Valemi indeks n

Külgede arv

Külje pikkus

Ümbermõõt

S_n

\ovalbox{K_0=3;  \; L_0=1;  \; Ü_0=3;\S_0=\frac{1}{2}·1·1\frac{\sqrt{3}}{4}=\frac{\sqrt{3}}{4}}

Tähised:
K_i −i−nda hulknurga külgede arv; L_i−i−nda hulknurga külje pikkus;
Ü_i−i−nda hulknurga ümbermõõt; S_i−i−nda hulknurga pindala.

\fbox{K_1=4·K_0=12; \;  L_1=\frac{1}{3}·L_0=\frac{1}{3}; \; Ü_1=\frac{4}{3} ·Ü_0=4;\S_1=S_0+\frac{K_0}{9}·S_0=\frac{\sqrt{3}}{4}+\frac{3}{9}·\frac{\sqrt{3}}{4}=\frac{\sqrt{3}}{3}.}

\doublebox{K_n=4·K_{n-1} \; L_n=\frac{1}{3}·L_{n-1} \; Ü_n=\frac{4}{3}·Ü_{n-1}\S_n=S_{n-1}+\frac{K_{n-1}}{9^n}·S_0x}

A2: 0
A3: 1
A4 = 2
A5 = 3
A6 = 4
A7 = 5
A8 = 6
A9 = 7
A10 = 8
A11 = 9
A12 = 10
A13 = 11
A14 = 12
A15 = 13
A16 = 14
A17 = 15
B2: 3
B3: (B2 * 4)
B4: (B3 * 4)
B5: (B4 * 4)
B6: (B5 * 4)
B7: (B6 * 4)
B8: (B7 * 4)
B9: (B8 * 4)
B10: (B9 * 4)
B11: (B10 * 4)
B12: (B11 * 4)
B13: (B12 * 4)
B14: (B13 * 4)
B15: (B14 * 4)
B16: (B15 * 4)
B17: (B16 * 4)
C2: 1
C3: (1 / 3 * C2)
C4: (1 / 3 * C3)
C5: (1 / 3 * C4)
C6: (1 / 3 * C5)
C7: (1 / 3 * C6)
C8: (1 / 3 * C7)
C9: (1 / 3 * C8)
C10: (1 / 3 * C9)
C11: (1 / 3 * C10)
C12: (1 / 3 * C11)
C13: (1 / 3 * C12)
C14: (1 / 3 * C13)
C15: (1 / 3 * C14)
C16: (1 / 3 * C15)
C17: (1 / 3 * C16)
D2: (C2 * B2)
D3: (C3 * B3)
D4: (C4 * B4)
D5: (C5 * B5)
D6: (C6 * B6)
D7: (C7 * B7)
D8: (C8 * B8)
D9: (C9 * B9)
D10: (C10 * B10)
D11: (C11 * B11)
D12: (C12 * B12)
D13: (C13 * B13)
D14: (C14 * B14)
D15: (C15 * B15)
D16: (C16 * B16)
D17: (C17 * B17)
E2: 3^(1 / 2) / 4
E3: E2 + (B2 * $E$2 / 9^(A3))
E4: E3 + (B3 * $E$2 / 9^(A4))
E5: E4 + (B4 * $E$2 / 9^(A5))
E6: E5 + (B5 * $E$2 / 9^(A6))
E7: E6 + (B6 * $E$2 / 9^(A7))
E8: E7 + (B7 * $E$2 / 9^(A8))
E9: E8 + (B8 * $E$2 / 9^(A9))
E10: E9 + (B9 * $E$2 / 9^(A10))
E11: E10 + (B10 * $E$2 / 9^(A11))
E12: E11 + (B11 * $E$2 / 9^(A12))
E13: E12 + (B12 * $E$2 / 9^(A13))
E14: E13 + (B13 * $E$2 / 9^(A14))
E15: E14 + (B14 * $E$2 / 9^(A15))
E16: E15 + (B15 * $E$2 / 9^(A16))
E17: E16 + (B16 * $E$2 / 9^(A17))
A = Point(yAxis)
B = (7.794228634059947, 4.5)
C = (7.794228634059947, 13.5)
t1, c, b, a = Polygon(B, A, C)
D = (8.660254037844386, 9)
u = Vector(A, D)
A' = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
E = (11.258330249197702, 7.5)
F = (11.258330249197702, 4.5)
G = (13.856406460551018, 6)
H = (16.454482671904334, 7.5)
I = (19.05255888325765, 9)
J = (16.454482671904334, 10.5)
K = (13.856406460551018, 12)
L = (11.258330249197702, 13.5)
M = (11.258330249197702, 10.5)
hulknurk1, a', e, f, g, b', h, i, j, c', k, l, m = Polygon(A', E, F, G, B', H, I, J, C', K, L, M)
t2, n, p, q = Polygon(C', A', B')
