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Four Color Theorem

Four Color Theorem
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2013-07-03 09:43
PolygonTransformationGeometric Construction
In collections Graph theory
This example demonstrates how to color a map using only four colors to ensure that no two adjacent regions have the same color. The core mathematical concepts include coloring problems in graph theory. Using commands like Polygon, Point, Rotate, and Segment, a complex map can be constructed and colored. Suitable for high school and above students to learn graph theory and combinatorics.

GeoGebra Commands & Parameters

  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