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Set Theory and Linear Regression Exploration

Set Theory and Linear Regression Exploration
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2019-07-05 12:59
Probability & Statistics
In collections Exploring Feyman's Triangle
This example demonstrates basic concepts of set theory and the application of linear regression. It involves set operations like intersection, union, and complement, as well as fitting a linear regression model. The construction uses commands such as Segment, Dilate, Intersect, and Polygon. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, B) → g
  3. Segment(A, C) → h
  4. Dilate(C, 1 / 3, A) → C'
  5. Dilate(A, 1 / 3, B) → A'
  6. Dilate(B, 1 / 3, C) → B'
  7. Segment(B, C') → i
  8. Segment(A, B') → j
  9. Segment(A', C) → k
  10. Intersect(k, i) → D
  11. Intersect(j, i) → E
  12. Intersect(k, j) → F
  13. Polygon(B, A, C) → t1, c, b, a
  14. Polygon(D, E, F) → t2, f_1, d, e
  15. Dilate(B, 1 / 2, A) → X
  16. Dilate(A, 1 / 2, C) → Y
  17. Dilate(B, 1 / 2, C) → Z
  18. Polygon(X, D, B) → t3, b_1, x_1, d_1
  19. Polygon(Z, F, C) → t4, c_1, z_1, f_2
  20. Polygon(E, A, Y) → t5, y_1, e_1, a_1

AI Drawing Prompt Reference

Draw a triangle ABC, then draw circles with radii 1/3 centered at A, B, and C. Get new points A', B', and C'. Draw line segment i from B to C', line segment j from A to B', and line segment k from A' to C. Find the intersection of line segment k and i as point D, the intersection of line segment j and i as point E, and the intersection of line segment k and j as point F. Draw triangle t1 with vertices B, A, and C, triangle t2 with vertices D, E, and F, triangle t3 with vertices A and C, triangle t4 with vertices B and D, and triangle t5 with vertices C and F.
The prompt above was compiled from the original drawing commands and is for reference only.