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四色定理

四色定理
几何画板及绘图内容加载中，请稍等……
2013-07-03 09:43
多边形变换几何作图
所属专题 Graph theory
本范例展示了如何使用四种颜色对地图进行着色，以确保相邻区域颜色不同。核心数学概念包括图论中的着色问题。通过使用Polygon, Point, Rotate, Segment等命令，可以构造出一个复杂的地图并进行着色。适合高中及以上学生学习图论和组合数学。

GeoGebra 命令及参数

  1. Polygon(C, D, 4) → poly1, a, b, c, d, E, F
  2. Point(Circle[G, a]) → H
  3. Rotate(H + (b, 0), Angle[E - D] + Angle[H - G] - Angle[D - C], H) → I
  4. Rotate(I + (c, 0), Angle[F - E] + Angle[I - H] - Angle[E - D], I) → J
  5. Polygon(G, H, I, J) → poly2, g, h, i, j
  6. Point(Circle[K, g]) → L
  7. Point(Circle[S, a]) → T
  8. Segment(G_{18}, G_{19}) → e_4
  9. Segment(G_{19}, G_{20}) → e_5
  10. Segment(G_{20}, G_{21}) → e_9
  11. Segment(G_{21}, G_{18}) → e_1
  12. Segment(G_{22}, G_{21}) → e_2
  13. Segment(G_{22}, G_{18}) → e_{18}
  14. Segment(G_{23}, G_{22}) → e_{13}
  15. Segment(G_{23}, G_{24}) → e_{16}
  16. Segment(G_{24}, G_{25}) → e_{14}
  17. Segment(G_{22}, G_{25}) → e_{17}
  18. Segment(G_{18}, G_{25}) → e_3
  19. Segment(G_{25}, G_{19}) → e_{15}
  20. Segment(G_{24}, G_{20}) → e_7
  21. Segment(G_{23}, G_{20}) → e_8
  22. Segment(G_{23}, G_{21}) → e_{10}
  23. Segment(G_{24}, G_{19}) → e_6
  24. Segment(G_{26}, G_{22}) → e_{12}
  25. Segment(G_{23}, G_{26}) → e_{11}
  26. Segment(G_{26}, G_{25}) → e
  27. Segment(G_{26}, G_{24}) → e_{19}
  28. Rotate(L + (h, 0), Angle[I - H] + Angle[L - K] - Angle[H - G], L) → M
  29. Rotate(M + (i, 0), Angle[J - I] + Angle[M - L] - Angle[I - H], M) → N
  30. Polygon(K, L, M, N) → poly3, k, l, m, n
  31. Point(Circle[O, a]) → P
  32. Rotate(P + (b, 0), Angle[E - D] + Angle[P - O] - Angle[D - C], P) → Q
  33. Rotate(Q + (c, 0), Angle[F - E] + Angle[Q - P] - Angle[E - D], Q) → R
  34. Polygon(O, P, Q, R) → poly4, o, p, q, r
  35. Rotate(T + (b, 0), Angle[E - D] + Angle[T - S] - Angle[D - C], T) → U
  36. Rotate(U + (c, 0), Angle[F - E] + Angle[U - T] - Angle[E - D], U) → V
  37. Polygon(S, T, U, V) → poly5, s_1, t, u, v