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Rotation and Polygon Construction

Rotation and Polygon Construction
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2016-05-11 02:45
PolygonAngleTransformationGeometric Construction
This example demonstrates the application of rotation transformations in polygon construction, showcasing dynamic changes and symmetry of shapes through rotation operations. Core mathematical concepts include rotation transformation, polygon construction, angle measurement, and analytical geometry. Key GeoGebra commands used in the construction are Polygon, Intersect, Rotate, Segment, and Angle. It is suitable for high school students learning geometric transformations, polygon properties, and the application of dynamic geometry software, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h_2, i, C_1, D
  2. Polygon(D, C_1, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a, b, I, J
  5. Polygon(J, I, 4) → poly5, c, d, e, f_1, K, L
  6. Polygon(K, I, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  7. Polygon(N, M, 4) → poly7, k_1, l_1, m_1, n_1, O, P
  8. Polygon(G, E, 4) → poly8, p_1, q_1, r_1, s_1, Q, R
  9. Polygon(A, L, P, O, I, G, R, Q, E, B) → poly9, a_1, b_1, l_2, p_2, o, i_2, g_2, r_2, q_2, e_1
  10. Intersect(xAxis, yAxis) → S
  11. Rotate(A, α, S) → A'
  12. Rotate(L, α, S) → L'
  13. Rotate(P, α, S) → P'
  14. Rotate(O, α, S) → O'
  15. Rotate(I, α, S) → I'
  16. Rotate(G, α, S) → G'
  17. Rotate(R, α, S) → R'
  18. Rotate(Q, α, S) → Q'
  19. Rotate(E, α, S) → E'
  20. Rotate(B, α, S) → B'
  21. Polygon(A', L', P', O', I', G', R', Q', E', B') → poly9', a', b', l', p', o', i', g', r', q', e'
  22. Rotate(A, β, C) → A''
  23. Rotate(L, β, C) → L'_1
  24. Rotate(P, β, C) → P'_1
  25. Rotate(O, β, C) → O'_1
  26. Rotate(I, β, C) → I'_1
  27. Rotate(G, β, C) → G'_1
  28. Rotate(R, β, C) → R'_1
  29. Rotate(Q, β, C) → Q'_1
  30. Rotate(E, β, C) → E'_1
  31. Rotate(B, β, C) → B''
  32. Polygon(A'', L'_1, P'_1, O'_1, I'_1, G'_1, R'_1, Q'_1, E'_1, B'') → poly9'_1, a'_1, b'_1, l'_1, p'_1, o'_1, i'_1, g'_1, r'_1, q'_1, e'_1
  33. Segment(B, S) → h
  34. Segment(S, B') → t_1
  35. Angle(B, S, B') → γ
  36. Segment(B, C) → c_1
  37. Segment(C, B'') → d_1
  38. Angle(B, C, B'') → δ