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Associative Geometric Forms

Associative Geometric Forms
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2020-03-13 16:13
PolygonCalculusOptimizationGeometric ConstructionGraphing
This GeoGebra example demonstrates the dynamic association of geometric forms, exploring the interplay between polygons, curves, and calculus concepts such as roots, surfaces, and differential calculus. It involves core ideas from linear programming and curve sketching, constructed using GeoGebra commands like Mod, If, Distance, Line, Point, and Segment. Dynamic objects and conditional logic illustrate how geometric constraints relate to optimization and root-finding, making it suitable for high school and higher education mathematics, particularly in calculus and optimization contexts.

GeoGebra Commands & Parameters

  1. Mod(Random[0, 100], 10) → aa
  2. If(aa ≟ 0, A, If[aa ≟ 1, B, If[aa ≟ 2, C, If[aa ≟ 3, D, If[aa ≟ 4, E, If[aa ≟ 5, F, If[aa ≟ 6, G, If[aa ≟ 7, H, If[aa ≟ 8, I, J]]]]]]]]) → M
  3. If(aa ≟ 0, B, If[aa ≟ 1, C, If[aa ≟ 2, D, If[aa ≟ 3, E, If[aa ≟ 4, F, If[aa ≟ 5, G, If[aa ≟ 6, H, If[aa ≟ 7, I, If[aa ≟ 8, J, A]]]]]]]]) → N
  4. If(aa ≟ 0, C, If[aa ≟ 1, D, If[aa ≟ 2, E, If[aa ≟ 3, F, If[aa ≟ 4, G, If[aa ≟ 5, H, If[aa ≟ 6, I, If[aa ≟ 7, J, If[aa ≟ 8, A, B]]]]]]]]) → K
  5. If(aa ≟ 0, D, If[aa ≟ 1, E, If[aa ≟ 2, F, If[aa ≟ 3, G, If[aa ≟ 4, H, If[aa ≟ 5, I, If[aa ≟ 6, J, If[aa ≟ 7, A, If[aa ≟ 8, B, C]]]]]]]]) → L
  6. If(aa ≟ 0, E, If[aa ≟ 1, F, If[aa ≟ 2, G, If[aa ≟ 3, H, If[aa ≟ 4, I, If[aa ≟ 5, J, If[aa ≟ 6, A, If[aa ≟ 7, B, If[aa ≟ 8, C, D]]]]]]]]) → O
  7. If(aa ≟ 0, F, If[aa ≟ 1, G, If[aa ≟ 2, H, If[aa ≟ 3, I, If[aa ≟ 4, J, If[aa ≟ 5, A, If[aa ≟ 6, B, If[aa ≟ 7, C, If[aa ≟ 8, D, E]]]]]]]]) → P
  8. If(aa ≟ 0, G, If[aa ≟ 1, H, If[aa ≟ 2, I, If[aa ≟ 3, J, If[aa ≟ 4, A, If[aa ≟ 5, B, If[aa ≟ 6, C, If[aa ≟ 7, D, If[aa ≟ 8, E, F]]]]]]]]) → Q
  9. If(aa ≟ 0, H, If[aa ≟ 1, I, If[aa ≟ 2, J, If[aa ≟ 3, A, If[aa ≟ 4, B, If[aa ≟ 5, C, If[aa ≟ 6, D, If[aa ≟ 7, E, If[aa ≟ 8, F, G]]]]]]]]) → R
  10. If(aa ≟ 0, I, If[aa ≟ 1, J, If[aa ≟ 2, A, If[aa ≟ 3, B, If[aa ≟ 4, C, If[aa ≟ 5, D, If[aa ≟ 6, E, If[aa ≟ 7, F, If[aa ≟ 8, G, H]]]]]]]]) → S
  11. If(aa ≟ 0, J, If[aa ≟ 1, A, If[aa ≟ 2, B, If[aa ≟ 3, C, If[aa ≟ 4, D, If[aa ≟ 5, E, If[aa ≟ 6, F, If[aa ≟ 7, G, If[aa ≟ 8, H, I]]]]]]]]) → T
  12. If(aa ≟ 0, BB, If[aa ≟ 1, CC, If[aa ≟ 2, DD, If[aa ≟ 3, EE, If[aa ≟ 4, FF, If[aa ≟ 5, GG, If[aa ≟ 6, HH, If[aa ≟ 7, II, If[aa ≟ 8, JJ, AA]]]]]]]]) → TT
  13. If(aa ≟ 0, CC, If[aa ≟ 1, DD, If[aa ≟ 2, EE, If[aa ≟ 3, FF, If[aa ≟ 4, GG, If[aa ≟ 5, HH, If[aa ≟ 6, II, If[aa ≟ 7, JJ, If[aa ≟ 8, AA, BB]]]]]]]]) → SS
  14. If(aa ≟ 0, DD, If[aa ≟ 1, EE, If[aa ≟ 2, FF, If[aa ≟ 3, GG, If[aa ≟ 4, HH, If[aa ≟ 5, II, If[aa ≟ 6, JJ, If[aa ≟ 7, AA, If[aa ≟ 8, BB, CC]]]]]]]]) → RR
  15. If(aa ≟ 0, EE, If[aa ≟ 1, FF, If[aa ≟ 2, GG, If[aa ≟ 3, HH, If[aa ≟ 4, II, If[aa ≟ 5, JJ, If[aa ≟ 6, AA, If[aa ≟ 7, BB, If[aa ≟ 8, CC, DD]]]]]]]]) → LL
  16. If(aa ≟ 0, FF, If[aa ≟ 1, GG, If[aa ≟ 2, HH, If[aa ≟ 3, II, If[aa ≟ 4, JJ, If[aa ≟ 5, AA, If[aa ≟ 6, BB, If[aa ≟ 7, CC, If[aa ≟ 8, DD, EE]]]]]]]]) → QQ
  17. If(aa ≟ 0, GG, If[aa ≟ 1, HH, If[aa ≟ 2, II, If[aa ≟ 3, JJ, If[aa ≟ 4, AA, If[aa ≟ 5, BB, If[aa ≟ 6, CC, If[aa ≟ 7, DD, If[aa ≟ 8, EE, FF]]]]]]]]) → KK
