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Interactive Polygonal Sinusoids

Interactive Polygonal Sinusoids
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2019-05-27 01:38
PolygonTrigonometryGeometric Construction
This example demonstrates the dynamic changes of interactive polygonal sinusoids. It involves core concepts of trigonometry and stochastic processes. Using GeoGebra commands such as Circle, Point, Rotate, Segment, Polygon, etc., a series of polygons are constructed and their sinusoidal curves are observed. Suitable for high school mathematics teaching and learning, particularly for trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Rotate(B, t, A) → B'
  4. Segment(A, B') → g
  5. Polygon(B, Rotate[B, (2 * π / n), A], n) → poly1, a, p, q, r, s, a_1, b_1, c_1, d_1, e_1, f_1, b, g_1, h_1, i_1, j_1, k_1, l_1, m_1, q_1, r_1, s_1, d, t_1, C, H, I, J, K, L, M, N, O, h, P, Q, R, S, T, U, V, W, Z, A_1, i, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, j, k, l, m
  6. Intersect(g, poly1) → D
  7. Point(poly1) → E
  8. Angle(B, A, D) → α
  9. Segment(A, D) → e
  10. Locus(G, t) → lieu2
  11. Segment(D, G) → f
  12. Segment(A, B) → n_1
  13. Segment(F, G) → p_1
  14. Segment((6.283185307179586, 1), (6.283185307179586, -1)) → a_2
  15. Segment(B, K_1) → b_2
  16. Circle(N_1, 1) → c_2
  17. Point(c_2) → CC
  18. Polygon(CC, Rotate[CC, 0.12566370614359174, N_1], 50) → poly2, d_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_3, b_3, c_3, e_2, d_3, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, f_2, n_3, p_3, q_3, r_3, s_3, t_3, a_4, b_4, c_4, d_4, g_2, e_4, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, h_2, p_4, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, i_2, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, j_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, k_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, l_2, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3
  19. Rotate(CC, t, N_1) → CC'
  20. Locus(GG, t) → lieu1
  21. Vector((0, -1.25), (0, 1.25)) → u
  22. Vector(OO + (0, -1.25), OO + (0, 1.25)) → v
  23. Segment(N_1, CC') → q_4
  24. Segment(CC, N_1) → r_4
  25. Segment(CC', GG) → s_4
  26. Ray(OO, OO + (15, 0)) → t_4
  27. Segment(CC, O_3) → a_5
  28. Angle(CC, N_1, CC') → β
  29. Segment(GG, P_3) → b_5
  30. Segment(N_1, QQ) → c_5
  31. Angle(QQ, N_1, CC) → γ
  32. Segment((6.28319, -2), (6.28319, -4)) → d_5
  33. Sequence(OO + (i, 0), i, 0, 12.566370614359172, 1.5707963267948966) → liste1

AI Drawing Prompt Reference

Create an interactive demonstration of polygonal sinusoids. Start with a unit circle and a point on it, which rotates around the center to form a dynamic angle. Construct a regular polygon with this point as a vertex, and let one side of the polygon intersect the rotating point on the circle. Draw a segment from the center to the intersection, and trace the locus of the intersection to form a sinusoidal curve. Then draw a second unit circle with a regular polygon having more sides, rotate a point on it, and connect the rotated point to the traced point to form another sinusoid. Add axes, vectors, and tick marks to show the dynamic changes of both sine waves.
The prompt above was compiled from the original drawing commands and is for reference only.