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整数乘法几何模型

整数乘法几何模型
几何画板及绘图内容加载中，请稍等……
2017-02-08 19:38
测试改名0多边形解析几何
该范例通过几何图形展示了整数乘法的概念。它利用矩形面积来直观地表示两个整数相乘的结果。通过调整矩形的长和宽，可以观察到乘积的变化。此模型涉及的核心数学概念包括几何构造、面积计算和整数乘法。使用了Polygon、Textfield、Circle等GeoGebra命令进行图形的构建。适合小学高年级和初中学生学习整数乘法和几何图形的关系。

GeoGebra 命令及参数

  1. Polygon(A_1, B, 4) → poly1, c, d, e, f, C, D
  2. Polygon(A_2, B_1, 4) → poly1_1, c_1, d_1, e_1, f_1, C_2, D_1
  3. Polygon(A_4, B_2, 4) → poly1_2, c_2, d_2, e_2, f_2, C_3, D_2
  4. Polygon(A_5, B_3, 4) → poly1_3, c_3, d_3, e_3, f_3, C_4, D_3
  5. Polygon(A_6, B_4, 4) → poly1_4, c_4, d_4, e_4, f_4, C_5, D_4
  6. Polygon(A_{11}, B_9, 4) → poly1_5, c_9, d_9, e_9, f_9, C_{10}, D_9
  7. Polygon(A_{10}, B_8, 4) → poly1_6, c_8, d_8, e_8, f_8, C_9, D_8
  8. Polygon(A_9, B_7, 4) → poly1_7, c_7, d_7, e_7, f_7, C_8, D_7
  9. Polygon(A_8, B_6, 4) → poly1_8, c_6, d_6, e_6, f_6, C_7, D_6
  10. Polygon(A_7, B_5, 4) → poly1_9, c_5, d_5, e_5, f_5, C_6, D_5
  11. Polygon(A_{22}, B_{19}, 4) → poly1_{10}, c_{19}, d_{19}, e_{19}, f_{19}, C_{21}, D_{19}
  12. Polygon(A_{21}, B_{18}, 4) → poly1_{11}, c_{18}, d_{18}, e_{18}, f_{18}, C_{20}, D_{18}
  13. Polygon(A_{20}, B_{17}, 4) → poly1_{12}, c_{17}, d_{17}, e_{17}, f_{17}, C_{19}, D_{17}
  14. Polygon(A_{19}, B_{16}, 4) → poly1_{13}, c_{16}, d_{16}, e_{16}, f_{16}, C_{18}, D_{16}
  15. Polygon(A_{18}, B_{15}, 4) → poly1_{14}, c_{15}, d_{15}, e_{15}, f_{15}, C_{17}, D_{15}
  16. Polygon(A_{17}, B_{14}, 4) → poly1_{15}, c_{14}, d_{14}, e_{14}, f_{14}, C_{16}, D_{14}
  17. Polygon(A_{16}, B_{13}, 4) → poly1_{16}, c_{13}, d_{13}, e_{13}, f_{13}, C_{15}, D_{13}
  18. Polygon(A_{15}, B_{12}, 4) → poly1_{17}, c_{12}, d_{12}, e_{12}, f_{12}, C_{14}, D_{12}
  19. Polygon(A_{14}, B_{11}, 4) → poly1_{18}, c_{11}, d_{11}, e_{11}, f_{11}, C_{13}, D_{11}
  20. Polygon(A_{13}, B_{10}, 4) → poly1_{19}, c_{10}, d_{10}, e_{10}, f_{10}, C_{12}, D_{10}
  21. Polygon(A_{29}, B_{24}, 4) → poly1_{20}, c_{24}, d_{24}, e_{24}, f_{24}, C_{28}, D_{24}
  22. Polygon(A_{28}, B_{23}, 4) → poly1_{21}, c_{23}, d_{23}, e_{23}, f_{23}, C_{27}, D_{23}
  23. Polygon(A_{27}, B_{22}, 4) → poly1_{22}, c_{22}, d_{22}, e_{22}, f_{22}, C_{26}, D_{22}
  24. Polygon(A_{26}, B_{21}, 4) → poly1_{23}, c_{21}, d_{21}, e_{21}, f_{21}, C_{25}, D_{21}
  25. Polygon(A_{25}, B_{20}, 4) → poly1_{24}, c_{20}, d_{20}, e_{20}, f_{20}, C_{24}, D_{20}
  26. Polygon(A_{55}, B_{49}, 4) → poly1_{25}, c_{49}, d_{49}, e_{49}, f_{49}, C_{54}, D_{49}
