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凸多边形外角

凸多边形外角
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2019-04-25 01:11
多边形角几何作图
①本范例演示凸多边形外角的性质与计算；②涉及核心概念包括外角和定理、多边形内角与外角关系；③构造要点：使用Segment、Polygon、DynamicCoordinates、Sequence、Angle、Sum、TableText等命令绘制多边形并计算外角和；④适合高中数学教学，用于理解多边形几何性质和函数应用。

GeoGebra 命令及参数

  1. Segment(C39, E39) → F39
  2. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  3. DynamicCoordinates(A5, If[D5, x(A5), x(C5)], If[D5, y(A5), y(C5)]) → B5
  4. DynamicCoordinates(A6, If[D6, x(A6), x(C6)], If[D6, y(A6), y(C6)]) → B6
  5. DynamicCoordinates(A7, If[D7, x(A7), x(C7)], If[D7, y(A7), y(C7)]) → B7
  6. DynamicCoordinates(A8, If[D8, x(A8), x(C8)], If[D8, y(A8), y(C8)]) → B8
  7. DynamicCoordinates(A9, If[D9, x(A9), x(C9)], If[D9, y(A9), y(C9)]) → B9
  8. DynamicCoordinates(A10, If[D10, x(A10), x(C10)], If[D10, y(A10), y(C10)]) → B10
  9. DynamicCoordinates(A11, If[D11, x(A11), x(C11)], If[D11, y(A11), y(C11)]) → B11
  10. DynamicCoordinates(A12, If[D12, x(A12), x(C12)], If[D12, y(A12), y(C12)]) → B12
  11. DynamicCoordinates(A13, If[D13, x(A13), x(C13)], If[D13, y(A13), y(C13)]) → B13
  12. DynamicCoordinates(A4, If[D4, x(A4), x(C4)], If[D4, y(A4), y(C4)]) → B4
  13. DynamicCoordinates(A18, If[D18, x(A18), x(C18)], If[D18, y(A18), y(C18)]) → B18
  14. DynamicCoordinates(A19, If[D19, x(A19), x(C19)], If[D19, y(A19), y(C19)]) → B19
  15. DynamicCoordinates(A20, If[D20, x(A20), x(C20)], If[D20, y(A20), y(C20)]) → B20
  16. DynamicCoordinates(A21, If[D21, x(A21), x(C21)], If[D21, y(A21), y(C21)]) → B21
  17. DynamicCoordinates(A22, If[D22, x(A22), x(C22)], If[D22, y(A22), y(C22)]) → B22
  18. DynamicCoordinates(A23, If[D23, x(A23), x(C23)], If[D23, y(A23), y(C23)]) → B23
  19. DynamicCoordinates(A24, If[D24, x(A24), x(C24)], If[D24, y(A24), y(C24)]) → B24
  20. DynamicCoordinates(A25, If[D25, x(A25), x(C25)], If[D25, y(A25), y(C25)]) → B25
  21. DynamicCoordinates(A26, If[D26, x(A26), x(C26)], If[D26, y(A26), y(C26)]) → B26
  22. DynamicCoordinates(A31, If[D31, x(A31), x(C31)], If[D31, y(A31), y(C31)]) → B31
  23. DynamicCoordinates(A32, If[D32, x(A32), x(C32)], If[D32, y(A32), y(C32)]) → B32
  24. DynamicCoordinates(A33, If[D33, x(A33), x(C33)], If[D33, y(A33), y(C33)]) → B33
  25. DynamicCoordinates(A29, If[D29, x(A29), x(C29)], If[D29, y(A29), y(C29)]) → B29
  26. DynamicCoordinates(A30, If[D30, x(A30), x(C30)], If[D30, y(A30), y(C30)]) → B30
  27. DynamicCoordinates(A34, If[D34, x(A34), x(C34)], If[D34, y(A34), y(C34)]) → B34
  28. DynamicCoordinates(A35, If[D35, x(A35), x(C35)], If[D35, y(A35), y(C35)]) → B35
  29. DynamicCoordinates(A36, If[D36, x(A36), x(C36)], If[D36, y(A36), y(C36)]) → B36
  30. DynamicCoordinates(A39, If[D39, x(A39), x(C39)], If[D39, y(A39), y(C39)]) → B39
  31. DynamicCoordinates(A40, If[D40, x(A40), x(C40)], If[D40, y(A40), y(C40)]) → B40