  18. If(aa ≟ 0, HH, If[aa ≟ 1, II, If[aa ≟ 2, JJ, If[aa ≟ 3, AA, If[aa ≟ 4, BB, If[aa ≟ 5, CC, If[aa ≟ 6, DD, If[aa ≟ 7, EE, If[aa ≟ 8, FF, GG]]]]]]]]) → OO
  19. If(aa ≟ 0, II, If[aa ≟ 1, JJ, If[aa ≟ 2, AA, If[aa ≟ 3, BB, If[aa ≟ 4, CC, If[aa ≟ 5, DD, If[aa ≟ 6, EE, If[aa ≟ 7, FF, If[aa ≟ 8, GG, HH]]]]]]]]) → NN
  20. If(aa ≟ 0, JJ, If[aa ≟ 1, AA, If[aa ≟ 2, BB, If[aa ≟ 3, CC, If[aa ≟ 4, DD, If[aa ≟ 5, EE, If[aa ≟ 6, FF, If[aa ≟ 7, GG, If[aa ≟ 8, HH, II]]]]]]]]) → PP
  21. If(aa ≟ 0, AA, If[aa ≟ 1, BB, If[aa ≟ 2, CC, If[aa ≟ 3, DD, If[aa ≟ 4, EE, If[aa ≟ 5, FF, If[aa ≟ 6, GG, If[aa ≟ 7, HH, If[aa ≟ 8, II, JJ]]]]]]]]) → MM
  22. Distance(M, MM) → mm
  23. Distance(N, NN) → nn
  24. Distance(L, LL) → ll
  25. Distance(O, OO) → oo
  26. Distance(P, PP) → pp
  27. Distance(Q, QQ) → qq
  28. Distance(R, RR) → rr
  29. Distance(S, SS) → ss
  30. Distance(K, KK) → kk
  31. Distance(T, TT) → tt
  32. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, 9) → res
  33. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, 8]) → resfin
  34. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, 6]]]) → f
  35. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 6, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 5, 4]]]]]) → g
  36. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 6, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 5, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 4, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 3, If[kk < 0.1 ∧ ll < 0.1 ∧ mm > 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 2, If[kk < 0.1 ∧ ll > 0.1 ∧ mm > 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 1, 0]]]]]]]]]) → gg
  37. Line(Z, A_1) → s
  38. If(kk < 0.1, 1, 0) → s1
  39. If(ll < 0.1, 1, 0) → s2
  40. If(mm < 0.1, 1, 0) → s3
  41. If(nn < 0.1, 1, 0) → s4
  42. If(oo < 0.1, 1, 0) → s5
  43. If(pp < 0.1, 1, 0) → s6
  44. If(qq < 0.1, 1, 0) → s7
  45. If(rr < 0.1, 1, 0) → s8
  46. If(ss < 0.1, 1, 0) → s9
  47. If(tt < 0.1, 1, 0) → s10
  48. Point(s) → C_1
  49. Segment(C_1, D_1) → b
  50. Text(If[d ≟ 1, "Rectangle", "Rectangle"]) → text40
  51. Text(If[d ≟ 1, "Diamond", "Losange"]) → texte41
  52. Text(If[d ≟ 1, "Pentagon", "Pentagone"]) → Texte50
  53. Text(If[d ≟ 1, "Circle", "Cercle"]) → texte51
  54. Text(If[d ≟ 1, "Semi circle", "Demi-cercle"]) → Texte52
  55. Text(If[d ≟ 1, "Octogon", "Octogone"]) → Texte53
  56. Text(If[d ≟ 1, "Square", "Carré"]) → Texte54
  57. Text(If[d ≟ 1, "Hexagon", "Hexagone"]) → Texte55
  58. Text(If[d ≟ 1, "Trapeze", "Trapèze"]) → Texte56
  59. If(d ≟ 1, "Associate objects on the right with objects on the left", "Associer les objets de droite aux objets de gauche") → Text60
  60. If(d ≟ 1, "Move the green dots on the red dots", "Déplacer les points verts sur les points rouges") → texte61

AI Drawing Prompt Reference

Create a dynamic geometric figure with two sets of ten points each, arranged as two polygons. Use a random number to determine the correspondence between points, then calculate distances between matched points. Based on whether these distances are below a threshold, progressively evaluate and display a score from 0 to 10. Include a line with a point on it to illustrate the relationship between geometric constraints and optimization. The construction emphasizes interactions among points, lines, polygons, and conditional logic.
The prompt above was compiled from the original drawing commands and is for reference only.