  27. Polygon(A_{54}, B_{48}, 4) → poly1_{26}, c_{48}, d_{48}, e_{48}, f_{48}, C_{53}, D_{48}
  28. Polygon(A_{53}, B_{47}, 4) → poly1_{27}, c_{47}, d_{47}, e_{47}, f_{47}, C_{52}, D_{47}
  29. Polygon(A_{52}, B_{46}, 4) → poly1_{28}, c_{46}, d_{46}, e_{46}, f_{46}, C_{51}, D_{46}
  30. Polygon(A_{51}, B_{45}, 4) → poly1_{29}, c_{45}, d_{45}, e_{45}, f_{45}, C_{50}, D_{45}
  31. Polygon(A_{50}, B_{44}, 4) → poly1_{30}, c_{44}, d_{44}, e_{44}, f_{44}, C_{49}, D_{44}
  32. Polygon(A_{49}, B_{43}, 4) → poly1_{31}, c_{43}, d_{43}, e_{43}, f_{43}, C_{48}, D_{43}
  33. Polygon(A_{48}, B_{42}, 4) → poly1_{32}, c_{42}, d_{42}, e_{42}, f_{42}, C_{47}, D_{42}
  34. Polygon(A_{47}, B_{41}, 4) → poly1_{33}, c_{41}, d_{41}, e_{41}, f_{41}, C_{46}, D_{41}
  35. Polygon(A_{46}, B_{40}, 4) → poly1_{34}, c_{40}, d_{40}, e_{40}, f_{40}, C_{45}, D_{40}
  36. Polygon(A_{45}, B_{39}, 4) → poly1_{35}, c_{39}, d_{39}, e_{39}, f_{39}, C_{44}, D_{39}
  37. Polygon(A_{44}, B_{38}, 4) → poly1_{36}, c_{38}, d_{38}, e_{38}, f_{38}, C_{43}, D_{38}
  38. Polygon(A_{43}, B_{37}, 4) → poly1_{37}, c_{37}, d_{37}, e_{37}, f_{37}, C_{42}, D_{37}
  39. Polygon(A_{42}, B_{36}, 4) → poly1_{38}, c_{36}, d_{36}, e_{36}, f_{36}, C_{41}, D_{36}
  40. Polygon(A_{41}, B_{35}, 4) → poly1_{39}, c_{35}, d_{35}, e_{35}, f_{35}, C_{40}, D_{35}
  41. Polygon(A_{40}, B_{34}, 4) → poly1_{40}, c_{34}, d_{34}, e_{34}, f_{34}, C_{39}, D_{34}
  42. Polygon(A_{39}, B_{33}, 4) → poly1_{41}, c_{33}, d_{33}, e_{33}, f_{33}, C_{38}, D_{33}
  43. Polygon(A_{38}, B_{32}, 4) → poly1_{42}, c_{32}, d_{32}, e_{32}, f_{32}, C_{37}, D_{32}
  44. Polygon(A_{37}, B_{31}, 4) → poly1_{43}, c_{31}, d_{31}, e_{31}, f_{31}, C_{36}, D_{31}
  45. Polygon(A_{36}, B_{30}, 4) → poly1_{44}, c_{30}, d_{30}, e_{30}, f_{30}, C_{35}, D_{30}
  46. Polygon(A_{35}, B_{29}, 4) → poly1_{45}, c_{29}, d_{29}, e_{29}, f_{29}, C_{34}, D_{29}
  47. Polygon(A_{34}, B_{28}, 4) → poly1_{46}, c_{28}, d_{28}, e_{28}, f_{28}, C_{33}, D_{28}
  48. Polygon(A_{33}, B_{27}, 4) → poly1_{47}, c_{27}, d_{27}, e_{27}, f_{27}, C_{32}, D_{27}
  49. Polygon(A_{32}, B_{26}, 4) → poly1_{48}, c_{26}, d_{26}, e_{26}, f_{26}, C_{31}, D_{26}
  50. Polygon(A_{31}, B_{25}, 4) → poly1_{49}, c_{25}, d_{25}, e_{25}, f_{25}, C_{30}, D_{25}
  51. Polygon(A_{110}, B_{99}, 4) → poly1_{50}, c_{99}, d_{99}, e_{99}, f_{99}, C_{109}, D_{99}
