帕斯卡三角行和求和模式

帕斯卡三角行和求和模式
几何画板及绘图内容加载中,请稍等……
2019-02-12 03:35
本范例演示帕斯卡三角的行和模式。涉及的核心数学概念包括数列和组合数学。通过使用GeoGebra命令如Sequence、Vector和Text,可以动态展示帕斯卡三角的生成过程及其行和的规律。适合高中一年级学生学习组合数学和数列的相关知识。

GeoGebra 命令及参数

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. Polygon(BLviewbox, (x(BLviewbox), y(TRviewbox)), TRviewbox, (x(TRviewbox), y(BLviewbox))) → viewbox, vb1, vb4, vb2, vb3
  4. Polygon(A, B, 6) → hexagon1, Aside_2, F, Aside_1, Aside_3, Aside_4, Aside_5, Aside_6, C, D, E
  5. Vector(A, E) → v
  6. Vector(F, B) → u
  7. Midpoint(F, C) → Center
  8. Sequence(Polygon[A + (A2 * u) + (i * v), B + (A2 * u) + (i * v), 6], i, 0, A2) → B2
  9. Sequence(Polygon[A + (A3 * u) + (i * v), B + (A3 * u) + (i * v), 6], i, 0, A3) → B3
  10. Sequence(Polygon[A + (A4 * u) + (i * v), B + (A4 * u) + (i * v), 6], i, 0, A4) → B4
  11. Sequence(Polygon[A + (A5 * u) + (i * v), B + (A5 * u) + (i * v), 6], i, 0, A5) → B5
  12. Sequence(Polygon[A + (A6 * u) + (i * v), B + (A6 * u) + (i * v), 6], i, 0, A6) → B6
  13. Sequence(Polygon[A + (A7 * u) + (i * v), B + (A7 * u) + (i * v), 6], i, 0, A7) → B7
  14. Sequence(Polygon[A + (A8 * u) + (i * v), B + (A8 * u) + (i * v), 6], i, 0, A8) → B8
  15. Sequence(Polygon[A + (A9 * u) + (i * v), B + (A9 * u) + (i * v), 6], i, 0, A9) → B9
  16. Sequence(nCr[A2, i], i, 0, A2) → D2
  17. Sequence(nCr[A3, i], i, 0, A3) → D3
  18. Sequence(nCr[A4, i], i, 0, A4) → D4
  19. Sequence(nCr[A5, i], i, 0, A5) → D5
  20. Sequence(nCr[A6, i], i, 0, A6) → D6
  21. Sequence(nCr[A7, i], i, 0, A7) → D7
  22. Sequence(nCr[A8, i], i, 0, A8) → D8
  23. Sequence(nCr[A9, i], i, 0, A9) → D9
  24. If(C2, ((("Row " * A2) * ": sum = ") * Sum[D2]), "") → F2
  25. If(C3, ((("Row " * A3) * ": sum = ") * Sum[D3]), "") → F3
  26. If(C4, ((("Row " * A4) * ": sum = ") * Sum[D4]), "") → F4
  27. If(C5, ((("Row " * A5) * ": sum = ") * Sum[D5]), "") → F5
  28. If(C6, ((("Row " * A6) * ": sum = ") * Sum[D6]), "") → F6
  29. If(C7, ((("Row " * A7) * ": sum = ") * Sum[D7]), "") → F7
  30. If(C8, ((("Row " * A8) * ": sum = ") * Sum[D8]), "") → F8
  31. If(C9, ((("Row " * A9) * ": sum = ") * Sum[D9]), "") → F9
  32. Sequence(Sequence[Polygon[A + (k * u) + (j * v), B + (k * u) + (j * v), 6], j, 0, k], k, 0, 7) → pascalOutline
  33. Text(F2, Center + ((A2 + 0.05) * u) + (Length[B2] * v)) → G2
  34. Text(F3, Center + ((A3 + 0.0500000000000002) * u) + (Length[B3] * v)) → G3
  35. Text(F4, Center + ((A4 + 0.0500000000000002) * u) + (Length[B4] * v)) → G4
  36. Text(F5, Center + ((A5 + 0.0500000000000002) * u) + (Length[B5] * v)) → G5
  37. Text(F6, Center + ((A6 + 0.0500000000000002) * u) + (Length[B6] * v)) → G6
  38. Text(F7, Center + ((A7 + 0.0500000000000002) * u) + (Length[B7] * v)) → G7
  39. Text(F8, Center + ((A8 + 0.0500000000000002) * u) + (Length[B8] * v)) → G8
  40. Text(F9, Center + ((A9 + 0.0500000000000002) * u) + (Length[B9] * v)) → G9
  41. Sequence(Text[Element[D2, i + 1], Center + (A2 * u) + (i * v) - (0.2 + ((Length[Text[Element[D2, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D2] - 1) → E2
  42. Sequence(Text[Element[D3, i + 1], Center + (A3 * u) + (i * v) - (0.2 + ((Length[Text[Element[D3, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D3] - 1) → E3
  43. Sequence(Text[Element[D4, i + 1], Center + (A4 * u) + (i * v) - (0.2 + ((Length[Text[Element[D4, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D4] - 1) → E4
  44. Sequence(Text[Element[D5, i + 1], Center + (A5 * u) + (i * v) - (0.2 + ((Length[Text[Element[D5, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D5] - 1) → E5
  45. Sequence(Text[Element[D6, i + 1], Center + (A6 * u) + (i * v) - (0.2 + ((Length[Text[Element[D6, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D6] - 1) → E6
  46. Sequence(Text[Element[D7, i + 1], Center + (A7 * u) + (i * v) - (0.2 + ((Length[Text[Element[D7, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D7] - 1) → E7
  47. Sequence(Text[Element[D8, i + 1], Center + (A8 * u) + (i * v) - (0.2 + ((Length[Text[Element[D8, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D8] - 1) → E8
  48. Sequence(Text[Element[D9, i + 1], Center + (A9 * u) + (i * v) - (0.2 + ((Length[Text[Element[D9, i + 1]]] - 1) * 0.2), 0.2)], i, 0, Length[D9] - 1) → E9
  49. Sequence((("SetValue(C" * i) * ",false)"), i, 2, 9) → cmdTurnOffAll
  50. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc

AI 绘图提示语参考

绘制帕斯卡三角形的行和行和的模式。首先,绘制一个六边形,然后使用向量和中点生成多个六边形,形成帕斯卡三角形的轮廓。接着,计算每个六边形的行数组合数,并在每个六边形内显示这些组合数。最后,显示每个六边形行数的和。
以上提示语为根据原始绘图命令整理而来,仅供参考。