□ ACDE a □ ABGF sú štvorce

Transformácia

obsah

strana

výška

Ďalší postup

1. Zostrojíme rovnobežník BAEJ pre d = 10

3. Zostrojíme rovnobežník FACK pre d = 20

K

A: (-8, -2)
B: (2, -2)
c_1 = Line(A, B)
o = Semicircle(A, B)
AC = 6 (slider from 4 to 7, step 0.1)
c_2 = Circle(A, AC)
C = Intersect(o, c_2, 1)
t1, c, a, b = Polygon(A, B, C)
text3: "Trojuholník ABC je pravouhlý s odvesnami b = " + AC + ", a = " + a + ""
mnohouholník1, h, i, j, k, D, E = Polygon(A, C, 4)
mnohouholník2, l, m, n, p, F, G = Polygon(B, A, 4)
r = Line(C, B)
d = 1.65 (slider from 0 to 30, step 0.05)
e = If(0.01 ≤ d ≤ 10, d / 10, 0)
f = If(10.01 ≤ d ≤ 20, (d - 10) / 10, 0)
g = If(20.01 ≤ d ≤ 30, (d - 20) / 10, 0)
text5: "Čísla d = " + d + ", e = " + e + " , f = " + f + ", g = " + g + " sú parametre transformácie"
q = Circle(D, (e * a))
H = Intersect(q, r, 2)
s = Line(E, H)
t = Line(A, s)
text6: "Pre 0 ≤ d < 10 zostrojíme pomocou kružnice q(D, " + e + " * " + a + ") bod H"
I = Intersect(r, t)
q1, a_1, i_1, h_1, e_1 = Polygon(A, I, H, E)
g_1 = Line(E, A)
k_0 = OrthogonalLine(H, g_1)
H_0 = Intersect(k_0, g_1)
k_1 = Segment(H, H_0)
f_1 = Line(E, c_1)
J = Intersect(f_1, r)
q2, a_2, b_1, j_1, e_2 = Polygon(A, B, J, E)
φ: (f * 90°)
A' = Rotate(A, (-φ), A)
B' = Rotate(B, (-φ), A)
J' = Rotate(J, (-φ), A)
E' = Rotate(E, (-φ), A)
text7: "2. Pre d > 10 otáčame BAEJ okolo A o uhol φ = " + φ + ""
q2', a', b', j', e' = Polygon(A', B', J', E')
l_1 = Line(A, F)
m_1 = Line(C, l_1)
n_1 = Line(A, C)
p_1 = Line(F, n_1)
K = Intersect(m_1, p_1)
q3, f_2, a_3, c_3, k_2 = Polygon(F, A, C, K)
q_1 = Line(F, G)
L = Intersect(q_1, m_1)
r_1 = Segment(K, L)
r_2: (g * Length[r_1])
d_1 = Circle(K, r_2)
M = Intersect(d_1, m_1, 2)
s_1 = Line(F, M)
t_1 = Line(A, s_1)
N = Intersect(m_1, t_1)
u = Vector(M, L)
q4, f_3, m_2, n_2, a_4 = Polygon(F, M, N, A)
text9: "4. Pre d > 20 posúvame bod K do bodu L pomocou g = " + g + ""