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除法运算演示

除法运算演示
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2018-10-20 13:22
向量函数三角函数解析几何几何作图
所属专题 Fraction Division (2018)
①本范例演示了除法运算 n ÷ a/b 的几何意义和计算过程；②涉及核心数学概念包括分数除法、有理数、比例和二维向量运算；③构造过程中使用了 GeoGebra 命令 If、Point、Polygon、Sequence、PolyLine，以及对象 a、p、q、unitAns、ansfraction、ansinteger、reciprocal2、numimproper、reciprocal1、reciprocal、exp3、ans、steps、exp1、exp2、numfraction、numinteger、nummixed、A、B、k、C、b、mixedfraction、button1、button2、button3、button4、step1、showstep1、step2、showstep2、step3、showstep3、step4、showstep4、list1、button5、button6、c；④适合初中及以上学生学习和理解分数除法的应用，也可用于数学教学演示。

GeoGebra 命令及参数

  1. If((p / q ≟ 1 ∨ p / q ≟ 2) ∧ (floor((a * q / p)) ≟ (a * q / p) ∨ a ≟ 1) ∨ p ≟ 1 ∧ a ≟ 1, 2, If[p / q < 1 ∨ a ≟ 1 ∨ (p / q ≟ 1 ∨ p / q ≟ 2) ∧ floor((a * q / p)) ≠ (a * q / p), 3, 4]) → steps
  2. Point(Segment[A - (0, 0), A - (0, 2.5)]) → B
  3. If(a ≥ p / q, 1, -1) → k
  4. Point(Sequence[A + (i, 0), i, 0, a, 1 / q]) → C
  5. Polygon({A, A + (a, 0), A + (a, 1), A + (0, 1)}) → poly2
  6. Sequence(Sequence[Segment[B + (i + j, 0), B + (i + j, 1)], j, 1 / q, (q - 1) / q, 1 / q], i, 0, m - 1) → list3
  7. Sequence(Polygon[{B + (i - 1, 0), B + (i, 0), B + (i, 1), B + (i - 1, 1)}], i, 2, m) → list2'
  8. Sequence(Polygon[{B + (i - 1, 0), B + (i, 0), B + (i, 1), B + (i - 1, 1)}], i, 1, 1) → list2
  9. Sequence(Sequence[Segment[A + (i + j, 0), A + (i + j, 1)], j, 1 / q, (q - 1) / q, 1 / q], i, 0, a - 1) → list6
  10. Sequence(Translate[Polygon[{A, A + (p / q, 0), A + (p / q, 1), A + (0, 1)}], Vector[(i * Vector[(p / q, 0)])]], i, 0, n - 1) → L_1
  11. Sequence(Sequence[Segment[A + ((i * p / q) + j, 0), A + ((i * p / q) + j, 1)], j, 1 / q, (p - 1) / q, 1 / q], i, 0, n - 1) → L_2
  12. Sequence(Translate[Polygon[{B, B + (p / q, 0), B + (p / q, 1), B + (0, 1)}], Vector[(i * Vector[(p / q, 0)])]], i, 0, 0) → list4
  13. Sequence(Sequence[Segment[B + ((i * p / q) + j, 0), B + ((i * p / q) + j, 1)], j, 1 / q, (p - 1) / q, 1 / q], i, 0, 0) → list5
  14. PolyLine(A + (0, 1.1), A + (0.015, 1.2), A + (0.5, 1.2), A + (0.5, 1.3), A + (0.5, 1.2), A + (0.985, 1.2), A + (1, 1.1)) → g
  15. Sequence(Translate[g, Vector[(i * Vector[(0, 0), (1, 0)])]], i, 1, a - 1) → L_3
  16. PolyLine(B - (0, 0.1), B + (0, -0.2), B + (p / ((2 * q)), -0.2), B + (p / ((2 * q)), -0.3), B + (p / ((2 * q)), -0.2), B + (p / q, -0.2), B + (p / q, -0.1)) → f
  17. Sequence(Text["1 cake", A + (((2 * i) - 1) / 2 - 0.35, 1.37)], i, 1, a) → L_4