Farbenie - mapa Európy
Author: Franz Rittenschober
Date: 1 July 2013

Now that we have created a coloured planar graph lets try to play with it. We know because of the four-colour-sentence, that there is a colouring with only 4 colours possible.
Follow the instruction at the bottom of the site.

1) Try to colour the graph without using cyan.
- Select the colour and then a point to change its colour.
- You must not colour two adjacent vertices in the same colour
2) Check your result

Aktivuj políčko a zobrazia sa názvy štátov USA

D = (-4.682332666666665, 4.234714000000005)
G: D
C = (-5.773752666666663, 4.234714000000005)
poly1, a, b, c, d, E, F = Polygon(C, D, 4)
H = Point(Circle[G, a])
K: H
I = Rotate(H + (b, 0), Angle[E - D] + Angle[H - G] - Angle[D - C], H)
J = Rotate(I + (c, 0), Angle[F - E] + Angle[I - H] - Angle[E - D], I)
poly2, g, h, i, j = Polygon(G, H, I, J)
L = Point(Circle[K, g])
S_1: L
T = Point(Circle[S_1, a])
G_{18} = (4.939354948335333, -1.5296204703216154)
G_{19} = (6.937357354588875, -4.477492872990777)
G_{20} = (7.428669421700402, -6.60651183047406)
G_{21} = (5.7254542557137755, -7.88392320496403)
G_{22} = (8.509555969345762, 0.894185727428584)
G_{23} = (10.081754584102647, -1.7261452971662261)
G_{24} = (9.52493424137625, -3.5603770143825932)
G_{25} = (9.819721481643167, -6.704774243896366)
G_{26} = (9.950738032872907, -8.670022512342474)
colour = 2 (slider from 1 to 5, step 1)
list1: {"Dark Green", "Red", "Yellow", "Blue", "Cyan"}
M = Rotate(L + (h, 0), Angle[I - H] + Angle[L - K] - Angle[H - G], L)
N = Rotate(M + (i, 0), Angle[J - I] + Angle[M - L] - Angle[I - H], M)
O: T
poly3, k, l, m, n = Polygon(K, L, M, N)
P = Point(Circle[O, a])
Q = Rotate(P + (b, 0), Angle[E - D] + Angle[P - O] - Angle[D - C], P)
R = Rotate(Q + (c, 0), Angle[F - E] + Angle[Q - P] - Angle[E - D], Q)
poly4, o, p, q, r = Polygon(O, P, Q, R)
U = Rotate(T + (b, 0), Angle[E - D] + Angle[T - S_1] - Angle[D - C], T)
V = Rotate(U + (c, 0), Angle[F - E] + Angle[U - T] - Angle[E - D], U)
poly5, s_1, t, u, v = Polygon(S_1, T, U, V)
G_1 = (-5.032754137807435, 3)
G_2 = (18.79435524088039, 0.20634883347244637)
G_3 = (28.58784244530349, -2.0536866752405776)
G_4 = (11.490182509822358, -6.868544932933541)
G_5 = (-2.7578674364119204, 3.514516752023394)
G_6 = (-4.199049499939066, 1.0579564164657598)
G_7 = (-2.49583433395244, -2.9380483960413257)
G_8 = (-4.3300660511688065, -3.4948687387677233)
G_9 = (-1.2511770972699043, 0.5011360737393648)
G_{10} = (0.22275910406467542, -3.691393565612334)
A = (-13.337453948213465, -14.66402973110311)
B = (-6.409953801940942, -12.67421585930142)
W = (21.201784369726823, -12.67421585930142)
G_{11} = (-0.2685529630468514, -6.803036657318671)
G_{12} = (2.056990821281042, 1.2544812433103705)
G_{13} = (2.777581853044615, -1.3658497812844397)
G_{14} = (3.2361397823487064, -4.05168908149412)
G_{15} = (2.6465653018148743, -5.984183212132793)
G_{16} = (4.775584259298157, 2.3353677909557296)
G_{17} = (4.742830121490722, 0.2391029712798815)
G_{27} = (12.702085608697457, -8.01493975619377)
G_{28} = (13.127889400194118, -5.329100455984092)
G_{29} = (13.815726294150252, -4.018934943686685)
G_{30} = (11.490182509822358, -3.4948687387677233)
G_{31} = (12.702085608697457, -3.396606325345418)
G_{32} = (10.769591478058786, -0.5469963360985616)
G_{33} = (17.615206279812725, -1.3330956434770047)
G_{34} = (-1.0546522704252943, -9.881925611217573)
G_{35} = (17.84448524446477, 0.7304150383914084)
G_{36} = (14.307038361261778, -2.9052942582338908)
G_{37} = (15.715466286981492, -2.9052942582338908)
G_{38} = (14.176021810032038, 0.6976609005839733)
G_{39} = (29.898007957600896, -7.720152515926855)
G_{40} = (28.882629685570407, -3.7896559790346394)
G_{41} = (4.611813570260981, -12.764289738271865)
G_{42} = (18.630584551843217, 1.3854977945401137)
G_{43} = (19.318421445799355, 1.1562188298880678)
G_{44} = (19.87524178852575, 1.909563999459073)
G_{45} = (19.58045454825883, 0.009824006627835603)
G_{46} = (19.02363420553244, -0.1539466824093383)
G_{47} = (18.892617654302697, -0.3177173714465157)
G_{48} = (17.647960417620162, -2.3812280533149286)
G_{49} = (18.27028903596143, -2.676015293581845)
G_{50} = (18.46681386280604, -1.7261452971662261)
G_{51} = (16.861861110241723, -3.5603770143825937)
G_{52} = (17.58245214200529, -4.837788388872563)
G_{53} = (15.518941460136878, -5.984183212132793)
G_{54} = (14.503563188106389, -6.9012990707409765)
G_{55} = (15.813728700403795, -9.292351130683741)
Z = (-8.096791899023845, -14.139963526184141)
A_1 = (23, -14)
S = false