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Base X 减法演示机

Base X 减法演示机
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2020-04-16 23:59
函数解析几何几何作图
①本范例演示了在任意进制下进行减法运算的可视化过程，通过条形图清晰展示数位相减的过程与借位逻辑；②涉及的核心数学概念包括进制转换、自然数运算、条形图表示、函数与几何图形（如抛物线、椭圆、金字塔）；③作图要点提炼自构造摘要，主要运用了Join、Polygon、IndexOf、First、If、Shuffle、Random、Textfield、Point等GeoGebra命令与对象，用于动态生成和调整减法运算的展示；④适合初中及以上数学学习者，用于理解不同进制运算及数据可视化。

GeoGebra 命令及参数

  1. Join({x31N, x32N}) → rx3N
  2. Join({x31P, x32P}) → rx3P
  3. Join({x11N, x12N}) → rx1N
  4. Join({x11P, x12P}) → rx1P
  5. Join({x21N, x22N}) → rx2N
  6. Join({x21P, x22P}) → rx2P
  7. Polygon(I_3, J_3, K_3, L_3) → X31, a14, a16, a32, a29
  8. Polygon(L_3, M_3, N_3, K_3) → X21, a1, a27, a28, a3
  9. Polygon(M_3, P_3, O_3, N_3) → X11, a5, a25, a26, a7
  10. Polygon(P_3, Q_3, R_3, O_3) → X01, a9, a17, a24, a10
  11. Polygon(S_3, V_3, U_3, T_3) → X32, a23, a20, a21, a22
  12. Polygon(V_3, W_3, Z_3, U_3) → X22, a11, a19, a18, a12
  13. Polygon(W_3, B_4, A_4, Z_3) → X12, a13, a4, a2, a15
  14. Polygon(B_4, C_4, D_4, A_4) → X02, a31, a6, a8, a30
  15. Polygon(I_3, L_3, U_3, T_3) → Rx3, r11, r10, r9, r7
  16. Polygon(L_3, M_3, Z_3, U_3) → Rx2, r5, r4, r2, r3
  17. Polygon(M_3, P_3, A_4, Z_3) → Rx1, r6, r1, r14, r12
  18. Polygon(P_3, Q_3, D_4, A_4) → Rx0, r16, r15, r13, r8
  19. IndexOf(false, FP) → tmpI
  20. IndexOf(false, FN12) → NDtmpI
  21. First(x31P) → TAtmpI
  22. If(NDtmpI ≟ NDtmpI, true, false) → NDH
  23. If(Length[x31P] - Length[x31N] ≟ Element[Coef1, IndexOf["x^3", Order1]], true, false) → Bx31
  24. If(Length[x21P] - Length[x21N] ≟ Element[Coef1, IndexOf["x^2", Order1]], true, false) → Bx21
  25. If(Length[x11P] - Length[x11N] ≟ Element[Coef1, IndexOf["x", Order1]], true, false) → Bx11
  26. If(Length[x01P] - Length[x01N] ≟ Element[Coef1, IndexOf["", Order1]], true, false) → Bx01
  27. Shuffle({1, 2, 3, 4}) → OrderS, {3, 2, 1, 4}
  28. Random(-5, 5) → L23Co01
  29. Random(-5, 5) → L23Co02
  30. Random(-5, 5) → L23Co32
  31. Random(-5, 5) → L23Co31
  32. Random(-5, 5) → L23Co22
  33. Random(-5, 5) → L23Co21
  34. Random(-5, 5) → L23Co12
  35. Random(-5, 5) → L23Co11
  36. Join({x01N, x02N}) → rx0N
  37. Join({x01P, x02P}) → rx0P
  38. If(TAPP ≟ true ∧ TANN ≟ true, true, false) → TAPN
  39. First(rx0P) → tmpP
  40. First(rx0N) → tmpN
  41. If(Element[tmpP, 1] ≟ Element[tmpP, 1], true, false) → tP
  42. If(Element[tmpN, 1] ≟ Element[tmpN, 1], true, false) → tN
  43. Textfield(Br3) → Ir3
  44. Textfield(Br2) → Ir2
  45. Textfield(Br1) → Ir1
  46. Textfield(Br0) → Ir0
  47. Random(0, 5) → L1Co01
  48. Random(0, 5) → L1Co02
  49. Random(0, 5) → L1Co11
  50. Random(0, 5) → L1Co12
  51. Random(0, 5) → L1Co21
  52. Random(0, 5) → L1Co22
  53. Random(0, 5) → L1Co31
  54. Random(0, 5) → L1Co32
  55. Random(1, 2) → SignL1
  56. Polygon(A, B, C, D) → Background, a, b_1, c, d
  57. IndexOf(false, FP) → PDtmpI
  58. If(PDtmpI ≟ PDtmpI, true, false) → PDH
  59. Polygon(E, F, K, J) → X33, b1, b3, b4, b2
  60. Polygon(F, G, L, K) → X23, b5, b6, b7, b8
  61. Polygon(G, H, M, L) → X13, b9, b10, b11, b12
  62. Polygon(H, I, N, M) → X03, b13, b16, b15, b14
  63. If(Length[x33P] - Length[x33N] ≟ Element[Coef2, IndexOf["x^3", Order2]], true, false) → Bx33
  64. If(Length[x23P] - Length[x23N] ≟ Element[Coef2, IndexOf["x^2", Order2]], true, false) → Bx23
  65. If(Length[x13P] - Length[x13N] ≟ Element[Coef2, IndexOf["x", Order2]], true, false) → Bx13
  66. If(Length[x03P] - Length[x03N] ≟ Element[Coef2, IndexOf["", Order2]], true, false) → Bx03
  67. If(Length[x32P] - Length[x32N] ≟ (-Element[Coef2, IndexOf["x^3", Order2]]), true, false) → Bx32
  68. If(Length[x22P] - Length[x22N] ≟ (-Element[Coef2, IndexOf["x^2", Order2]]), true, false) → Bx22
  69. If(Length[x12P] - Length[x12N] ≟ (-Element[Coef2, IndexOf["x", Order2]]), true, false) → Bx12
  70. If(Length[x02P] - Length[x02N] ≟ (-Element[Coef2, IndexOf["", Order2]]), true, false) → Bx02
  71. Point(xAxis) → R
  72. Polygon(O, P, Q, R) → PolyP2a, o, p, q, r
  73. If(SelectedIndex[Level] ≟ 3 ∧ Stage ≟ 1, true, false) → BL3
  74. If(SelectedIndex[Level] ≟ 2 ∧ Stage ≟ 1, true, false) → BL2
  75. If(SelectedIndex[Level] ≟ 1 ∧ Stage ≟ 1, true, false) → BL1
  76. If(SelectedIndex[Level] ≟ 3, true, false) → BL3N
  77. If(SelectedIndex[Level] ≟ 2, true, false) → BL2N
  78. If(SelectedIndex[Level] ≟ 1, true, false) → BL1N
  79. If(x11P ≠ {}, true, false) → TAPH
  80. If(x11N ≠ {}, true, false) → TANH

AI 绘图提示语参考

画一个基于任意进制的减法机器，包括两个数的减法过程，通过条形图展示每一位的减法和借位逻辑。使用四个条形图表示两个数的每一位，通过条形图的长度差表示减法结果，使用多边形连接条形图的端点，展示借位过程。最后，使用文本框显示计算过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。