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正方形拼图 by John Golden

正方形拼图 by John Golden
几何画板及绘图内容加载中，请稍等……
2015-05-31 02:03
多边形变换几何作图
这个范例展示了如何通过拼接多个图形形成一个正方形。涉及的核心数学概念包括几何变换和多边形。通过使用GeoGebra命令如Segment, LineBisector, Intersect等，可以构造出复杂的几何图形。适合初中及以上学生学习几何变换和多边形相关知识。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(b, a) → C
  4. Circle(C, B) → c
  5. Intersect(c, b, 1) → D
  6. Point(a) → E
  7. OrthogonalLine(A, a) → d
  8. Rotate(D, 90*°, D) → D'
  9. Rotate(E, 90*°, D) → E'
  10. Ray(D', E') → e
  11. Polygon(E, D, E', A) → poly1, e_1, d_1, e', a_1
  12. Point(Circle[F, Distance[A, E]]) → F_2
  13. Rotate(Polygon[Translate[E, F - A], Translate[D, F - A], Translate[E', F - A], Translate[A, F - A]], (-Angle[F_2, F, Translate[E, F - A]]), F) → poly2
  14. Point(Circle[G, Distance[A, E']]) → G_2
  15. Rotate(Polygon[Translate[E, G - A], Translate[D, G - A], Translate[E', G - A], Translate[A, G - A]], (-Angle[G_2, G, Translate[E', G - A]]), G) → poly3
  16. Point(Circle[H, Distance[D', E']]) → H_2
  17. Rotate(Polygon[Translate[E, H - D'], Translate[D, H - D'], Translate[E', H - D'], Translate[A, H - D']], (-Angle[H_2, H, Translate[E', H - D']]), H) → poly4
  18. Point(Circle[I, Distance[D', E]]) → I_2
  19. Rotate(Polygon[Translate[E, I - D'], Translate[D, I - D'], Translate[E', I - D'], Translate[A, I - D']], (-Angle[I_2, I, Translate[E, I - D']]), I) → poly5