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波浪多边形

波浪多边形
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2017-05-22 18:44
多边形函数积分
这个范例展示了波浪状的多边形。它涉及到了多边形、积分和函数的概念。通过使用GeoGebra命令如Sequence、Element等，可以构造出具有波浪效果的多边形。适合高中数学教学或学生探索几何与函数的结合。

GeoGebra 命令及参数

  1. Sequence(Sequence[(i, j) + (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) + (Mod[i + j, 2] * (v(a + j), g(a + i))), i, 0, n], j, 0, n) → Ld
  2. Sequence(Sequence[(i, j) - (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) - (Mod[i + j, 2] * (v(a + j), g(a + i))), i, 0, n], j, 0, n) → Lg
  3. Element(Element[Lg, 2], 2) → Lg22
  4. Element(Element[Ld, 1], 1) → Ld11
  5. Element(Element[Lg, 3], 3) → Lg33
  6. Element(Element[Ld, 2], 1) → Ld21
  7. Element(Element[Ld, 2], 2) → Ld22
  8. Element(Element[Lg, 2], 1) → Lg21
  9. Element(Element[Lg, 1], 2) → Lg12
  10. Sequence(Sequence[Segment[Element[Element[Ld, i], j], Element[Element[Lg, i - 1], j + 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T4
  11. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j + 1]], i, 1, n + 2, 2], j, 1, n + 2, 2) → T5
  12. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j - 1]], i, 1, n + 2, 2], j, 1, n + 2, 2) → T6
  13. Sequence(Sequence[Segment[Element[Element[Lg, i + 1], j], Element[Element[Ld, i], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T7
  14. Sequence(Sequence[Segment[Element[Element[Ld, i + 0], j + 2], Element[Element[Lg, i + 1], j + 1]], i, 2, n + 2, 2], j, 1, n + 2, 2) → T8
  15. Sequence(Sequence[Segment[Element[Element[Lg, i], j], Element[Element[Ld, i + 1], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T1
  16. Element(Ld, 1) → Ld1
  17. Element(Lg, 1) → Lg2
  18. Sequence(Sequence[Segment[(i, j) - (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) - (Mod[i + j, 2] * (v(a + j), g(a + i))), (i, j) + (Mod[i + j + 1, 2] * (g(a + i), v(a + j))) + (Mod[i + j, 2] * (v(a + j), g(a + i)))], i, 0, n], j, 0, n) → LT
  19. Sequence(Sequence[Circle[Element[Element[Lg, i], j], Element[Element[Ld, i - 1], j - 1]], i, 2, n + 2, 2], j, 2, n + 2, 2) → T2
  20. Sequence(Sequence[Polygon[Element[Element[Ld, i], j], Element[Element[Lg, i + 1], j + 1], sid], i, 2, n + 2, 2], j, 2, n + 3, 2) → T3