Changing Quantities of Red and Blue Paint in a Fixed Ratio

Changing Quantities of Red and Blue Paint in a Fixed Ratio
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2020-01-14 22:20
This example demonstrates how the quantities of red and blue paint change under a fixed ratio. Key mathematical concepts include ratio and linear functions. Using GeoGebra commands such as Point, Intersect, Rotate, etc., you can dynamically adjust the ratio and observe the changes in paint quantities. Suitable for students at the junior high school level and above to learn about ratios and linear functions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Rotate(A, α, B) → A'
  4. Angle(A, B, A') → β
  5. Ray(B, A') → f
  6. OrthogonalLine(B, f) → g
  7. Circle(B, 0.7) → c
  8. Intersect(c, g, 2) → C
  9. Intersect(c, yAxis, 1) → D
  10. Circle(D, 0.5) → d
  11. Circle(C, 0.5) → e
  12. Intersect(e, g, 2) → E
  13. Intersect(d, yAxis, 1) → F
  14. Line(D, xAxis) → h
  15. Line(F, h) → i
  16. Line(C, f) → j
  17. Line(E, f) → k
  18. Circle(F, a) → p
  19. Circle(E, a) → q
  20. Intersect(p, i, 2) → G
  21. Intersect(q, k, 2) → H
  22. Circle(G, a) → r
  23. Intersect(r, i, 2) → I
  24. Circle(I, a) → s
  25. Intersect(s, i, 2) → J
  26. Circle(J, a) → t
  27. Intersect(t, i, 2) → K
  28. Circle(H, a) → c_1
  29. Intersect(c_1, k, 2) → L
  30. Circle(L, a) → d_1
  31. Intersect(d_1, k, 2) → M
  32. Circle(F, 0.3) → e_1
  33. Circle(E, 0.3) → f_1
  34. Intersect(e_1, yAxis, 1) → N
  35. Intersect(f_1, g, 2) → O
  36. Line(O, k) → l
  37. Line(N, i) → m
  38. Line(M, g) → n
  39. OrthogonalLine(K, i) → b
  40. Intersect(m, b) → P
  41. Intersect(l, n) → Q
  42. Intersect(j, n) → R
  43. Intersect(h, b) → S
  44. Line(L, n) → g_1
  45. Line(H, g_1) → h_1
  46. Line(J, b) → i_1
  47. Line(I, b) → j_1
  48. Line(G, b) → k_1
  49. Intersect(j, h_1) → T
  50. Intersect(j, g_1) → U
  51. Intersect(h, k_1) → V
  52. Intersect(h, j_1) → W
  53. Intersect(h, i_1) → Z
  54. Segment(N, P) → l_1
  55. Segment(O, Q) → m_1
  56. Polygon(F, G, V, D) → q1, f_2, g_2, v, d_2
  57. Polygon(G, I, W, V) → q2, g_3, i_2, w, v_1
  58. Polygon(I, J, Z, W) → q3, i_3, j_2, z_1, w_1
  59. Polygon(J, K, S, Z) → q4, j_3, k_2, s_1, z_2
  60. Polygon(C, T, H, E) → q5, c_2, t_1, h_2, e_2
  61. Polygon(T, U, L, H) → q6, t_2, u, l_2, h_3
  62. Polygon(U, R, M, L) → q7, u_1, r_1, m_2, l_3

AI Drawing Prompt Reference

Draw a coordinate system with a point on the x-axis and the origin at the intersection with the y-axis. Rotate the point around the origin by angle α to get a new point. Draw a circle centered at the origin and intersect it with the rotated line at two points. Create smaller circles centered at these points and intersect them with the line. Repeat this process to form multiple geometric shapes, connecting the centers and intersection points to show linear functions and ratio relationships.
The prompt above was compiled from the original drawing commands and is for reference only.