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整数求和2

整数求和2
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2016-10-19 15:21
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①本范例演示整数求和的几何表示方法；②涉及核心数学概念包括整数、箱线图、二次方程、直角三角形、上下和或黎曼和、菱形；③作图要点提炼了Polygon（多边形）、Vector（向量）、Sequence（数列）、Segment（线段）、Rotate（旋转）等GeoGebra命令；④适合高中数学教学，用于理解积分与几何图形的关系。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Vector((0, 0), (1, 0)) → u
  3. Vector((0, 0), (0, -1)) → v
  4. Sequence(Translate[poly1, Vector[(k * v)]], k, 1, 層數 - 1) → list_{orange1}
  5. Sequence(Translate[poly1, Vector[(k * v) + u]], k, 1, 層數 - 1) → list_{orange2}
  6. Sequence(Translate[poly1, Vector[(k * v) + (2 * u)]], k, 2, 層數 - 1) → list_{orange3}
  7. Sequence(Translate[poly1, Vector[(k * v) + (3 * u)]], k, 3, 層數 - 1) → list_{orange4}
  8. Sequence(Translate[poly1, Vector[(k * v) + (4 * u)]], k, 4, 層數 - 1) → list_{orange5}
  9. Sequence(Translate[poly1, Vector[(k * v) + (5 * u)]], k, 5, 層數 - 1) → list_{orange6}
  10. Sequence(Translate[poly1, Vector[(k * v) + (6 * u)]], k, 6, 層數 - 1) → list_{orange7}
  11. Sequence(Translate[poly1, Vector[(k * v) + (7 * u)]], k, 7, 層數 - 1) → list_{orange8}
  12. Sequence(Translate[poly1, Vector[(k * v) + (8 * u)]], k, 8, 層數 - 1) → list_{orange9}
  13. Sequence(Translate[poly1, Vector[(k * v) + (9 * u)]], k, 9, 層數 - 1) → list_{orange10}
  14. Segment(E, F) → j
  15. Segment(G, H) → k
  16. Sequence(Translate[poly1, Vector[((層數 + 1.5) * u) + (k * v)]], k, 1, 層數 - 1) → list_{blue2}
  17. Sequence(Translate[poly1, Vector[((層數 + 2.5) * u) + (k * v)]], k, 2, 層數 - 1) → list_{blue3}
  18. Sequence(Translate[poly1, Vector[((層數 + 3.5) * u) + (k * v)]], k, 3, 層數 - 1) → list_{blue4}
  19. Sequence(Translate[poly1, Vector[((層數 + 4.5) * u) + (k * v)]], k, 4, 層數 - 1) → list_{blue5}
  20. Sequence(Translate[poly1, Vector[((層數 + 5.5) * u) + (k * v)]], k, 5, 層數 - 1) → list_{blue6}
  21. Sequence(Translate[poly1, Vector[((層數 + 6.5) * u) + (k * v)]], k, 6, 層數 - 1) → list_{blue7}
  22. Sequence(Translate[poly1, Vector[((層數 + 7.5) * u) + (k * v)]], k, 7, 層數 - 1) → list_{blue8}
  23. Sequence(Translate[poly1, Vector[((層數 + 8.5) * u) + (k * v)]], k, 8, 層數 - 1) → list_{blue9}
  24. Sequence(Translate[poly1, Vector[((層數 + 9.5) * u) + (k * v)]], k, 9, 層數 - 1) → list_{blue10}
  25. Rotate(list_{blue2}, rotate, I) → Rotate_{b2}
  26. Rotate(list_{blue3}, rotate, I) → Rotate_{b3}
  27. Rotate(list_{blue4}, rotate, I) → Rotate_{b4}
  28. Rotate(list_{blue5}, rotate, I) → Rotate_{b5}
  29. Rotate(list_{blue6}, rotate, I) → Rotate_{b6}
  30. Rotate(list_{blue7}, rotate, I) → Rotate_{b7}
  31. Rotate(list_{blue8}, rotate, I) → Rotate_{b8}
  32. Rotate(list_{blue9}, rotate, I) → Rotate_{b9}
  33. Rotate(list_{blue10}, rotate, I) → Rotate_{b10}
  34. Sequence(Translate[poly1, Vector[((層數 + 0.5) * u) + (k * v)]], k, 0, 層數 - 1) → list_{blue1}