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GeoGebra Example: Functions, Statistics, and Geometric Transformations

GeoGebra Example: Functions, Statistics, and Geometric Transformations
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2019-07-05 18:05
FunctionTrigonometryGeometric ConstructionGraphing
In collections Exploring Feyman's Triangle
This example dynamically demonstrates the relationships between function graphs, secant lines, sine waves, and statistical charts, revealing the intrinsic connection between functions and geometric transformations. Core concepts include function graphing, the relationship between secants and tangents, trigonometric properties, statistical data analysis, and geometric transformations (rotation, dilation). GeoGebra commands and objects used in construction are Segment, Dilate, Intersect, Polygon, Rotate, Distance, Perimeter, and PointIn. Suitable for high school and above learners to understand the integrated application of function properties, geometric transformations, and data analysis.

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) → E
  11. Intersect(j, i) → D
  12. Intersect(k, j) → F
  13. Polygon(B, A, C) → t1, c, b, a
  14. Polygon(E, D, 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, E, B) → t3, b_1, x_1, d_1
  19. Polygon(Z, F, C) → t4, c_1, z_1, f_2
  20. Polygon(D, A, Y) → t5, y_1, e_1, a_1
  21. Rotate(X, (-(180°)), X) → X'
  22. Rotate(E, (-(180°)), X) → D'
  23. Rotate(B, (-(180°)), X) → B'_1
  24. Polygon(X', D', B'_1) → t3', b'_1, x', d'
  25. Rotate(D, (-(180°)), Y) → E'
  26. Rotate(A, (-(180°)), Y) → A'_1
  27. Rotate(Y, (-(180°)), Y) → Y'
  28. Polygon(E', A'_1, Y') → t5', y', e', a'_1
  29. Rotate(Z, (-(180°)), Z) → Z'
  30. Rotate(F, (-(180°)), Z) → F'
  31. Rotate(C, (-(180°)), Z) → C'_1
  32. Polygon(Z', F', C'_1) → t4', c'_1, z', f'
  33. Polygon(E, D', A, D) → q1, d_2, l, a_2, e_2
  34. Polygon(B, E, F, F') → q2, b_2, d_3, f_3, m
  35. Polygon(F, D, E', C) → q3, f_4, e_3, n, c_2
  36. Segment(D', D) → p
  37. Segment(E', F) → q
  38. Segment(F', E) → r
  39. Distance(D', A) → distanceD'A
  40. Distance(A, D) → distanceAD
  41. Distance(E, D) → distanceED
  42. Distance(D', E) → distanceD'E
  43. Distance(D', D) → distanceD'D
  44. Distance(B, E) → distanceBE
  45. Distance(E, F') → distanceEF'
  46. Distance(B, F') → distanceBF'
  47. Distance(D, F) → distanceDF
  48. Distance(D, E') → distanceDE'
  49. Distance(F, E') → distanceFE'
  50. Distance(F, C) → distanceFC
  51. Perimeter(q2) → perimeterq2
  52. PointIn(q2) → Pointq2
  53. Distance(E', C) → distanceE'C
  54. Distance(E, F) → distanceEF
  55. Distance(F', F) → distanceF'F

AI Drawing Prompt Reference

Draw a function graph and demonstrate its relationship with secant lines, sine waves, and statistical charts. Start by constructing three points and connecting them to form a triangle. Then scale each vertex to create new points and connect them to form new segments. Intersect the segments to find points, and use these points to construct multiple polygons. Rotate some polygons and calculate distances between key points. The final image should include original and rotated polygons, segments, and intersection points, clearly showing the connection between functions, geometric transformations, and statistical data.
The prompt above was compiled from the original drawing commands and is for reference only.