MathPlotAI Logo MathPlotAI

Plastic Ratio Calipers

Plastic Ratio Calipers
Loading the math board and drawing, please wait…
2019-03-16 10:44
TransformationGeometric Construction
This is a caliper model designed to measure the plastic ratio. Through geometric construction, we can intuitively understand the concept of ratio. The core mathematical concepts involved include ratio, similarity transformation, and geometric construction. Using GeoGebra commands such as Circle, Point, Segment, Intersect, Line, Midpoint, and Distance, an accurate caliper model can be constructed. Suitable for high school mathematics education and learning about ratio concepts.

GeoGebra Commands & Parameters

  1. Circle(A, 10) → c
  2. Point(c) → B
  3. Point(c) → C
  4. Segment(A, B) → f
  5. Segment(A, C) → g
  6. Point(Circle[B, 4.0795]) → D_2
  7. Circle(A, 2.4513) → p
  8. Circle(A, 5.6985) → q
  9. Intersect(p, g, 1) → G_2
  10. Intersect(q, g, 1) → H_2
  11. Line(G_2, f) → i
  12. Line(H_2, i) → j
  13. Circle(H_2, 2.1508) → r
  14. Intersect(r, j, 2) → I
  15. Line(I, g) → l
  16. Intersect(i, l) → J_2
  17. Midpoint(A, B) → K_2
  18. Line(K_2, l) → m
  19. Intersect(i, m) → L_2
  20. Segment(B, C) → h
  21. Intersect(i, h) → D
  22. Intersect(j, h) → E
  23. Segment(H_2, E) → k
  24. Segment(G_2, D) → n
  25. Segment(J_2, I) → s
  26. Segment(K_2, L_2) → t
  27. Circle(G, 10) → c_1
  28. Point(c_1) → H
  29. Point(c_1) → J
  30. Segment(G, H) → f_1
  31. Segment(G, J) → g_1
  32. Point(Circle[H, 4.0795]) → D_1
  33. Circle(G, 2.4513) → p_1
  34. Circle(G, 5.6985) → q_1
  35. Intersect(p_1, g_1, 1) → G_1
  36. Intersect(q_1, g_1, 1) → H_1
  37. Line(G_1, f_1) → i_1
  38. Line(H_1, i_1) → j_1
  39. Circle(H_1, 2.1508) → r_1
  40. Intersect(r_1, j_1, 2) → I_1
  41. Line(I_1, g_1) → l_1
  42. Intersect(i_1, l_1) → J_1
  43. Midpoint(G, H) → K_1
  44. Line(K_1, l_1) → m_1
  45. Intersect(i_1, m_1) → L_1
  46. Segment(H, J) → h_1
  47. Intersect(i_1, h_1) → K
  48. Intersect(j_1, h_1) → L
  49. Segment(H_1, L) → k_1
  50. Segment(G_1, K) → n_1
  51. Segment(J_1, I_1) → s_1
  52. Segment(K_1, L_1) → t_1
  53. Segment(B, D) → e_1
  54. Segment(D, E) → f_2
  55. Segment(E, C) → g_2
  56. Segment(H, K) → h_2
  57. Segment(K, L) → i_2
  58. Segment(L, J) → j_2
  59. Distance(D, E) → DE
  60. Distance(B, D) → BE
  61. Distance(E, C) → EC
  62. Distance(H, K) → HK
  63. Distance(L, K) → KL
  64. Distance(L, J) → LJ

AI Drawing Prompt Reference

Create a caliper model to understand the concept of ratio through geometric construction. Start by drawing two circles with point A as the center, then get points B and C. Construct line segments AB and AC. Use circles and line segments to find other key points and segments, such as f, g, h, i, and j, and their relationships to form the caliper model.
The prompt above was compiled from the original drawing commands and is for reference only.