MathPlotAI Logo MathPlotAI

Spiral Construction Demonstration

Spiral Construction Demonstration
Loading the math board and drawing, please wait…
2019-05-26 00:49
FunctionTrigonometryGeometric ConstructionSlider AnimationGraphing
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates the dynamic construction process of a spiral and its geometric properties. It involves core mathematical concepts such as power functions, tangent functions, symmetry, quadratic equations, and confidence intervals. The construction highlights GeoGebra commands and objects like Polygon, Point, OrthogonalLine, Intersect, and PointIn. Suitable for high school and above learners to understand function graphs, geometric transformations, and data analysis.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Point(yAxis) → D
  3. OrthogonalLine(C, f) → i
  4. Polygon(C, D, 3) → poly2, j, k, l, E
  5. Intersect(g, k) → F
  6. Polygon(C, F, 3) → poly3, m, n, p, G
  7. Intersect(l, n) → H
  8. Polygon(C, H, 3) → poly4, q, r, s, I
  9. Intersect(p, r) → J
  10. Polygon(C, J, 3) → poly5, t, a, b, K
  11. Intersect(s, a) → L
  12. Polygon(C, L, 3) → poly6, c, d, e, M
  13. Intersect(d, b) → N
  14. Polygon(C, N, 3) → poly7, f_1, g_1, h_1, O
  15. Intersect(i, e) → P
  16. Intersect(g_1, i) → Q
  17. Polygon(C, Q, 3) → poly8, i_1, j_1, k_1, R
  18. Intersect(g, j_1) → S
  19. Intersect(j_1, h_1) → T
  20. Polygon(C, T, 3) → poly9, l_1, m_1, n_1, U
  21. Intersect(k_1, m_1) → V
  22. Polygon(C, V, 3) → poly10, p_1, q_1, r_1, W
  23. Intersect(poly9, poly10) → Z, A_1, B_1, C_1, D_1, E_1, F_1
  24. Polygon(C, E_1, 3) → poly11, s_1, t_1, a_1, G_1
  25. Intersect(r_1, t_1) → H_1
  26. Polygon(C, H_1, 3) → poly12, b_1, c_1, d_1, I_1
  27. Intersect(h, a_1) → J_1
  28. Intersect(c_1, h) → K_1
  29. Polygon(C, K_1, 3) → poly13, e_1, f_2, g_2, L_1
  30. Intersect(i, j) → M_1
  31. Intersect(poly1, poly2) → N_1, O_1, P_1, Q_1, R_1, S_1, T_1
  32. Intersect(f_2, i) → U_1
  33. Polygon(C, U_1, 3) → poly14, h_2, i_2, j_2, V_1
  34. Intersect(g, m) → W_1
  35. Intersect(g, m) → Z_1
  36. Intersect(i_2, poly2) → A_2
  37. Intersect(i_2, g) → B_2
  38. Polygon(C, B_2, 3) → poly15, k_2, l_2, m_2, C_2
  39. Intersect(l_2, l) → D_2
  40. Polygon(C, D_2, 3) → poly16, n_2, p_2, q_2, E_2
  41. PointIn(poly1) → Pointpoly1
  42. PointIn(poly2) → Pointpoly2
  43. PointIn(poly3) → Pointpoly3
  44. PointIn(poly4) → Pointpoly4
  45. PointIn(poly5) → Pointpoly5
  46. PointIn(poly6) → Pointpoly6

AI Drawing Prompt Reference

Draw a spiral starting from point C, passing through points F, H, J, L, N, P, Q, S, T, V, H1, K1, E1, H1, J1, K1, L1, U1, V1, A2, B2, C2, D2, E2, to form a series of polygons, demonstrating the dynamic construction of the spiral.
The prompt above was compiled from the original drawing commands and is for reference only.