Author: A.M.Vuković
Date: 2009.

Vrsta trokuta

Pomiči t pomoću miša ili strelica na tipkovnici

Aleksandra-Maria Vuković, 2011.

A = (-3, -2)
B = (4, -2)
C = (2.5, 2.5)
mnogokut1, c, a, b = Polygon(A, B, C)
β = Angle(A, B, C)
α = Angle(C, A, B)
γ = Angle(A, C, B)
d = Circle(A, 2)
e = Circle(B, 2)
f = Circle(C, 2)
D = Intersect(d, b)
E = Intersect(d, c)
F = Intersect(e, c)
G = Intersect(e, a)
H = Intersect(f, b)
I = Intersect(f, a)
u = Vector(A, C)
t = 0 (slider from 0 to 4, step 0.1)
A' = If(t ≤ 1, Translate[A, Vector[t * u]], Translate[A, u])
D' = If(t ≤ 1, Translate[D, Vector[t * u]], Translate[D, u])
E' = If(t ≤ 1, Translate[E, Vector[t * u]], Translate[E, u])
g = Segment(A', D')
h = Segment(A', E')
δ = Angle(D', A', E')
tekst1: "α = " + α
v = Vector(B, C)
B' = If(t ≤ 1, Translate[B, Vector[0 * v]], If[(t > 1) ∧ (t ≤ 2), Translate[B, Vector[(t - 1) * v]], Translate[B, v]])
G' = If(t ≤ 1, Translate[G, Vector[0 * v]], If[(t > 1) ∧ (t ≤ 2), Translate[G, Vector[(t - 1) * v]], Translate[G, v]])
F' = If(t ≤ 1, Translate[F, Vector[0 * v]], If[(t > 1) ∧ (t ≤ 2), Translate[F, Vector[(t - 1) * v]], Translate[F, v]])
i = Segment(G', B')
j = Segment(F', B')
ε = Angle(F', B', G')
tekst2: "β = " + β
I' = If(t ≤ 2, Rotate[I, 0*°, C], If[(t > 2) ∧ (t ≤ 3), Rotate[I, ((t - 2) * 180)°, C], Rotate[I, 180*°, C]])
H' = If(t ≤ 2, Rotate[H, 0*°, C], If[(t > 2) ∧ (t ≤ 3), Rotate[H, ((t - 2) * 180)°, C], Rotate[H, 180*°, C]])
l = Segment(C, I')
ζ = Angle(H', C, I')
tekst3: "γ = " + γ
tekst4 = If(t ≤ 3, Text[""], If[(t > 3) ∧ (t < 4), Text["α + β + γ = ???"], Text["α + β + γ = 180°"]])
P_b = Midpoint(b)
P_c = Midpoint(c)
P_a = Midpoint(a)
k = 1 (slider from -5 to 5, step 0.1)
zaokr_a: floor(10^(k) * a + 0.5) / 10^(k)
zaokr_b: floor(10^(k) * b + 0.5) / 10^(k)
zaokr_c: floor(10^(k) * c + 0.5) / 10^(k)
tekst6 = If((γ < 90°) ∧ (α < 90°) ∧ (β < 90°), "šiljastokutan", If[γ ≟ 90° ∨ α ≟ 90° ∨ β ≟ 90°, "pravokutan", "tupokutan"])
tekst7 = If((zaokr_a ≠ zaokr_b) ∧ (zaokr_a ≠ zaokr_c) ∧ (zaokr_b ≠ zaokr_c), "raznostraničan", If[zaokr_a ≟ zaokr_b ∧ zaokr_a ≟ zaokr_c ∧ zaokr_b ≟ zaokr_c, "jednakostraničan", "jednakokračan"])