ZAKLJUČAK:

Prosinac 2006. Niko Grgić

Pomiči vrhove trokuta i uvjeri se da  je tako.

Q = (-1768.0968831380221, -1063.2946929931666)
J = (-1819.9954182942722, -3874.4653472900454)
pomiči = 0 (slider from 0 to 4, step 0.02)
s: (1 + sgn(1 - pomiči + 0)) / 2
t: (1 + sgn(2 - pomiči + 0)) / 2
o: (1 + sgn(3 - pomiči + 0)) / 2
a_4: (1 - s) (1 - t) (1 - o)
a_1: s t o
a_3: (1 - s) (1 - t) o
a_2: (1 - s) t o
A = (-1365.883235677084, -224.26837463379024)
B = (-215.46570638020725, -206.96886291504023)
C = (-535.5066731770827, 251.46819763183544)
P, c, a_5, b = Polygon(A, B, C)
d = Circle(B, a_5)
e = Circle(A, a_5)
f = Circle(C, a_5)
g = Ray(B, C)
h = Ray(C, A)
i = Ray(A, B)
E = Intersect(e, h, 1)
F, G = Intersect(d, i)
j = Segment(A, E)
k = Segment(B, F)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
H = (1021.4493815104196, 35.224301147460125)
u = Vector(B, H)
v = Vector(C, H)
w = Vector(A, H)
b_2: a_2 (pomiči - 1) + a_3 + a_4
b_3: a_3 (pomiči - 2) + a_4
b_1: a_1 pomiči + a_2 + a_3 + a_4
B_1: B + b_1 u
D = Intersect(f, g, 1)
l = Segment(C, D)
F_1: F + b_1 u
C_1: C + b_1 u
a = Segment(C_1, B_1)
n = Segment(B_1, F_1)
β_1 = Angle(F_1, B_1, C_1)
C_2: C + b_2 v
D_1: D + b_2 v
A_1: A + b_2 v
p = Segment(D_1, C_2)
q = Segment(C_2, A_1)
γ_1 = Angle(D_1, C_2, A_1)
A_2: A + b_3 w
B_2: B + b_3 w
E_1: E + b_3 w
r = Segment(A_2, E_1)
c_1 = Segment(A_2, B_2)
α_1 = Angle(E_1, A_2, B_2)
T1: "α + β + γ   =  " + α + " + " + β + " + " + γ + "  =  " + (α + β + γ)
T2: "α_1 + β_1 + γ_1  =  " + α_1 + " + " + β_1 + " + " + γ_1 + "  =  " + (α_1 + β_1 + γ_1) + "
Zbroj veličina vanjskih kutova svakog trokuta je 360°."
I = (-1525.9037190755216, -812.4517730712911)
b_4: a_4 (pomiči - 3)
K = If(pomiči > 3.4, I, J)
L = If(pomiči > 3, I, J)
N = (610.5859781901065, -1132.4927398681666)
M = If(pomiči == 4, N, J)
O = If(pomiči > 3.7, Q, J)