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代数小方块进行代数因式分解

代数小方块进行代数因式分解
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2018-01-14 12:12
向量几何作图
这个范例使用代数小方块演示代数因式分解的过程。核心数学概念包括代数、矩形和正方形。通过Vector, Segment, Point等GeoGebra命令，用户可以直观地理解代数因式分解的几何意义。适合初中及以上学生学习代数。

GeoGebra 命令及参数

  1. Vector((0, 0), (0, (-n) - q)) → v_1
  2. Segment((x(L) + q, y(L)), (x(L) + (b_3 * m) + ((b_3 - 1) * q), y(L))) → l
  3. Point(l) → M
  4. KeepIf(x < x(M), Sequence[x(L) + ((t - 1) * m) + ((t - 1) * q), t, 1, b_3]) → Re1
  5. Length(Re1) → r_1
  6. Segment((x(K), y(K) - q), (x(K), y(K) - (b_1 * n) - ((b_1 - 1) * q))) → k
  7. Point(k) → I
  8. KeepIf(x > y(I), Sequence[y(K) - ((t - 1) * n) - ((t - 1) * q), t, 1, b_1]) → Bq2
  9. Length(Bq2) → a_1
  10. Vector((0, 0), (n + q, 0)) → v
  11. Segment((x(H) + q, y(H)), (x(H) + (b_1 * n) + ((b_1 - 1) * q), y(H))) → j
  12. Point(j) → J
  13. KeepIf(x < x(J), Sequence[x(H) + ((t - 1) * n) + ((t - 1) * q), t, 1, b_1]) → Bq1
  14. Length(Bq1) → a_2
  15. Segment((x(R), y(R) - q), (x(R), y(R) - (b_3 * m) - ((b_3 - 1) * q))) → s
  16. Point(s) → S
  17. KeepIf(x > y(S), Sequence[y(R) - ((t - 1) * m) - ((t - 1) * q), t, 1, b_3]) → Re2
  18. Length(Re2) → r_2
  19. Segment((x(T) + q, y(T)), (x(T) + (b_2 * m) + ((b_2 - 1) * q), y(T))) → t
  20. Point(t) → U
  21. Segment((x(V), y(V) - q), (x(V), y(V) - (b_2 * m) - ((b_2 - 1) * q))) → a
  22. Point(a) → W
  23. KeepIf(x > y(W), Sequence[y(V) - ((t - 1) * m) - ((t - 1) * q), t, 1, b_2]) → Sq2
  24. KeepIf(x < x(U), Sequence[x(T) + ((t - 1) * m) + ((t - 1) * q), t, 1, b_2]) → Sq1
  25. Length(Sq1) → e_2
  26. Length(Sq2) → e_1
  27. Vector((0, 0), (m + q, 0)) → u
  28. Sequence(Translate[Sequence[Polygon[(x(B) + (0.5 * n), y(B) + (0.5 * m) - (p * (m + q))), (x(B) - (0.5 * n), y(B) + (0.5 * m) - (p * (m + q))), (x(B) - (0.5 * n), y(B) - (0.5 * m) - (p * (m + q))), (x(B) + (0.5 * n), y(B) - (0.5 * m) - (p * (m + q)))], p, 0, r_2 - 1], Vector[(r * v)]], r, 0, a_2 - 1) → Rh2
  29. Vector((0, 0), (0, -2)) → w
  30. Ray(E, w) → f
  31. Point(f) → F
  32. Circle(F, E) → g
  33. OrthogonalLine(F, f) → h
  34. Intersect(g, h, 1) → G
  35. Ray(G, F) → i
  36. SelectedIndex(Bahasa) → nn
  37. Sequence(Translate[Sequence[Polygon[(x(C) + (0.5 * m), y(C) + (0.5 * m) - (p * (m + q))), (x(C) - (0.5 * m), y(C) + (0.5 * m) - (p * (m + q))), (x(C) - (0.5 * m), y(C) - (0.5 * m) - (p * (m + q))), (x(C) + (0.5 * m), y(C) - (0.5 * m) - (p * (m + q)))], p, 0, e_1 - 1], Vector[(r * u)]], r, 0, e_2 - 1) → Sqs
  38. Sequence(Translate[Sequence[Polygon[(x(D) + (0.5 * n), y(D) + (0.5 * n) - (p * (n + q))), (x(D) - (0.5 * n), y(D) + (0.5 * n) - (p * (n + q))), (x(D) - (0.5 * n), y(D) - (0.5 * n) - (p * (n + q))), (x(D) + (0.5 * n), y(D) - (0.5 * n) - (p * (n + q)))], p, 0, a_1 - 1], Vector[(r * v)]], r, 0, a_2 - 1) → Sqb
  39. Sequence((x(Rp) + ((r + 0.5) * n) + (0.5 * m) + ((r + 1) * q), y(Rp)), r, 0, b_1 - 1) → Lp2
  40. Sequence((x(Rp), y(Rp) - ((r + 0.5) * n) - (0.5 * m) - ((r + 1) * q)), r, 0, b_1 - 1) → Lp3
  41. Sequence(Translate[Sequence[Polygon[(x(A) + (0.5 * m) + (p * (m + q)), y(A) + (0.5 * n)), (x(A) - (0.5 * m) + (p * (m + q)), y(A) + (0.5 * n)), (x(A) - (0.5 * m) + (p * (m + q)), y(A) - (0.5 * n)), (x(A) + (0.5 * m) + (p * (m + q)), y(A) - (0.5 * n))], p, 0, r_1 - 1], Vector[(r * v_1)]], r, 0, a_1 - 1) → Rh1
  42. Sequence((x(Rp) + ((r + 0.5) * n) + (0.5 * m) + ((r + 1) * q), y(Rp) - (0.5 * n) - q - (0.5 * m)), r, 0, b_1 - 1) → Lp1
  43. Sequence((x(A), y(Rp) - ((r + 0.5) * n) - (0.5 * m) - ((r + 1) * q)), r, 0, b_1 - 1) → Lp1a