kor_kozelitese_szabalyos_sokszogekkel
Author: K.Festarini
Date: 19 October 2013

As you move the slider, n, the number of sides of the polygon changes.  Then you can compare the area of the circle to the area of the circumscribed polygon.  The difference between the areas is shown.

n növelése

Kör területe

t_n

T_n

Nyomvonal

Kör területe

Nagyobb érték
megadása n-re:

Köré írható sokszög

Körbe írható sokszög

n =

n értéke

szög

körül

belül

A beviteli mezőben megadott értéknek 
3, vagy annál nagyobb egész számnak
kell lennie!

r = 3 (slider from 0.1 to 10, step 0.1)
n = 3 (slider from 3 to 30, step 1)
A = Intersect(xAxis, yAxis)
c = Circle(A, r)
B = Point(c)
B' = Rotate(B, (360 / n)°, A)
α = Angle(B, A, B')
poly1, b, b_1, d, e, f, g, h_1, i, j, k, l, m, p, q, a, h, s, a_1, c_1, d_1, e_1, f_1, g_1, i_1, j_1, b_3, d_3, f_3, h_3, j_3, l_3, m_3, q_3, s_3, t_3, c_4, d_4, g_4, i_4, k_4, l_4, p_4, r_4, s_4, b_5, c_5, f_5, h_5, j_5, k_5, n_5, q_5, s_5, a_6, c_6, e_6, f_6, i_6, k_6, l_6, p_6, r_6, s_6, t_6, d_7, e_7, f_7, j_7, k_7, l_7, q_7, s_7, t_7, c_8, d_8, g_8, h_8, k_8, l_8, p_8, q_8, r_8, b_9, c_9, f_9, h_9, j_9, k_9, n_{12}, q_9, r_9, a_{10}, b_{10}, e_{10}, f_{10}, g_{10}, k_{10}, l_{10}, p_{10}, q_{10}, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A_1, D_2, F_2, H_2, J_2, L_2, N_2, O_2, R_2, T_2, U_2, Z_2, A_3, D_3, F_3, H_3, I_3, L_3, N_3, O_3, R_3, S_3, V_3, Z_3, B_4, C_4, F_4, H_4, J_4, L_4, N_4, P_4, Q_4, T_4, V_4, W_4, B_5, D_5, E_5, F_5, J_5, K_5, L_5, P_5, Q_5, R_5, V_5, Z_5, A_6, D_6, E_6, H_6, I_6, L_6, M_6, P_6, Q_6, R_6, V_6, W_6, B_7, D_7, F_7, G_7, J_7, L_7, M_7, P_7, Q_7, T_7, U_7, V_7, B_8, C_8, F_8, G_8 = Polygon(B, B', n)
t = LineBisector(b)
r_{11} = Tangent(B, c)
k_1 = Tangent(B', c)
l_1 = Tangent(C, c)
B_1 = Intersect(k_1, l_1)
C_1 = Intersect(r_{11}, l_1)
D_1 = Intersect(r_{11}, k_1)
poly2, m_1, n_1, p_1, q_1, r_1, s_1, t_1, a_2, b_2, e_2, f_2, g_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_3, c_3, e_3, g_3, i_3, k_3, n_3, p_3, r_3, a_4, b_4, e_4, f_4, h_4, j_4, m_4, n_4, q_4, t_4, a_5, d_5, e_5, g_5, i_5, l_5, m_5, p_5, r_5, t_5, b_6, d_6, g_6, h_6, j_6, m_6, n_6, q_6, a_7, b_7, c_7, g_7, h_7, i_7, m_7, n_7, p_7, r_7, a_8, b_8, e_8, f_8, i_8, j_8, m_8, n_8, s_8, t_8, a_9, d_9, e_9, g_9, i_9, l_9, m_9, p_9, s_9, t_9, c_{10}, d_{10}, h_{10}, i_{10}, j_{10}, m_{10}, n_{10}, r_{10}, s_{10}, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, E_2, G_2, I_2, K_2, M_2, P_2, Q_2, S_2, V_2, W_2, B_3, C_3, E_3, G_3, J_3, K_3, M_3, P_3, Q_3, T_3, U_3, W_3, A_4, D_4, E_4, G_4, I_4, K_4, M_4, O_4, R_4, S_4, U_4, Z_4, A_5, C_5, G_5, H_5, I_5, M_5, N_5, O_5, S_5, T_5, U_5, W_5, B_6, C_6, F_6, G_6, J_6, K_6, N_6, O_6, S_6, T_6, U_6, Z_6, A_7, C_7, E_7, H_7, I_7, K_7, N_7, O_7, R_7, S_7, W_7, Z_7, A_8, D_8, E_8, H_8, I_8 = Polygon(D_1, B_1, n)
c_2 = Segment(A, D_1)
d_2 = Segment(A, B_1)
J_8 = Intersect(q_1, r_1)
Szövegpoly1: " területe = " + poly1
Pontpoly1 = PointIn(poly1)
Pontpoly2 = PointIn(poly2)
o = Area(c)
Pontc = PointIn(c)
Szövegpoly2: " területe = " + poly2 + ""
o_1 = Area(poly1)
o_2 = Area(poly2)
h1: o - o_1
h2: o_2 - o
n_9 = 30
D_9: (0, o)
t_{10} = OrthogonalLine(D_9, yAxis)
lista1: {}
E_9: (n, o_1)
T_9: (n, o_2)
n_{11} = 50 (slider from 1 to 50, step 1)
u = true
K_8 = Point(t_{10})
L_8 = Intersect(t_{10}, yAxis)
a_{11} = Ray(L_8, K_8)
β: 360 / n_9
t0: ((((n_9 * r) * r) * sin(β°))) / 2
v: o - t0
w: ((n_9 * sqrt((r / cos((β / 2)°))^(2) - (r * r))) * r)
poligon1, b_{11} = panelfent(180)
u_1: w - o
Szövegc: "" + (Name[c]) + " területe = " + o + ""
szöveg4: "eltérés: " + h1 + ""
szöveg5: "eltérés: " + h2 + ""
szöveg10: "eltérés: " + u_1 + ""
szöveg8: "eltérés: " + v + ""
z = true
v_1 = true
szöveg1: "r = " + r + " sugarú kör területe: " + o + ""
beviteliMező1 = Textfield(n_9)
A2 = 3
A3 = 4
A4: (2 * A3) - A2
A5: (2 * A4) - A3
A6: (2 * A5) - A4
A7: (2 * A6) - A5
A8: (2 * A7) - A6
A9: (2 * A8) - A7
A10: (2 * A9) - A8
A11: (2 * A10) - A9
A12: (2 * A11) - A10
A13: (2 * A12) - A11
A14: (2 * A13) - A12
A15: (2 * A14) - A13
A16: (2 * A15) - A14
A17: (2 * A16) - A15
A18: (2 * A17) - A16
A19: (2 * A18) - A17
A20: (2 * A19) - A18
A21: (2 * A20) - A19
A22: (2 * A21) - A20
A23: (2 * A22) - A21
A24: (2 * A23) - A22
A25: (2 * A24) - A23
A26: (2 * A25) - A24
A27: (2 * A26) - A25
A28: (2 * A27) - A26
B2: 360 / A2
B3: 360 / A3
B4: 360 / A4
B5: 360 / A5
B6: 360 / A6
B7: 360 / A7
B8: 360 / A8
B9: 360 / A9
B10: 360 / A10
B11: 360 / A11
B12: 360 / A12
B13: 360 / A13
B14: 360 / A14
B15: 360 / A15
B16: 360 / A16
B17: 360 / A17
B18: 360 / A18
B19: 360 / A19
B20: 360 / A20
B21: 360 / A21
B22: 360 / A22
B23: 360 / A23
B24: 360 / A24
B25: 360 / A25
B26: 360 / A26
B27: 360 / A27
B28: 360 / A28
D2: ((((A2 * r) * r) * sin(B2°))) / 2
D3: ((((A3 * r) * r) * sin(B3°))) / 2
D4: ((((A4 * r) * r) * sin(B4°))) / 2
D5: ((((A5 * r) * r) * sin(B5°))) / 2
D6: ((((A6 * r) * r) * sin(B6°))) / 2
