QL-L8: QL-Centroids Line

QL-L8 is the line through 4 Quadrilateral points, all related to Centroids.

These points are:

• QL-P8 = Centroid QL-Diagonal Triangle
• QL-P12 = QL-Centroid or Lateral Centroid
• QL-P14 = 1^st QL-Quasi Centroid
• QL-P15 = 2^nd QL-Quasi Centroid

1st CT-coefficient

l (6 l⁴ m⁴ – 3 l³ m⁵ – 10 l⁴ m³ n – 5 l³ m⁴ n + 5 l² m⁵ n + 8 l⁴ m² n² + 8 l³ m³ n² – 4 l² m⁴ n² – l m⁵ n² – 10 l⁴ m n³ + 8 l³ m² n³ – l m⁴ n³ – m⁵ n³ + 6 l⁴ n⁴ – 5 l³ m n⁴ – 4 l² m² n⁴ – l m³ n⁴ + 4 m⁴ n⁴ – 3 l³ n⁵ + 5 l² m n⁵ – l m² n⁵ – m³ n⁵)

1st DT-coefficient

(l² – n²) (l² n² – m⁴) + (l² – m²) (l² m² – n⁴)

Properties

• The ratio of distances between QL-P8, QL-P15, QL-P12, QL-P14 in this order is 2 : 1 : 1.
• The QL-Centroids Line QL-L8 is the QA-Centroids Line (QA-L3) of the Quadrangle with the centroids of the Component Triangles of the Reference Quadrilateral as its vertices, where QL-P12 ~ QA-P1, QL-P8 ~ QA-P5, QL-P14 ~ QA-P10, QL-P18 ~ QA-P20 (Eckart Schmidt, September 18, 2012).

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