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分配律的面积模型

分配律的面积模型
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2020-02-10 00:07
解析几何几何作图
该范例通过面积模型演示了分配律。涉及的核心数学概念包括分配律和几何构造。使用了DynamicCoordinates, Polygon, Point, Segment, Midpoint, Distance, Intersect, If, Vector, Text等GeoGebra命令。适合初中及以上学生学习分配律和几何构造。

GeoGebra 命令及参数

  1. DynamicCoordinates(A', If[x(A') < 6, 6, x(A')], If[y(A') < 6, 6, y(A')]) → A
  2. Polygon(A, B, C, D) → q, s1, s2, s4, s3
  3. Point(s3) → V'
  4. Point(s4) → H'
  5. DynamicCoordinates(V', x(V'), floor(y(V'))) → V
  6. DynamicCoordinates(H', floor(x(H')), 0) → H
  7. Segment(H, H_1) → f
  8. Segment(V, V_1) → g
  9. Midpoint(B, V_1) → M1
  10. Midpoint(C, V_1) → M2
  11. Midpoint(B, H_1) → M3
  12. Midpoint(H_1, A) → M4
  13. Distance(B, V_1) → a
  14. Distance(V_1, C) → b
  15. Distance(B, H_1) → c
  16. Distance(H_1, A) → d
  17. Intersect(f, g) → I
  18. Midpoint(C, I) → M6
  19. Midpoint(V_1, H_1) → M5
  20. Midpoint(I, A) → M7
  21. Midpoint(H, V) → M8
  22. Polygon(H_1, B, V_1, I) → q2, h_1, b_1, v_1, i
  23. If(Defined[Intersect[b_1, v_1]], Intersect[b_1, v_1], B) → E
  24. Polygon(I, E, C, H) → q3, i_1, e, c_1, h
  25. If(Defined[Intersect[h_1, i]], Intersect[h_1, i], B) → F
  26. Polygon(A, F, I, V) → q4, a_1, f_1, i_2, v
  27. Polygon(V, I, H, D) → q1, v_2, i_3, h_2, d_1
  28. Vector(J, K) → u
  29. Vector(K, J) → w
  30. Vector(L, M) → j
  31. Vector(M, L) → k
  32. Midpoint(J, K) → M9
  33. Midpoint(L, M) → M10
  34. Segment(J - (0, 0.5), J + (0, 0.5)) → l
  35. Segment(K - (0, 0.5), K + (0, 0.5)) → m
  36. Segment(M - (0.5, 0), M + (0.5, 0)) → n
  37. Segment(L - (0.5, 0), L + (0.5, 0)) → p
  38. Midpoint(C, A) → M0
  39. If(eval, Text[((a + b) * (c + d))], "" + (a + b) + "×" + (c + d) + "") → text11
  40. If(eval, Text[(a * c)], "" + a + "×" + c + "") → text5
  41. If(eval, Text[(b * c)], "" + b + "×" + c + "") → text7
  42. If(eval, Text[(a * d)], "" + a + "×" + d + "") → text6
  43. If(eval, Text[(b * d)], "" + b + "×" + d + "") → text8
  44. Text(((a + b) * (c + d))) → textArea