凸多边形对角线数量

凸多边形对角线数量
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2019-04-27 04:26
①本范例演示了如何动态计算凸多边形的对角线数量;②涉及的核心数学概念包括多边形、对角线、组合数学;③作图要点——使用了Polygon、DynamicCoordinates、Sequence、Segment、TableText等GeoGebra命令和对象;④适合高中数学教学,用于理解多边形性质和计算技巧。

GeoGebra 命令及参数

  1. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  2. Polygon({C5, C6, C7, C8, C9, C10, C11, C12, C13}) → H4
  3. Polygon({C19, C20, C21, C22, C23, C24, C25, C26}) → H18
  4. Polygon({C30, C31, C32, C33, C34, C35, C36}) → H29
  5. Polygon({C40, C41, C42, C43, C44, C45}) → H39
  6. Polygon({C65, C66, C67}) → H64
  7. Polygon({C58, C59, C60, C61}) → H57
  8. Polygon(C50, C51, C52, C53, C54) → H49, c50, c51, c52, c53, c54
  9. DynamicCoordinates(A5, If[D5, x(A5), x(C5)], If[D5, y(A5), y(C5)]) → B5
  10. DynamicCoordinates(A6, If[D6, x(A6), x(C6)], If[D6, y(A6), y(C6)]) → B6
  11. DynamicCoordinates(A7, If[D7, x(A7), x(C7)], If[D7, y(A7), y(C7)]) → B7
  12. DynamicCoordinates(A8, If[D8, x(A8), x(C8)], If[D8, y(A8), y(C8)]) → B8
  13. DynamicCoordinates(A9, If[D9, x(A9), x(C9)], If[D9, y(A9), y(C9)]) → B9
  14. DynamicCoordinates(A10, If[D10, x(A10), x(C10)], If[D10, y(A10), y(C10)]) → B10
  15. DynamicCoordinates(A11, If[D11, x(A11), x(C11)], If[D11, y(A11), y(C11)]) → B11
  16. DynamicCoordinates(A12, If[D12, x(A12), x(C12)], If[D12, y(A12), y(C12)]) → B12
  17. DynamicCoordinates(A13, If[D13, x(A13), x(C13)], If[D13, y(A13), y(C13)]) → B13
  18. DynamicCoordinates(A4, If[D4, x(A4), x(C4)], If[D4, y(A4), y(C4)]) → B4
  19. DynamicCoordinates(A18, If[D18, x(A18), x(C18)], If[D18, y(A18), y(C18)]) → B18
  20. DynamicCoordinates(A19, If[D19, x(A19), x(C19)], If[D19, y(A19), y(C19)]) → B19
  21. DynamicCoordinates(A20, If[D20, x(A20), x(C20)], If[D20, y(A20), y(C20)]) → B20
  22. DynamicCoordinates(A21, If[D21, x(A21), x(C21)], If[D21, y(A21), y(C21)]) → B21
  23. DynamicCoordinates(A22, If[D22, x(A22), x(C22)], If[D22, y(A22), y(C22)]) → B22
  24. DynamicCoordinates(A23, If[D23, x(A23), x(C23)], If[D23, y(A23), y(C23)]) → B23
  25. DynamicCoordinates(A24, If[D24, x(A24), x(C24)], If[D24, y(A24), y(C24)]) → B24
  26. DynamicCoordinates(A25, If[D25, x(A25), x(C25)], If[D25, y(A25), y(C25)]) → B25
  27. DynamicCoordinates(A26, If[D26, x(A26), x(C26)], If[D26, y(A26), y(C26)]) → B26
  28. Polygon(C18:C26) → G18
  29. DynamicCoordinates(A31, If[D31, x(A31), x(C31)], If[D31, y(A31), y(C31)]) → B31
  30. DynamicCoordinates(A32, If[D32, x(A32), x(C32)], If[D32, y(A32), y(C32)]) → B32
  31. DynamicCoordinates(A33, If[D33, x(A33), x(C33)], If[D33, y(A33), y(C33)]) → B33
  32. DynamicCoordinates(A29, If[D29, x(A29), x(C29)], If[D29, y(A29), y(C29)]) → B29
  33. DynamicCoordinates(A30, If[D30, x(A30), x(C30)], If[D30, y(A30), y(C30)]) → B30
