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平移变换与球体角度关系演示

平移变换与球体角度关系演示
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2018-02-03 02:41
立体几何变换几何作图
①本范例演示了球体在二维平面上的平移变换及其角度关系；②涉及核心数学概念包括平移变换、球体几何、角度测量、实数运算、正切函数及标准差；③作图要点提炼自GeoGebra命令：Polygon（多边形）、Segment（线段）、Translate（平移）；④适合高中及以上数学学习者，用于理解空间变换与几何性质。

GeoGebra 命令及参数

  1. Polygon((-1, 13.4), (30, 13.4), (30, 17), (-1, 17)) → TopBox, f, g, h, i
  2. Polygon((17.4, 15), (30, 15), (30, -1), (17.4, -1)) → RightBox, j, k, l, m
  3. Segment(A, B) → AB
  4. Segment(B, C) → BC
  5. Segment(C, A) → CA
  6. Translate(A, (htrans, vtrans)) → A'
  7. Translate(B, (htrans, vtrans)) → B'
  8. Translate(C, (htrans, vtrans)) → C'
  9. Segment(A', B') → AB'
  10. Segment(B', C') → BC'
  11. Segment(C', A') → CA'
  12. Polygon(A', A' + (1.5, 0), A' + (1.5, 1.5), A' + (0, 1.5)) → BoxA, a', n, p, q
  13. Polygon(B', B' + (1.5, 0), B' + (1.5, -1.5), B' + (0, -1.5)) → BoxB, r, s, t, d
  14. Polygon(C', C' + (-1.5, 0), C' + (-1.5, -1.5), C' + (0, -1.5)) → BoxC, a, b, c, e
  15. Polygon((18, 12), (28, 12), (28, 10), (18, 10)) → LabelBox, f_1, g_1, h_1, i_1
  16. Polygon(PtA, PtA + (1.5, 0), PtA + (1.5, -1.5), PtA + (0, -1.5)) → DragBoxA, pta, j_1, k_1, l_1
  17. Polygon(PtB, PtB + (1.5, 0), PtB + (1.5, -1.5), PtB + (0, -1.5)) → DragBoxB, ptb, m_1, n_1, p_1
  18. Polygon(PtC, PtC + (1.5, 0), PtC + (1.5, -1.5), PtC + (0, -1.5)) → DragBoxC, ptc, q_1, r_1, s_1