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Tower Bridge Geometry: Polygon and Rotation Construction

Tower Bridge Geometry: Polygon and Rotation Construction
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2020-10-08 02:33
PolygonAngleTransformationGeometric ConstructionSlider Animation
This example demonstrates how to construct a geometric model of London's Tower Bridge using GeoGebra. Key commands include Polygon for the main bridge towers, Rotate for opening/closing animations, Angle and CircleArc for suspension cables, Mirror for symmetry, and OrthogonalLine for critical intersections. The construction involves orthocenter concepts and linear equation solving, showcasing polynomial functions and integer operations. Suitable for middle to high school mathematics teaching, covering polygon properties, rotation transformations, axial symmetry, and angle calculations. Ideal for math modeling practice and GeoGebra skill development.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Line(B, yAxis) → f
  5. Line(C, yAxis) → g
  6. Point(yAxis) → D
  7. OrthogonalLine(D, f) → h
  8. Intersect(f, h) → E
  9. Intersect(g, h) → F
  10. CircleArc(B, A, E) → c
  11. CircleArc(C, F, A) → d
  12. Point(c) → G
  13. Point(d) → H
  14. Segment(G, B) → i
  15. Segment(H, C) → j
  16. Rotate(G, a°, B) → G'
  17. Angle(G, B, G') → α
  18. Rotate(H, ((-a))°, C) → H'
  19. Angle(H', C, H) → β
  20. Polygon(G', B, 4) → poly1, k, l, m, n, I, J
  21. Polygon(C, H', 4) → poly2, p, q, r, s, K, L
  22. Segment(G', J) → t
  23. Segment(B, I) → b
  24. Segment(B, G') → e
  25. Segment(C, H') → f_1
  26. Segment(H', K) → g_1
  27. Segment(C, L) → h_1
  28. Point(t) → Q
  29. Point(b) → R
  30. OrthogonalLine(A, j) → i_1
  31. Mirror(Q, i_1) → Q'
  32. Mirror(R, i_1) → R'
  33. Polygon(G', B, R, Q) → q1, g', b_1, r_1, q_1
  34. Polygon(H', C, R', Q') → q2, h', c_1, r', q'
  35. Segment(W, Z) → j_1
  36. Point(j_1) → A_1
  37. Point(Circle[A_1, 4]) → B_1
  38. Segment(A_1, B_1) → k_1
  39. Polygon(A_1, B_1, 4) → poly3, l_1, m_1, n_1, p_1, C_1, D_1

AI Drawing Prompt Reference

Draw a geometric model of London's Tower Bridge, including the main towers, suspension cables, and rotation animation. Start by drawing the base of the towers, then create the cables using rotation and mirroring, and finally use arcs and lines to construct the tower outlines. Add rotation and symmetry effects to complete the bridge structure.
The prompt above was compiled from the original drawing commands and is for reference only.