  52. Polygon(A_{109}, B_{98}, 4) → poly1_{51}, c_{98}, d_{98}, e_{98}, f_{98}, C_{108}, D_{98}
  53. Polygon(A_{108}, B_{97}, 4) → poly1_{52}, c_{97}, d_{97}, e_{97}, f_{97}, C_{107}, D_{97}
  54. Polygon(A_{107}, B_{96}, 4) → poly1_{53}, c_{96}, d_{96}, e_{96}, f_{96}, C_{106}, D_{96}
  55. Polygon(A_{106}, B_{95}, 4) → poly1_{54}, c_{95}, d_{95}, e_{95}, f_{95}, C_{105}, D_{95}
  56. Polygon(A_{105}, B_{94}, 4) → poly1_{55}, c_{94}, d_{94}, e_{94}, f_{94}, C_{104}, D_{94}
  57. Polygon(A_{104}, B_{93}, 4) → poly1_{56}, c_{93}, d_{93}, e_{93}, f_{93}, C_{103}, D_{93}
  58. Polygon(A_{103}, B_{92}, 4) → poly1_{57}, c_{92}, d_{92}, e_{92}, f_{92}, C_{102}, D_{92}
  59. Polygon(A_{102}, B_{91}, 4) → poly1_{58}, c_{91}, d_{91}, e_{91}, f_{91}, C_{101}, D_{91}
  60. Polygon(A_{101}, B_{90}, 4) → poly1_{59}, c_{90}, d_{90}, e_{90}, f_{90}, C_{100}, D_{90}
  61. Polygon(A_{100}, B_{89}, 4) → poly1_{60}, c_{89}, d_{89}, e_{89}, f_{89}, C_{99}, D_{89}
  62. Polygon(A_{99}, B_{88}, 4) → poly1_{61}, c_{88}, d_{88}, e_{88}, f_{88}, C_{98}, D_{88}
  63. Polygon(A_{98}, B_{87}, 4) → poly1_{62}, c_{87}, d_{87}, e_{87}, f_{87}, C_{97}, D_{87}
  64. Polygon(A_{97}, B_{86}, 4) → poly1_{63}, c_{86}, d_{86}, e_{86}, f_{86}, C_{96}, D_{86}
  65. Polygon(A_{96}, B_{85}, 4) → poly1_{64}, c_{85}, d_{85}, e_{85}, f_{85}, C_{95}, D_{85}
  66. Polygon(A_{95}, B_{84}, 4) → poly1_{65}, c_{84}, d_{84}, e_{84}, f_{84}, C_{94}, D_{84}
  67. Polygon(A_{94}, B_{83}, 4) → poly1_{66}, c_{83}, d_{83}, e_{83}, f_{83}, C_{93}, D_{83}
  68. Polygon(A_{93}, B_{82}, 4) → poly1_{67}, c_{82}, d_{82}, e_{82}, f_{82}, C_{92}, D_{82}
  69. Polygon(A_{92}, B_{81}, 4) → poly1_{68}, c_{81}, d_{81}, e_{81}, f_{81}, C_{91}, D_{81}
  70. Polygon(A_{91}, B_{80}, 4) → poly1_{69}, c_{80}, d_{80}, e_{80}, f_{80}, C_{90}, D_{80}
  71. Polygon(A_{90}, B_{79}, 4) → poly1_{70}, c_{79}, d_{79}, e_{79}, f_{79}, C_{89}, D_{79}
  72. Polygon(A_{89}, B_{78}, 4) → poly1_{71}, c_{78}, d_{78}, e_{78}, f_{78}, C_{88}, D_{78}
  73. Polygon(A_{88}, B_{77}, 4) → poly1_{72}, c_{77}, d_{77}, e_{77}, f_{77}, C_{87}, D_{77}
  74. Polygon(A_{87}, B_{76}, 4) → poly1_{73}, c_{76}, d_{76}, e_{76}, f_{76}, C_{86}, D_{76}
  75. Polygon(A_{86}, B_{75}, 4) → poly1_{74}, c_{75}, d_{75}, e_{75}, f_{75}, C_{85}, D_{75}
  76. Polygon(A_{85}, B_{74}, 4) → poly1_{75}, c_{74}, d_{74}, e_{74}, f_{74}, C_{84}, D_{74}
  77. Polygon(A_{84}, B_{73}, 4) → poly1_{76}, c_{73}, d_{73}, e_{73}, f_{73}, C_{83}, D_{73}