  32. DynamicCoordinates(A41, If[D41, x(A41), x(C41)], If[D41, y(A41), y(C41)]) → B41
  33. DynamicCoordinates(A42, If[D42, x(A42), x(C42)], If[D42, y(A42), y(C42)]) → B42
  34. DynamicCoordinates(A43, If[D43, x(A43), x(C43)], If[D43, y(A43), y(C43)]) → B43
  35. DynamicCoordinates(A44, If[D44, x(A44), x(C44)], If[D44, y(A44), y(C44)]) → B44
  36. DynamicCoordinates(A45, If[D45, x(A45), x(C45)], If[D45, y(A45), y(C45)]) → B45
  37. DynamicCoordinates(A49, If[D49, x(A49), x(C49)], If[D49, y(A49), y(C49)]) → B49
  38. DynamicCoordinates(A50, If[D50, x(A50), x(C50)], If[D50, y(A50), y(C50)]) → B50
  39. DynamicCoordinates(A51, If[D51, x(A51), x(C51)], If[D51, y(A51), y(C51)]) → B51
  40. DynamicCoordinates(A52, If[D52, x(A52), x(C52)], If[D52, y(A52), y(C52)]) → B52
  41. DynamicCoordinates(A53, If[D53, x(A53), x(C53)], If[D53, y(A53), y(C53)]) → B53
  42. DynamicCoordinates(A57, If[D57, x(A57), x(C57)], If[D57, y(A57), y(C57)]) → B57
  43. DynamicCoordinates(A58, If[D58, x(A58), x(C58)], If[D58, y(A58), y(C58)]) → B58
  44. DynamicCoordinates(A59, If[D59, x(A59), x(C59)], If[D59, y(A59), y(C59)]) → B59
  45. DynamicCoordinates(A60, If[D60, x(A60), x(C60)], If[D60, y(A60), y(C60)]) → B60
  46. DynamicCoordinates(A61, If[D61, x(A61), x(C61)], If[D61, y(A61), y(C61)]) → B61
  47. DynamicCoordinates(A64, If[D64, x(A64), x(C64)], If[D64, y(A64), y(C64)]) → B64
  48. DynamicCoordinates(A65, If[D65, x(A65), x(C65)], If[D65, y(A65), y(C65)]) → B65
  49. DynamicCoordinates(A66, If[D66, x(A66), x(C66)], If[D66, y(A66), y(C66)]) → B66
  50. DynamicCoordinates(A67, If[D67, x(A67), x(C67)], If[D67, y(A67), y(C67)]) → B67
  51. DynamicCoordinates(A54, If[D54, x(A54), x(C54)], If[D54, y(A54), y(C54)]) → B54
  52. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col1, i]) * "}"), ("" * Element[col1, i])], i, 1, maxSides - 1) → col1Display
  53. Sequence(If[i ≟ numSides - 1, (("\cellcolor{#fff59d}{" * Element[col2, i]) * "}"), Element[col2, i]], i, 1, maxSides - 1) → col2Display
  54. Segment(C4, E4) → F4
  55. Segment(C5, E5) → F5
  56. Segment(C6, E6) → F6
  57. Segment(C7, E7) → F7
  58. Segment(C8, E8) → F8
  59. Segment(C9, E9) → F9
  60. Segment(C10, E10) → F10
  61. Segment(C11, E11) → F11
  62. Segment(C12, E12) → F12
  63. Segment(C13, E13) → F13
  64. Polygon({C4, C5, C6, C7, C8, C9, C10, C11, C12, C13}) → B3
  65. Angle(E4, C4, C5) → G4
  66. Angle(E5, C5, C6) → G5
  67. Angle(E6, C6, C7) → G6
  68. Angle(E7, C7, C8) → G7
  69. Angle(E8, C8, C9) → G8
  70. Angle(E9, C9, C10) → G9
  71. Angle(E10, C10, C11) → G10
  72. Angle(E11, C11, C12) → G11
  73. Angle(E12, C12, C13) → G12
  74. Angle(E13, C13, C4) → G13
  75. Segment(C18, E18) → F18
  76. Segment(C19, E19) → F19
  77. Segment(C20, E20) → F20
  78. Segment(C21, E21) → F21
