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Rotation Exploration (F shape 1)

Rotation Exploration (F shape 1)
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2016-09-28 10:22
Coordinate GeometryGeometric Construction
This example demonstrates the rotation transformation of an F-shaped figure and its geometric properties. It involves core math concepts like rotation, means, circumcircle, correlation, algebra, and normal distribution. The construction uses commands such as Polygon, Intersect, Rotate, Segment, and Angle. Suitable for high school mathematics, illustrating the integration of geometric transformations and data analysis.

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