Külgede arv

Külje pikkus

Ümbermõõt

S_n

Valemi indeks n

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.

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

\ovalbox{
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}.}

\ovalbox{
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_0}

Kochi lumehelbe ümbermõõt ja pindala

B2: 3
C2: 1
D2: 3
A2: 0
A3: 1
E2: sqrt(3) / 4
E3: E2 + (B2 * $E$2 / 9^(A3))
A4 = 2
A5 = 3
A6 = 4
A7 = 5
A8 = 6
A9 = 7
A10 = 8
A11 = 9
A12 = 10
A13 = 11
A14 = 12
A15 = 13
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)
C3: C2 / 3
C4: C3 / 3
C5: C4 / 3
C6: C5 / 3
C7: C6 / 3
C8: C7 / 3
C9: C8 / 3
C10: C9 / 3
C11: C10 / 3
C12: C11 / 3
C13: C12 / 3
C14: C13 / 3
C15: C14 / 3
C16: C15 / 3
D3: (D2 * 4 / 3)
D4: (D3 * 4 / 3)
D5: (D4 * 4 / 3)
D6: (D5 * 4 / 3)
D7: (D6 * 4 / 3)
D8: (D7 * 4 / 3)
D9: (D8 * 4 / 3)
D10: (D9 * 4 / 3)
D11: (D10 * 4 / 3)
D12: (D11 * 4 / 3)
D13: (D12 * 4 / 3)
D14: (D13 * 4 / 3)
D15: (D14 * 4 / 3)
D16: (D15 * 4 / 3)
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))
A16 = 14
A17 = 15
B17: (B16 * 4)
C17: C16 / 3
D17: (D16 * 4 / 3)
E16: E15 + (B15 * $E$2 / 9^(A16))
E17: E16 + (B16 * $E$2 / 9^(A17))
A = (1.7320508075688772, 3.222222222222222)
B = (2.598076211353316, 2.722222222222222)
C = (2.598076211353316, 3.722222222222222)
t1, c, a, b = Polygon(A, B, C)
D = (2.694301256218253, 3.222222222222222)
E = (3.5603266600026915, 2.722222222222222)
F = (3.5603266600026915, 3.722222222222222)
t2, f, d, e = Polygon(D, E, F)
G = Point(f)
H = (2.982976390813066, 2.722222222222222)
I = Point(f)
J = Point(e)
K = (2.982976390813066, 3.722222222222222)
L = Point(e)
M = Point(d)
N = (3.849001794597505, 3.222222222222222)
O = Point(d)
hulknurk1, d_1, g, h, i, e_1, o, n, m, f_1, j, k, l = Polygon(D, G, H, I, E, O, N, M, F, J, K, L)
u = Vector((0, 0), (12 / 9, 0))
D' = Translate(D, u)
G' = Translate(G, u)
H' = Translate(H, u)
I' = Translate(I, u)
E' = Translate(E, u)
O' = Translate(O, u)
N' = Translate(N, u)
M' = Translate(M, u)
F' = Translate(F, u)
J' = Translate(J, u)
K' = Translate(K, u)
L' = Translate(L, u)
hulknurk1', d', g', h', i', e', o', n', m', f', j', k', l' = Polygon(D', G', H', I', E', O', N', M', F', J', K', L')
P = (4.137676929192317, 3.166666666666666)
Q = (4.137676929192317, 3.0555555555555554)
R = (4.233901974057255, 3.1111111111111107)
S = (4.330127018922192, 2.944444444444444)
T = (4.233901974057255, 2.888888888888889)
U = (4.330127018922192, 2.833333333333333)
V = (4.42635206378713, 2.7777777777777777)
W = (4.522577108652068, 2.722222222222222)
Z = (4.522577108652068, 2.833333333333333)
A_1 = (4.715027198381943, 2.833333333333333)
B_1 = (4.715027198381943, 2.722222222222222)
C_1 = (4.811252243246881, 2.7777777777777777)
D_1 = (4.907477288111818, 2.833333333333333)
E_1 = (5.003702332976756, 2.888888888888889)
F_1 = (4.907477288111818, 2.944444444444444)
G_1 = (5.003702332976756, 3.1111111111111107)
H_1 = (5.099927377841693, 3.0555555555555554)
I_1 = (5.099927377841693, 3.166666666666666)
J_1 = (5.099927377841693, 3.2777777777777772)
K_1 = (5.099927377841693, 3.3888888888888884)
L_1 = (5.003702332976756, 3.333333333333333)
M_1 = (4.907477288111818, 3.5)
N_1 = (5.003702332976756, 3.5555555555555554)
O_1 = (4.907477288111818, 3.6111111111111107)
P_1 = (4.811252243246881, 3.6666666666666665)
Q_1 = (4.715027198381943, 3.722222222222222)
R_1 = (4.715027198381943, 3.6111111111111107)
S_1 = (4.522577108652068, 3.6111111111111107)
T_1 = (4.522577108652068, 3.722222222222222)
U_1 = (4.42635206378713, 3.6666666666666665)
V_1 = (4.330127018922192, 3.6111111111111107)
W_1 = (4.233901974057255, 3.5555555555555554)
Z_1 = (4.330127018922192, 3.5)
A_2 = (4.233901974057255, 3.333333333333333)
B_2 = (4.137676929192317, 3.3888888888888884)
C_2 = (4.137676929192317, 3.2777777777777772)
hulknurk2, p, p_1, q, r, s, s_1, t, u_1, g_1, v, w, z_1, h_1, a_1, b_1, c_1, i_1, j_1, k_1, l_1, m_1, n_1, q_1, r_1, t_1, f_2, g_2, h_2, i_2, j_2, k_2, o_1, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_2, v_1, w_1, b_2, c_2, d_2, e_2, f_3 = Polygon(D', P, Q, R, G', S, T, U, H', V, W, Z, I', A_1, B_1, C_1, E', D_1, E_1, F_1, O', G_1, H_1, I_1, N', J_1, K_1, L_1, M', M_1, N_1, O_1, F', P_1, Q_1, R_1, J', S_1, T_1, U_1, K', V_1, W_1, Z_1, L', A_2, B_2, C_2)
t3, f_4, d_3, e_3 = Polygon(D, E, F)
D'_1 = Translate(D, u)
G'_1 = Translate(G, u)
H'_1 = Translate(H, u)
I'_1 = Translate(I, u)
E'_1 = Translate(E, u)
O'_1 = Translate(O, u)
N'_1 = Translate(N, u)
M'_1 = Translate(M, u)
F'_1 = Translate(F, u)
J'_1 = Translate(J, u)
K'_1 = Translate(K, u)
L'_1 = Translate(L, u)
hulknurk1'_1, d'_1, g'_1, h'_1, i'_1, e'_1, o'_1, n'_1, m'_1, f'_1, j'_1, k'_1, l'_1 = Polygon(D'_1, G'_1, H'_1, I'_1, E'_1, O'_1, N'_1, M'_1, F'_1, J'_1, K'_1, L'_1)
Export_1 = (1.4858889763808283, 4.431871238676486)
Export_2 = (5.558247916100563, 2.022684753863847)