N = (20.784609690826528, 9)
v = Vector(A', N)
A'' = Translate(A', v)
E' = Translate(E, v)
F' = Translate(F, v)
G' = Translate(G, v)
B'' = Translate(B', v)
H' = Translate(H, v)
I' = Translate(I, v)
J' = Translate(J, v)
C'' = Translate(C', v)
K' = Translate(K, v)
L' = Translate(L, v)
M' = Translate(M, v)
hulknurk1', a'', e', f', g', b'', h', i', j', c'', k', l', m' = Polygon(A'', E', F', G', B'', H', I', J', C'', K', L', M')
O = (21.650635094610966, 8.5)
P = (21.650635094610966, 7.5)
Q = (22.516660498395403, 8)
R = (23.38268590217984, 6.5)
S = (22.516660498395403, 6)
T = (23.38268590217984, 5.5)
U = (24.24871130596428, 5)
V = (25.11473670974872, 4.5)
W = (25.11473670974872, 5.5)
Z = (26.846787517317598, 5.5)
A_1 = (26.846787517317598, 4.5)
B_1 = (27.712812921102035, 5)
C_1 = (28.578838324886473, 5.5)
D_1 = (29.444863728670914, 6)
E_1 = (28.578838324886473, 6.5)
F_1 = (29.444863728670914, 8)
G_1 = (30.31088913245535, 7.5)
H_1 = (30.31088913245535, 8.5)
I_1 = (30.31088913245535, 9.5)
J_1 = (30.31088913245535, 10.5)
K_1 = (29.444863728670914, 10)
L_1 = (28.578838324886473, 11.5)
M_1 = (29.444863728670914, 12)
N_1 = (28.578838324886473, 12.5)
O_1 = (27.712812921102035, 13)
P_1 = (26.846787517317598, 13.5)
Q_1 = (26.846787517317598, 12.5)
R_1 = (25.11473670974872, 12.5)
S_1 = (25.11473670974872, 13.5)
T_1 = (24.24871130596428, 13)
U_1 = (23.38268590217984, 12.5)
V_1 = (22.516660498395403, 12)
W_1 = (23.38268590217984, 11.5)
Z_1 = (22.516660498395403, 10)
A_2 = (21.650635094610966, 10.5)
B_2 = (21.650635094610966, 9.5)
hulknurk2, r, o, p_1, q_1, s, r_1, s_1, t, d, u_1, v_1, w, f_1, z_1, a_1, b_1, g_1, c_1, d_1, e_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, t_1, f_2, g_2, h_2, i_2, j_2, o_1, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, w_1, a_2, b_2, c_2, d_2 = Polygon(A'', O, P, Q, E', R, S, T, F', U, V, W, G', Z, A_1, B_1, B'', C_1, D_1, E_1, H', F_1, G_1, H_1, I', I_1, J_1, K_1, J', L_1, M_1, N_1, C'', O_1, P_1, Q_1, K', R_1, S_1, T_1, L', U_1, V_1, W_1, M', Z_1, A_2, B_2)
A''_{1} = Translate(A', v)
E'_{1} = Translate(E, v)
F'_{1} = Translate(F, v)
G'_{1} = Translate(G, v)
B''_{1} = Translate(B', v)
H'_{1} = Translate(H, v)
I'_{1} = Translate(I, v)
J'_{1} = Translate(J, v)
C''_{1} = Translate(C', v)
K'_{1} = Translate(K, v)
L'_{1} = Translate(L, v)
M'_{1} = Translate(M, v)
hulknurk1'_{1}, a''_{1}, e'_{1}, f'_{1}, g'_{1}, b''_{1}, h'_{1}, i'_{1}, j'_{1}, c''_{1}, k'_{1}, l'_{1}, m'_{1} = Polygon(A''_{1}, E'_{1}, F'_{1}, G'_{1}, B''_{1}, H'_{1}, I'_{1}, J'_{1}, C''_{1}, K'_{1}, L'_{1}, M'_{1})