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4×10面积模型与矩形

4×10面积模型与矩形
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2018-01-30 03:31
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该范例展示了4根长度为1×10的棒子如何通过移动形成一个4×10的矩形。核心数学概念包括几何、乘法和矩形面积。使用了Segment, Line, OrthogonalLine, Intersect, Polygon, Point, Rotate, PointIn, Circle等GeoGebra命令。适合小学高年级或初中学生学习几何和乘法概念。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Line(C, a) → g
  3. OrthogonalLine(A, a) → h
  4. OrthogonalLine(B, a) → i
  5. Intersect(g, h) → D
  6. Intersect(g, i) → E
  7. Polygon(A, B, E, D) → q1, a_1, b, e, d
  8. Point(Circle[F, Segment[A, B]]) → G
  9. Rotate(G + (Segment[B, E], 0), Angle[E - B] + Angle[G - F] - Angle[B - A], G) → H
  10. Rotate(H + (Segment[E, D], 0), Angle[D - E] + Angle[H - G] - Angle[E - B], H) → I
  11. Polygon(F, G, H, I) → q2, f, g_1, h_1, i_1
  12. Point(Circle[J, Segment[A, B]]) → K
  13. Rotate(K + (Segment[B, E], 0), Angle[E - B] + Angle[K - J] - Angle[B - A], K) → L
  14. Rotate(L + (Segment[E, D], 0), Angle[D - E] + Angle[L - K] - Angle[E - B], L) → M
  15. Polygon(J, K, L, M) → q3, j, k, l, m
  16. Point(Circle[N, Segment[A, B]]) → O
  17. Rotate(O + (Segment[B, E], 0), Angle[E - B] + Angle[O - N] - Angle[B - A], O) → P
  18. Rotate(P + (Segment[E, D], 0), Angle[D - E] + Angle[P - O] - Angle[E - B], P) → Q
  19. Polygon(N, O, P, Q) → q4, n, o, p, q
  20. PointIn(q1) → Pointq1
  21. PointIn(q3) → Pointq3
  22. PointIn(q4) → Pointq4
  23. PointIn(q2) → Pointq2
  24. Polygon(D, F, G, E) → q5, d_1, f_1, g_2, e_1
  25. PointIn(q5) → Pointq5
  26. Circle(A, D) → c_1
  27. Intersect(c_1, h) → T, U
  28. Circle(U, A) → k_1
  29. Intersect(k_1, h) → V, W
  30. Circle(W, U) → p_1
  31. Polygon(D, A, 4) → poly1, r, s, t, c, R, S