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从面积求正方形边长

从面积求正方形边长
几何画板及绘图内容加载中，请稍等……
2014-04-02 03:28
多边形几何作图
①本范例演示如何通过正方形的面积计算其边长；②涉及核心数学概念包括面积公式、平方根运算及逆运算；③构造要点：使用 GeoGebra 命令 Sequence（数列）、Polygon（多边形）、Area（面积）、AttachCopyToView（视图复制）、Vector（向量）、Point（点）；④适合初中及以上学生学习平方根及面积计算，也可用于微积分逆运算教学。

GeoGebra 命令及参数

  1. Sequence(Segment[(0, i), (a, i)], i, 0, a, 1) → liste1
  2. Sequence(Segment[(i, 0), (i, a)], i, 0, a, 1) → liste2
  3. Polygon({(0, 0), (a, 0), (a, a), (0, a)}) → çokgen1, , , ,
  4. Area(çokgen1) → b
  5. AttachCopyToView(PolyLine[(-5.4200000000000035, 1.8200000000000018), (-5.360000000000003, 1.880000000000002), (-5.300000000000003, 1.900000000000002), (-5.260000000000003, 1.960000000000002), (-5.200000000000003, 2.020000000000002), (-5.160000000000003, 2.080000000000002), (-5.120000000000003, 2.140000000000002), (-5.080000000000003, 2.200000000000002), (-5.040000000000003, 2.260000000000002), (-4.980000000000003, 2.280000000000002), (-4.920000000000003, 2.320000000000002), (-4.860000000000003, 2.360000000000002), (-4.940000000000003, 2.360000000000002), (-5.020000000000003, 2.360000000000002), (-5.100000000000003, 2.360000000000002), (-5.020000000000003, 2.360000000000002), (-4.940000000000003, 2.360000000000002), (-4.860000000000003, 2.360000000000002), (-4.780000000000003, 2.360000000000002), (-4.700000000000003, 2.360000000000002), (-4.7600000000000025, 2.300000000000002), (-4.8000000000000025, 2.240000000000002), (-4.820000000000003, 2.180000000000002), (-4.8400000000000025, 2.120000000000002), (NaN, NaN), (-6.700000000000004, 1.8200000000000018), (-6.700000000000004, 1.900000000000002), (-6.700000000000004, 1.9800000000000018), (-6.700000000000004, 2.060000000000002), (-6.760000000000003, 2.100000000000002), (-6.800000000000003, 2.160000000000002), (-6.840000000000003, 2.220000000000002), (-6.8800000000000034, 2.280000000000002), (-6.9200000000000035, 2.340000000000002), (-6.940000000000004, 2.400000000000002), (-6.980000000000004, 2.340000000000002), (-6.980000000000004, 2.260000000000002), (-6.980000000000004, 2.180000000000002), (-6.980000000000004, 2.260000000000002), (-6.980000000000004, 2.340000000000002), (-6.980000000000004, 2.420000000000002), (-6.980000000000004, 2.500000000000002), (-6.980000000000004, 2.5800000000000023), (-6.9200000000000035, 2.5400000000000023), (-6.900000000000004, 2.480000000000002), (-6.8800000000000034, 2.420000000000002), (-6.820000000000004, 2.360000000000002), (-6.760000000000003, 2.340000000000002), (-6.700000000000004, 2.300000000000002), true], 1, (-7.980000000000004, -3.08), (15.020000000000005, 8.660000000000004), (0, 587), (1150, 0)) → çizgi1
  6. Vector((-0.3, 0), (-0.3, a)) → u
  7. Vector((0, a + 0.3), (a, a + 0.3)) → v
  8. AttachCopyToView(PolyLine[(-6.500000000000004, 4.8000000000000025), (-6.5800000000000045, 4.8000000000000025), (-6.640000000000005, 4.820000000000003), (-6.700000000000005, 4.860000000000003), (-6.780000000000005, 4.860000000000003), (-6.860000000000005, 4.860000000000003), (-6.920000000000005, 4.880000000000003), (-7.000000000000004, 4.880000000000003), (-7.060000000000005, 4.8400000000000025), (-7.1200000000000045, 4.8000000000000025), (-7.140000000000005, 4.740000000000003), (-7.140000000000005, 4.660000000000003), (-7.140000000000005, 4.580000000000003), (-7.1200000000000045, 4.520000000000003), (-7.0800000000000045, 4.460000000000003), (-7.0400000000000045, 4.400000000000003), (-7.000000000000004, 4.3400000000000025), (-6.940000000000005, 4.3000000000000025), (-6.860000000000005, 4.3000000000000025), (-6.780000000000005, 4.3000000000000025), (-6.700000000000005, 4.3000000000000025), (-6.6200000000000045, 4.3000000000000025), (-6.560000000000005, 4.280000000000003), (-6.460000000000004, 4.280000000000003), (-6.420000000000004, 4.3400000000000025), (-6.380000000000004, 4.400000000000003), (-6.380000000000004, 4.480000000000003), (-6.400000000000005, 4.540000000000003), (-6.400000000000005, 4.620000000000003), (-6.400000000000005, 4.700000000000003), (-6.420000000000004, 4.7600000000000025), (-6.480000000000005, 4.780000000000003), (-6.5400000000000045, 4.8000000000000025), (-6.600000000000005, 4.820000000000003), (-6.680000000000005, 4.820000000000003), true], 1, (-7.980000000000005, -3.08), (15.020000000000003, 8.660000000000004), (0, 587), (1150, 0)) → çizgi2
  9. Point({(0, 0)}) → A
  10. Point({(a, 0)}) → B
  11. Point({(a, a)}) → C
  12. Point({(0, a)}) → D

AI 绘图提示语参考

绘制一个边长为a的正方形，其四个顶点分别位于原点、x轴、对角点和y轴上。在正方形内部，用等间距的水平和垂直线段构成网格，间距为1个单位。在正方形左侧和上方分别添加一条带箭头的线段，表示边长a。在图形旁边用文字标注正方形的面积值，并显示面积与边长的关系。整体布局清晰，突出正方形面积与边长的计算关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。