  78. Polygon(A_{83}, B_{72}, 4) → poly1_{77}, c_{72}, d_{72}, e_{72}, f_{72}, C_{82}, D_{72}
  79. Polygon(A_{82}, B_{71}, 4) → poly1_{78}, c_{71}, d_{71}, e_{71}, f_{71}, C_{81}, D_{71}
  80. Polygon(A_{81}, B_{70}, 4) → poly1_{79}, c_{70}, d_{70}, e_{70}, f_{70}, C_{80}, D_{70}
  81. Polygon(A_{80}, B_{69}, 4) → poly1_{80}, c_{69}, d_{69}, e_{69}, f_{69}, C_{79}, D_{69}
  82. Polygon(A_{79}, B_{68}, 4) → poly1_{81}, c_{68}, d_{68}, e_{68}, f_{68}, C_{78}, D_{68}
  83. Polygon(A_{78}, B_{67}, 4) → poly1_{82}, c_{67}, d_{67}, e_{67}, f_{67}, C_{77}, D_{67}
  84. Polygon(A_{77}, B_{66}, 4) → poly1_{83}, c_{66}, d_{66}, e_{66}, f_{66}, C_{76}, D_{66}
  85. Polygon(A_{76}, B_{65}, 4) → poly1_{84}, c_{65}, d_{65}, e_{65}, f_{65}, C_{75}, D_{65}
  86. Polygon(A_{75}, B_{64}, 4) → poly1_{85}, c_{64}, d_{64}, e_{64}, f_{64}, C_{74}, D_{64}
  87. Polygon(A_{74}, B_{63}, 4) → poly1_{86}, c_{63}, d_{63}, e_{63}, f_{63}, C_{73}, D_{63}
  88. Polygon(A_{73}, B_{62}, 4) → poly1_{87}, c_{62}, d_{62}, e_{62}, f_{62}, C_{72}, D_{62}
  89. Polygon(A_{72}, B_{61}, 4) → poly1_{88}, c_{61}, d_{61}, e_{61}, f_{61}, C_{71}, D_{61}
  90. Polygon(A_{71}, B_{60}, 4) → poly1_{89}, c_{60}, d_{60}, e_{60}, f_{60}, C_{70}, D_{60}
  91. Polygon(A_{70}, B_{59}, 4) → poly1_{90}, c_{59}, d_{59}, e_{59}, f_{59}, C_{69}, D_{59}
  92. Polygon(A_{69}, B_{58}, 4) → poly1_{91}, c_{58}, d_{58}, e_{58}, f_{58}, C_{68}, D_{58}
  93. Polygon(A_{68}, B_{57}, 4) → poly1_{92}, c_{57}, d_{57}, e_{57}, f_{57}, C_{67}, D_{57}
  94. Polygon(A_{67}, B_{56}, 4) → poly1_{93}, c_{56}, d_{56}, e_{56}, f_{56}, C_{66}, D_{56}
  95. Polygon(A_{66}, B_{55}, 4) → poly1_{94}, c_{55}, d_{55}, e_{55}, f_{55}, C_{65}, D_{55}
  96. Polygon(A_{65}, B_{54}, 4) → poly1_{95}, c_{54}, d_{54}, e_{54}, f_{54}, C_{64}, D_{54}
  97. Polygon(A_{64}, B_{53}, 4) → poly1_{96}, c_{53}, d_{53}, e_{53}, f_{53}, C_{63}, D_{53}
  98. Polygon(A_{63}, B_{52}, 4) → poly1_{97}, c_{52}, d_{52}, e_{52}, f_{52}, C_{62}, D_{52}
  99. Polygon(A_{62}, B_{51}, 4) → poly1_{98}, c_{51}, d_{51}, e_{51}, f_{51}, C_{61}, D_{51}
  100. Polygon(A_{61}, B_{50}, 4) → poly1_{99}, c_{50}, d_{50}, e_{50}, f_{50}, C_{60}, D_{50}
  101. Textfield(a) → inputBox1
  102. Textfield() → inputBox2
  103. Circle(M, 0.4) → g
  104. Circle(N, 0.4) → h

AI 绘图提示语参考

画一个几何模型来展示整数乘法的概念，使用多个正方形和三角形组合成一个矩形，通过调整矩形的长度和宽度来观察乘积的变化，每个正方形和三角形都标有对应的数值，以便理解乘法运算的几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。