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Zero Correlation Triangle

Zero Correlation Triangle
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2013-04-28 23:17
Probability & StatisticsGeometric Construction
This example demonstrates a statistical phenomenon of zero correlation within a triangle through geometric constructions. Core math concepts include correlation coefficient (PMCC), geometric constructions (e.g., intersections, midpoints, orthogonal lines), coordinate systems, and statistical distributions. GeoGebra commands used in its construction are: Intersect, Dilate, Segment, Midpoint, OrthogonalLine, PMCC, LaTeX, Polygon, Circle, Angle, Line, and Centroid. Suitable for high school and above learners to understand the intersection of geometry, conics, and statistics.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → G_1
  2. Dilate(A, -0.5, G_1) → A'
  3. Dilate(B, -1, A') → C
  4. Segment(A, B) → c
  5. Segment(A, C) → b
  6. Segment(C, B) → a
  7. Midpoint(b) → D
  8. OrthogonalLine(D, xAxis) → d
  9. OrthogonalLine(D, yAxis) → e
  10. PMCC({A, B, C}) → r
  11. LaTeX(r, true, true) → text1
  12. LaTeX(g, true, true) → text2
  13. Polygon(Z_A, Z_C, Z_B) → poly1, z_b, z_a, z_c
  14. Circle(Z_A, Z_C, Z_B) → f
  15. Angle(poly1) → α, β, γ
  16. Line(G_1, B) → i
  17. Centroid(poly1) → G

AI Drawing Prompt Reference

Draw a triangle with its vertices intersecting the coordinate axes, construct midpoints of the vertices and lines perpendicular to the axes, calculate and display the zero correlation coefficient of the vertex coordinates, and draw a polygon and circle containing the three vertices, label the angles formed by the vertices, and finally mark the centroid of the polygon and the line segments connecting the vertices.
The prompt above was compiled from the original drawing commands and is for reference only.