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Number of Diagonals in a Convex Polygon

Number of Diagonals in a Convex Polygon
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2019-04-27 04:26
PolygonGeometric Construction
This example demonstrates how to dynamically calculate the number of diagonals in a convex polygon. Key math concepts include polygons, diagonals, and combinatorial mathematics. Construction highlights involve commands like Polygon, DynamicCoordinates, Sequence, Segment, and TableText in GeoGebra. Suitable for high school mathematics education to understand polygon properties and calculation techniques.

GeoGebra Commands & Parameters

  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