三角形、梯形、八边形几何构造

三角形、梯形、八边形几何构造
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2017-02-17 19:54
①本范例演示了三角形、梯形和八边形的几何构造与性质;②涉及的核心数学概念包括多边形、向量、几何变换、坐标几何;③作图要点提炼了使用 GeoGebra 命令如 Intersect(交点)、Point(点)、Polygon(多边形)、Mirror(镜像)、Segment(线段)、Midpoint(中点)、If(条件)、Vector(向量)、Translate(平移);④适合高中数学教学或几何爱好者学习多边形构造与变换。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  4. Polygon(A, E, B) → poly2, b, a, e
  5. Mirror(E, a) → E'
  6. Mirror(B, a) → B'
  7. Mirror(C, a) → C'
  8. Segment(C', B) → n
  9. Midpoint(C', A) → I
  10. Segment(I, B) → p
  11. If(0 < c < 1, Dilate[B, 1 - c, C], Dilate[B, 0, C]) → B'_1
  12. Vector(B, B'_1) → u
  13. Polygon(I, B, C') → poly3, c', i_1, b_1
  14. Translate(I, u) → I'
  15. Translate(B, u) → B'_2
  16. Translate(C', u) → C''
  17. Polygon(I', B'_2, C'') → poly3', c'', i', b'_2
  18. If(1 ≤ c < 2, Polygon[Rotate[I', (((-π)) / 4 * (c - 1)), C], Rotate[B'_2, (((-π)) / 4 * (c - 1)), C], Rotate[C'', (((-π)) / 4 * (c - 1)), C]], Polygon[Rotate[I', ((-π)) / 4, C], Rotate[B'_2, ((-π)) / 4, C], Rotate[C'', ((-π)) / 4, C]]) → poly4
  19. Polygon(A, I, B) → poly5, b_2, a_1, i_2
  20. If(3 ≤ c < 4, Dilate[B, 4 - c, E], Dilate[B, 0, E]) → K
  21. Vector(B, K) → v
  22. Translate(A, v) → A'
  23. Translate(I, v) → I'_1
  24. Translate(B, v) → B'_3
  25. Polygon(A', I'_1, B'_3) → poly5', b'_3, a', i'_1
  26. If(3 ≤ c < 4, Polygon[Rotate[A', ((3 * π / 4) * (c - 3)), K], Rotate[I'_1, ((3 * π / 4) * (c - 3)), K], Rotate[B'_3, ((3 * π / 4) * (c - 3)), K]], Polygon[Rotate[A', (3 * π / 4), K], Rotate[I'_1, (3 * π / 4), K], Rotate[B'_3, (3 * π / 4), K]]) → poly6
  27. Polygon(E, C', B) → poly7, b_3, e_1, c'_1
  28. If(c ≥ 5, Dilate[C', 6 - c, C], Dilate[C', 0, C]) → J
  29. Polygon(E, J, B) → poly8, b_4, e_2, j_1
  30. Polygon(E, A, B) → poly9, b_5, e_3, a_2