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Rose and Lavender Oil Varying Proportionally

Rose and Lavender Oil Varying Proportionally
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2019-03-10 15:25
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the proportional relationship between rose and lavender oil. It involves key mathematical concepts such as proportion. Using GeoGebra commands like Intersect, Circle, and Line, the proportional changes can be visually represented. Suitable for middle school and above students to learn about proportion and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 0.5) → c
  3. Intersect(c, yAxis, 2) → B
  4. Intersect(c, yAxis, 1) → C
  5. Line(B, xAxis) → f
  6. Line(C, xAxis) → g
  7. Circle(B, 0.4) → d
  8. Circle(C, 0.4) → e
  9. Intersect(d, yAxis, 2) → D
  10. Intersect(e, yAxis, 1) → E
  11. Line(D, f) → h
  12. Line(E, g) → i
  13. Circle(E, a) → k
  14. Intersect(k, i, 2) → F
  15. Circle(F, a) → p
  16. Intersect(p, i, 2) → G
  17. Circle(G, a) → q
  18. Intersect(q, i, 2) → H
  19. Circle(H, a) → r
  20. Intersect(r, i, 2) → I
  21. Circle(I, a) → s
  22. Intersect(s, i, 2) → J
  23. Circle(J, a) → t
  24. Intersect(t, i, 2) → K
  25. Circle(K, a) → c_1
  26. Intersect(c_1, i, 2) → L
  27. Circle(L, a) → d_1
  28. Intersect(d_1, i, 2) → M
  29. OrthogonalLine(F, i) → j
  30. OrthogonalLine(G, i) → l
  31. OrthogonalLine(H, i) → m
  32. OrthogonalLine(I, i) → n
  33. OrthogonalLine(J, i) → b
  34. OrthogonalLine(K, i) → f_1
  35. OrthogonalLine(L, i) → g_1
  36. OrthogonalLine(M, i) → h_1
  37. Intersect(g, j) → N
  38. Intersect(f, j) → O
  39. Intersect(h, j) → P
  40. Intersect(g, l) → Q
  41. Intersect(g, m) → R
  42. Intersect(g, n) → S
  43. Intersect(g, b) → T
  44. Intersect(g, f_1) → U
  45. Intersect(g, g_1) → V
  46. Intersect(g, h_1) → W
  47. Intersect(f, l) → Z
  48. Intersect(h, l) → A_1
  49. Intersect(f, m) → B_1
  50. Intersect(h, m) → C_1
  51. Intersect(f, n) → D_1
  52. Intersect(h, n) → E_1
  53. Intersect(f, b) → F_1
  54. Intersect(h, b) → G_1
  55. Polygon(B, O, P, D) → q1, b_1, o, p_1, d_2
  56. Polygon(O, Z, A_1, P) → q2, o_1, z_1, a_1, p_2
  57. Polygon(Z, B_1, C_1, A_1) → q3, z_2, b_2, c_2, a_2
  58. Polygon(B_1, D_1, E_1, C_1) → q4, b_3, d_3, e_1, c_3
  59. Polygon(D_1, F_1, G_1, E_1) → q5, d_4, f_2, g_2, e_2
  60. Polygon(E, F, N, C) → q6, e_3, f_3, n_1, c_4
  61. Polygon(F, G, Q, N) → q7, f_4, g_3, q_1, n_2
  62. Polygon(G, H, R, Q) → q8, g_4, h_2, r_1, q_2
  63. Polygon(H, I, S, R) → q9, h_3, i_1, s_1, r_2
  64. Polygon(I, J, T, S) → q10, i_2, j_1, t_1, s_2
  65. Polygon(J, K, U, T) → q11, j_2, k_1, u, t_2
  66. Polygon(K, L, V, U) → q12, k_2, l_1, v, u_1
  67. Polygon(L, M, W, V) → q13, l_2, m_1, w, v_1

AI Drawing Prompt Reference

Draw a coordinate system with a circle centered at the origin with radius 0.5. Intersect this circle with the y-axis at y=1 and y=2, draw lines from these points to the x-axis, and create circles with radius 0.4 centered at these intersection points. Repeat this process, drawing lines and circles to show proportional relationships, creating a series of intersecting lines and concentric circles.
The prompt above was compiled from the original drawing commands and is for reference only.