  34. DynamicCoordinates(A34, If[D34, x(A34), x(C34)], If[D34, y(A34), y(C34)]) → B34
  35. DynamicCoordinates(A35, If[D35, x(A35), x(C35)], If[D35, y(A35), y(C35)]) → B35
  36. DynamicCoordinates(A36, If[D36, x(A36), x(C36)], If[D36, y(A36), y(C36)]) → B36
  37. Polygon(C29:C36) → G29
  38. DynamicCoordinates(A39, If[D39, x(A39), x(C39)], If[D39, y(A39), y(C39)]) → B39
  39. DynamicCoordinates(A40, If[D40, x(A40), x(C40)], If[D40, y(A40), y(C40)]) → B40
  40. DynamicCoordinates(A41, If[D41, x(A41), x(C41)], If[D41, y(A41), y(C41)]) → B41
  41. DynamicCoordinates(A42, If[D42, x(A42), x(C42)], If[D42, y(A42), y(C42)]) → B42
  42. DynamicCoordinates(A43, If[D43, x(A43), x(C43)], If[D43, y(A43), y(C43)]) → B43
  43. DynamicCoordinates(A44, If[D44, x(A44), x(C44)], If[D44, y(A44), y(C44)]) → B44
  44. DynamicCoordinates(A45, If[D45, x(A45), x(C45)], If[D45, y(A45), y(C45)]) → B45
  45. Polygon(C39:C45) → G39
  46. DynamicCoordinates(A49, If[D49, x(A49), x(C49)], If[D49, y(A49), y(C49)]) → B49
  47. DynamicCoordinates(A50, If[D50, x(A50), x(C50)], If[D50, y(A50), y(C50)]) → B50
  48. DynamicCoordinates(A51, If[D51, x(A51), x(C51)], If[D51, y(A51), y(C51)]) → B51
  49. DynamicCoordinates(A52, If[D52, x(A52), x(C52)], If[D52, y(A52), y(C52)]) → B52
  50. DynamicCoordinates(A53, If[D53, x(A53), x(C53)], If[D53, y(A53), y(C53)]) → B53
  51. Polygon(C49:C54) → G49
  52. DynamicCoordinates(A57, If[D57, x(A57), x(C57)], If[D57, y(A57), y(C57)]) → B57
  53. DynamicCoordinates(A58, If[D58, x(A58), x(C58)], If[D58, y(A58), y(C58)]) → B58
  54. DynamicCoordinates(A59, If[D59, x(A59), x(C59)], If[D59, y(A59), y(C59)]) → B59
  55. DynamicCoordinates(A60, If[D60, x(A60), x(C60)], If[D60, y(A60), y(C60)]) → B60
  56. DynamicCoordinates(A61, If[D61, x(A61), x(C61)], If[D61, y(A61), y(C61)]) → B61
  57. Polygon(C57:C61) → G57
  58. DynamicCoordinates(A64, If[D64, x(A64), x(C64)], If[D64, y(A64), y(C64)]) → B64
  59. DynamicCoordinates(A65, If[D65, x(A65), x(C65)], If[D65, y(A65), y(C65)]) → B65
  60. DynamicCoordinates(A66, If[D66, x(A66), x(C66)], If[D66, y(A66), y(C66)]) → B66
  61. DynamicCoordinates(A67, If[D67, x(A67), x(C67)], If[D67, y(A67), y(C67)]) → B67
  62. Polygon(C64:C67) → G64
  63. DynamicCoordinates(A54, If[D54, x(A54), x(C54)], If[D54, y(A54), y(C54)]) → B54
  64. Polygon({C4, C5, C6, C7, C8, C9, C10, C11, C12, C13}) → G4
  65. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col1, i]) * "}"), ("" * Element[col1, i])], i, 1, maxSides - 1) → col1Display
  66. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col2, i]) * "}"), Element[col2, i]], i, 1, maxSides - 1) → col2Display
  67. Segment(C64, C66) → F63
  68. TableText({col1Display, col2Display}, "vc|_") → dataTable