  79. Segment(C22, E22) → F22
  80. Segment(C23, E23) → F23
  81. Segment(C24, E24) → F24
  82. Segment(C25, E25) → F25
  83. Segment(C26, E26) → F26
  84. Polygon(C18:C26) → B17
  85. Angle(E18, C18, C19) → G18
  86. Angle(E19, C19, C20) → G19
  87. Angle(E20, C20, C21) → G20
  88. Angle(E21, C21, C22) → G21
  89. Angle(E22, C22, C23) → G22
  90. Angle(E23, C23, C24) → G23
  91. Angle(E24, C24, C25) → G24
  92. Angle(E25, C25, C26) → G25
  93. Angle(E26, C26, C18) → G26
  94. Polygon(C29:C36) → B28
  95. Segment(C29, E29) → F29
  96. Segment(C30, E30) → F30
  97. Segment(C31, E31) → F31
  98. Segment(C32, E32) → F32
  99. Segment(C33, E33) → F33
  100. Segment(C34, E34) → F34
  101. Segment(C35, E35) → F35
  102. Segment(C36, E36) → F36
  103. Angle(E30, C30, C31) → G30
  104. Angle(E31, C31, C32) → G31
  105. Angle(E32, C32, C33) → G32
  106. Angle(E33, C33, C34) → G33
  107. Angle(E34, C34, C35) → G34
  108. Angle(E35, C35, C36) → G35
  109. Angle(E36, C36, C29) → G36
  110. Angle(E29, C29, C30) → G29
  111. Polygon(C39:C45) → B38
  112. Segment(C40, E40) → F40
  113. Segment(C41, E41) → F41
  114. Segment(C42, E42) → F42
  115. Segment(C43, E43) → F43
  116. Segment(C44, E44) → F44
  117. Segment(C45, E45) → F45
  118. Angle(E39, C39, C40) → G39
  119. Angle(E40, C40, C41) → G40
  120. Angle(E41, C41, C42) → G41
  121. Angle(E42, C42, C43) → G42
  122. Angle(E43, C43, C44) → G43
  123. Angle(E44, C44, C45) → G44
  124. Angle(E45, C45, C39) → G45
  125. Sum(H29:H34) → test
  126. Polygon(C49:C54) → B48
  127. Segment(C49, E49) → F49
  128. Segment(C50, E50) → F50
  129. Segment(C51, E51) → F51
  130. Segment(C52, E52) → F52
  131. Segment(C53, E53) → F53
  132. Segment(C54, E54) → F54
  133. Angle(E49, C49, C50) → G49
  134. Angle(E50, C50, C51) → G50
  135. Angle(E51, C51, C52) → G51
  136. Angle(E52, C52, C53) → G52
  137. Angle(E53, C53, C54) → G53
  138. Angle(E54, C54, C49) → G54
  139. Polygon(C57:C61) → B56
  140. Segment(C57, E57) → F57
  141. Segment(C58, E58) → F58
  142. Segment(C59, E59) → F59
  143. Segment(C60, E60) → F60
  144. Segment(C61, E61) → F61
  145. Angle(E57, C57, C58) → G57
  146. Angle(E58, C58, C59) → G58
  147. Angle(E59, C59, C60) → G59
  148. Angle(E60, C60, C61) → G60
  149. Angle(E61, C61, C57) → G61
  150. Polygon(C64:C67) → B63
  151. Segment(C64, E64) → F64
  152. Segment(C65, E65) → F65
  153. Segment(C66, E66) → F66
  154. Segment(C67, E67) → F67
  155. Angle(E64, C64, C65) → G64
  156. Angle(E65, C65, C66) → G65
  157. Angle(E66, C66, C67) → G66
  158. Angle(E67, C67, C64) → G67
  159. TableText({col1Display, col2Display}, "vc|_") → dataTable

AI 绘图提示语参考

请绘制一个凸多边形，并展示其外角和。图形应包含多边形本身、各个顶点、连接这些顶点的边，以及每个顶点处的外角。构造顺序为：先画一条线段作为参考，然后根据动态坐标生成多边形的顶点，最后将这些顶点连接形成多边形，并标注外角。确保图形清晰，便于理解外角与内角的关系及外角和定理的应用。
以上提示语为根据原始绘图命令整理而来，仅供参考。