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Geometric Similarity from a Variable-Parts Perspective by Sybilla Beckmann

Geometric Similarity from a Variable-Parts Perspective by Sybilla Beckmann
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2018-12-11 09:32
Coordinate GeometryTransformationGeometric Construction
This example demonstrates geometric similarity from a variable-parts perspective, involving concepts like dilation, linear regression, and normal distribution. It uses GeoGebra commands such as Point, Polygon, Ray, Circle, Intersect, Line, and Segment. Suitable for high school and above, it illustrates the integration of geometric transformations and data analysis.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → D
  3. Polygon(A, B, C, D) → q1, a, b, c, d
  4. Polygon(B, E, C) → t1, c_1, b_1, e
  5. Point(yAxis) → F
  6. Point(xAxis) → G
  7. Ray(F, G) → g
  8. Point(yAxis) → H
  9. Ray(F, H) → h
  10. Circle(F, f) → k
  11. Intersect(g, xAxis) → I
  12. Intersect(g, xAxis) → J
  13. Intersect(g, xAxis) → K
  14. Intersect(k, g) → L,
  15. Intersect(k, h, 1) → M
  16. Circle(L, f) → p
  17. Circle(M, f) → q
  18. Intersect(q, h, 2) → N
  19. Intersect(p, g, 2) → O
  20. Circle(N, f) → r
  21. Circle(O, f) → s
  22. Intersect(r, h, 2) → P
  23. Intersect(s, g, 2) → Q
  24. Circle(P, f) → t
  25. Circle(Q, f) → d_1
  26. Intersect(t, h, 2) → R
  27. Intersect(d_1, g, 2) → S
  28. Line(R, g) → i
  29. Line(P, i) → j
  30. Line(N, j) → l
  31. Line(M, l) → m
  32. Line(S, h) → n
  33. Line(Q, h) → f_1
  34. Line(O, h) → g_1
  35. Line(L, h) → h_1
  36. Intersect(i, h_1) → T
  37. Intersect(i, g_1) → U
  38. Intersect(i, f_1) → V
  39. Intersect(i, n) → W
  40. Intersect(j, n) → Z
  41. Intersect(l, n) → A_1
  42. Intersect(m, n) → B_1
  43. Segment(F, S) → i_1
  44. Segment(M, B_1) → j_1
  45. Segment(N, A_1) → k_1
  46. Segment(P, Z) → l_1
  47. Segment(R, W) → m_1
  48. Segment(F, R) → n_1
  49. Segment(L, T) → p_1
  50. Segment(O, U) → q_1
  51. Segment(Q, V) → r_1
  52. Segment(S, W) → s_1
  53. Intersect(k_1, r_1) → C_1
  54. Polygon(F, N, C_1, Q) → q2, f_2, n_2, c_2, q_2
  55. Intersect(l_1, p_1) → D_1
  56. Polygon(N, D_1, C_1) → t2, c_3, n_3, d_2