectors
nL-n-Luc3: nL-Sum of Vectors Point
nL-n-Luc4: nL-Mean Vector Point
nL-n-Luc5: nL-Ref/Per/Par-Constructions
nL-n-Luc5a: nL-Ref/Par1-Construction
nL-n-Luc5b: nL-Ref/Par2-Construction
nL-n-Luc5c: nL-Ref/Per1-Construction
nL-n-Luc5d: nL-Ref/Per2-Construction
nL-n-Luc5e: nL-Par1/Par2-Construction
nL-n-Luc5f: nL-Par1/Per1-Construction
nL-n-Luc5g: nL-Par1/Per2-Construction
nL-n-Luc5h: nL-Par2/Per1-Construction
nL-n-Luc5i: nL-Par2/Per2-Construction
nL-n-Luc5j: nL-Per1/Per2-Construction
____________________________________ N-GON ITEMS
n-Gon General Information
nG-0: Menu n-Gon Objects
nG-1: General Information
n-Gon Lines
nG-n-L1 nG-Centroids Line
n-Gon Specials
nG-n-iRg1 Regular PDN-n-Gons
n = 5 exclusive ------------------------------
5-Gon Points
5G-s-P1: 5G-CommonNewtonLinesPoint
5G-s-P2: 5G-Bicircles Crosspoint
5G-s-P3: 5G-Inner Miquel Points Center
5G-s-P4: 5G-Miquel-Catalan Point
5G-s-P5 1st 5G-Hung’s Point
5G-s-P6 2nd 5G-Hung’s Point
5G-s-P7 3rd 5G-Hung’s Point
5G-s-P8 4th 5G-Hung’s Point
5G-s-P9 5G-Schmidt Point
5-Gon Conics
5G-s-Co1: 5G-Schmidt Orthogonal Hyperbola
n = 6 exclusive ------------------------------
6-Gon Points
6G-s-P1: 1st 6G-Hung’s Point
6G-s-P2: 2nd 6G-Hung’s Point

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