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单位正方形多用途模板：面积与几何度量的可视化

单位正方形多用途模板：面积与几何度量的可视化
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2021-01-08 12:05
多边形向量立体几何几何作图滑块动画
所属专题 Perimeter & Area Elementary Math Resources
本范例通过单位正方形网格化的构造方式，展示如何用同一套“单位尺度”去度量和组织图形（如矩形、正方形及由其组合形成的区域）的面积与周长关系。核心数学概念包括：面积与周长、矩形与正方形的几何性质、等腰三角形（作为由单位单元组合得到的典型构型）、以及质心/重心（在由离散单元或多边形区域组合时的理解）。作图要点是利用 GeoGebra 的多边形与标注组件搭建单位单元序列：构造摘要表明主要使用了 Polygon（生成大量多边形对象 poly1 及其变体 poly1_1…poly1_39）与 Textfield（用于在图中呈现标签、坐标或参数文本）。适合用于中学几何与探究式学习，也适合作为课堂演示模板：让学生用单位正方形快速验证面积守恒、周长计数以及质心直观定位等任务。

GeoGebra 命令及参数

  1. Polygon((0, 7), (1, 7), 4) → poly1
  2. Polygon((9, 8), (10, 8), 4) → poly1_{1}
  3. Polygon((4, 9), (5, 9), 4) → poly1_{2}
  4. Polygon((8, 9), (9, 9), 4) → poly1_{3}
  5. Polygon((10, 9), (11, 9), 4) → poly1_{4}
  6. Polygon((3, 8), (4, 8), 4) → poly1_{5}
  7. Polygon((6, 9), (7, 9), 4) → poly1_{6}
  8. Polygon((5, 8), (6, 8), 4) → poly1_{7}
  9. Polygon((1, 8), (2, 8), 4) → poly1_{8}
  10. Polygon((1, 6), (2, 6), 4) → poly1_{9}
  11. Polygon((7, 8), (8, 8), 4) → poly1_{10}
  12. Polygon((11, 8), (12, 8), 4) → poly1_{11}
  13. Polygon((0, 9), (1, 9), 4) → poly1_{12}
  14. Polygon((2, 7), (3, 7), 4) → poly1_{13}
  15. Polygon((2, 9), (3, 9), 4) → poly1_{14}
  16. Polygon((4, 7), (5, 7), 4) → poly1_{15}
  17. Polygon((3, 6), (4, 6), 4) → poly1_{16}
  18. Polygon((6, 7), (7, 7), 4) → poly1_{17}
  19. Polygon((5, 6), (6, 6), 4) → poly1_{18}
  20. Polygon((8, 7), (9, 7), 4) → poly1_{19}
  21. Polygon((7, 6), (8, 6), 4) → poly1_{20}
  22. Polygon((10, 7), (11, 7), 4) → poly1_{21}
  23. Polygon((9, 6), (10, 6), 4) → poly1_{22}
  24. Polygon((0, 5), (1, 5), 4) → poly1_{23}
  25. Polygon((11, 6), (12, 6), 4) → poly1_{24}
  26. Polygon((2, 5), (3, 5), 4) → poly1_{25}
  27. Polygon((1, 4), (2, 4), 4) → poly1_{26}
  28. Polygon((4, 5), (5, 5), 4) → poly1_{27}
  29. Polygon((3, 4), (4, 4), 4) → poly1_{28}
  30. Polygon((6, 5), (7, 5), 4) → poly1_{29}
  31. Polygon((5, 4), (6, 4), 4) → poly1_{30}
  32. Polygon((8, 5), (9, 5), 4) → poly1_{31}
  33. Polygon((7, 4), (8, 4), 4) → poly1_{32}
  34. Polygon((10, 5), (11, 5), 4) → poly1_{33}
  35. Polygon((9, 4), (10, 4), 4) → poly1_{34}
  36. Polygon((0, 3), (1, 3), 4) → poly1_{35}
  37. Polygon((11, 4), (12, 4), 4) → poly1_{36}
  38. Polygon((2, 3), (3, 3), 4) → poly1_{37}
  39. Polygon((1, 2), (2, 2), 4) → poly1_{38}
  40. Polygon((4, 3), (5, 3), 4) → poly1_{39}
  41. Polygon((3, 2), (4, 2), 4) → poly1_{40}
  42. Polygon((6, 3), (7, 3), 4) → poly1_{41}
  43. Polygon((5, 2), (6, 2), 4) → poly1_{42}
  44. Polygon((8, 3), (9, 3), 4) → poly1_{43}
  45. Polygon((7, 2), (8, 2), 4) → poly1_{44}
  46. Polygon((10, 3), (11, 3), 4) → poly1_{45}
  47. Polygon((9, 2), (10, 2), 4) → poly1_{46}
  48. Polygon((0, 1), (1, 1), 4) → poly1_{47}
  49. Polygon((11, 2), (12, 2), 4) → poly1_{48}
  50. Polygon((2, 1), (3, 1), 4) → poly1_{49}
  51. Polygon((1, 0), (2, 0), 4) → poly1_{50}
  52. Polygon((4, 1), (5, 1), 4) → poly1_{51}
  53. Polygon((3, 0), (4, 0), 4) → poly1_{52}
  54. Polygon((6, 1), (7, 1), 4) → poly1_{53}
  55. Polygon((5, 0), (6, 0), 4) → poly1_{54}
  56. Polygon((8, 1), (9, 1), 4) → poly1_{55}
  57. Polygon((7, 0), (8, 0), 4) → poly1_{56}
  58. Polygon((10, 1), (11, 1), 4) → poly1_{57}
  59. Polygon((9, 0), (10, 0), 4) → poly1_{58}
  60. Polygon((11, 0), (12, 0), 4) → poly1_{60}
  61. Textfield(a) → InputBox1

AI 绘图提示语参考

在网格上绘制多个正方形，每个正方形边长为1，从左上角开始，第一行绘制7个，第二行绘制8个，第三行绘制9个，以此类推，直到第十行绘制7个。每个正方形之间留有空隙，形成一个整齐的阵列。使用不同颜色或填充效果区分每个正方形，以便观察和计算面积与周长。
以上提示语为根据原始绘图命令整理而来，仅供参考。