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Wordless Proof: Metric Relation (1)

Wordless Proof: Metric Relation (1)
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2020-04-22 14:55
VectorCoordinate GeometryGeometric Construction
This example demonstrates the metric relationship between a rectangle and linear functions through dynamic geometry. Key math concepts include coordinate geometry, vectors, rotation, and translation. Construction highlights involve commands like Circle, Midpoint, Polygon, OrthogonalLine, Intersect, Angle, Segment, Rotate, Translate, Vector, and Centroid. Suitable for high school and above learners to explore geometric transformations and metric properties.

GeoGebra Commands & Parameters

  1. Circle(C, B) → c
  2. Midpoint(C, B) → C_1
  3. Circle(C_1, B) → d
  4. Point(d) → A
  5. Polygon(C, B, A) → t1, d_1, a, b
  6. OrthogonalLine(A, d_1) → f
  7. Intersect(d_1, f) → H
  8. Angle(C, A, B) → α
  9. Angle(B, H, A) → β
  10. Segment(A, H) → g
  11. Segment(H, B) → h
  12. Rotate(H, If[a < π / 2, a / (π / 2), π / 2], H) → H'
  13. Rotate(B, If[Animation < π / 2, ((-Animation)) / (π / 2), ((-π)) / 2], H) → B'
  14. Segment(H', B') → h'
  15. Translate(H', Vector[(If[π / 2 < Animation < 5, (Animation - π / 2) / 5, 1] * Vector[H, C])]) → H''
  16. Translate(B', Vector[(If[π / 2 < Animation < 5, (Animation - π / 2) / 5, 1] * Vector[H, C])]) → B''
  17. Segment(H'', B'') → h''
  18. Segment(H, C) → l
  19. Translate(H, Vector[(If[π / 2 < Animation < 5, (Animation - π / 2) / 5, 1] * Vector[H, B'])]) → H'_1
  20. Translate(C, Vector[(If[π / 2 < Animation < 5, (Animation - π / 2) / 5, 1] * Vector[H, B'])]) → C'
  21. Segment(H'_1, C') → l'
  22. Polygon(C, H, B', B'') → q1, c_1, h_1, b', b''
  23. Rotate(H, If[5 < Animation < 5 + π / 2, (Animation - 5) / (π / 2), π / 2], A) → A'
  24. Segment(A', A) → i
  25. Rotate(A, If[5 < Animation < 5 + π / 2, ((-(Animation - 5))) / (π / 2), ((-π)) / 2], H) → A'_1
  26. Segment(H, A'_1) → j
  27. Rotate(A, If[8 < Animation < 10, (Animation - 8) / (π / 2), π / 2], A') → A'_2
  28. Segment(A', A'_2) → k
  29. Polygon(A, A', A'_1, H) → q2, a_1, a', a'_1, h_2
  30. Vector(A, C) → u
  31. Vector(H, B'') → v
  32. Vector(A'_2, B') → w
  33. Vector(A', H) → e
  34. Translate(A, Vector[(If[11 < Animation < 14, (Animation - 11) / 3, 1] * u)]) → A'_3
  35. Translate(H, Vector[(If[11 < Animation < 14, (Animation - 11) / 3, 1] * v)]) → H'_2
  36. Translate(A', Vector[(If[11 < Animation < 14, (Animation - 11) / 3, 1] * e)]) → A''
  37. Translate(A'_2, Vector[(If[11 < Animation < 14, (Animation - 11) / 3, 1] * w)]) → D
  38. Polygon(A'_3, H'_2, D, A'') → q3, a'_3, h'_2, d_2, a''
  39. Centroid(q2) → E
  40. Centroid(q1) → F