D7: ((((A7 * r) * r) * sin(B7°))) / 2
D8: ((((A8 * r) * r) * sin(B8°))) / 2
D9: ((((A9 * r) * r) * sin(B9°))) / 2
D10: ((((A10 * r) * r) * sin(B10°))) / 2
D11: ((((A11 * r) * r) * sin(B11°))) / 2
D12: ((((A12 * r) * r) * sin(B12°))) / 2
D13: ((((A13 * r) * r) * sin(B13°))) / 2
D14: ((((A14 * r) * r) * sin(B14°))) / 2
D15: ((((A15 * r) * r) * sin(B15°))) / 2
D16: ((((A16 * r) * r) * sin(B16°))) / 2
D17: ((((A17 * r) * r) * sin(B17°))) / 2
D18: ((((A18 * r) * r) * sin(B18°))) / 2
D19: ((((A19 * r) * r) * sin(B19°))) / 2
D20: ((((A20 * r) * r) * sin(B20°))) / 2
D21: ((((A21 * r) * r) * sin(B21°))) / 2
D22: ((((A22 * r) * r) * sin(B22°))) / 2
D23: ((((A23 * r) * r) * sin(B23°))) / 2
D24: ((((A24 * r) * r) * sin(B24°))) / 2
D25: ((((A25 * r) * r) * sin(B25°))) / 2
D26: ((((A26 * r) * r) * sin(B26°))) / 2
D27: ((((A27 * r) * r) * sin(B27°))) / 2
D28: ((((A28 * r) * r) * sin(B28°))) / 2
C2: ((A2 * sqrt((r / cos((B2 / 2)°))^(2) - (r * r))) * r)
C3: ((A3 * sqrt((r / cos((B3 / 2)°))^(2) - (r * r))) * r)
C4: ((A4 * sqrt((r / cos((B4 / 2)°))^(2) - (r * r))) * r)
C5: ((A5 * sqrt((r / cos((B5 / 2)°))^(2) - (r * r))) * r)
C6: ((A6 * sqrt((r / cos((B6 / 2)°))^(2) - (r * r))) * r)
C7: ((A7 * sqrt((r / cos((B7 / 2)°))^(2) - (r * r))) * r)
C8: ((A8 * sqrt((r / cos((B8 / 2)°))^(2) - (r * r))) * r)
C9: ((A9 * sqrt((r / cos((B9 / 2)°))^(2) - (r * r))) * r)
C10: ((A10 * sqrt((r / cos((B10 / 2)°))^(2) - (r * r))) * r)
C11: ((A11 * sqrt((r / cos((B11 / 2)°))^(2) - (r * r))) * r)
C12: ((A12 * sqrt((r / cos((B12 / 2)°))^(2) - (r * r))) * r)
C13: ((A13 * sqrt((r / cos((B13 / 2)°))^(2) - (r * r))) * r)
C14: ((A14 * sqrt((r / cos((B14 / 2)°))^(2) - (r * r))) * r)
C15: ((A15 * sqrt((r / cos((B15 / 2)°))^(2) - (r * r))) * r)
C16: ((A16 * sqrt((r / cos((B16 / 2)°))^(2) - (r * r))) * r)
C17: ((A17 * sqrt((r / cos((B17 / 2)°))^(2) - (r * r))) * r)
C18: ((A18 * sqrt((r / cos((B18 / 2)°))^(2) - (r * r))) * r)
C19: ((A19 * sqrt((r / cos((B19 / 2)°))^(2) - (r * r))) * r)
C20: ((A20 * sqrt((r / cos((B20 / 2)°))^(2) - (r * r))) * r)
C21: ((A21 * sqrt((r / cos((B21 / 2)°))^(2) - (r * r))) * r)
C22: ((A22 * sqrt((r / cos((B22 / 2)°))^(2) - (r * r))) * r)
C23: ((A23 * sqrt((r / cos((B23 / 2)°))^(2) - (r * r))) * r)
C24: ((A24 * sqrt((r / cos((B24 / 2)°))^(2) - (r * r))) * r)
C25: ((A25 * sqrt((r / cos((B25 / 2)°))^(2) - (r * r))) * r)
C26: ((A26 * sqrt((r / cos((B26 / 2)°))^(2) - (r * r))) * r)
C27: ((A27 * sqrt((r / cos((B27 / 2)°))^(2) - (r * r))) * r)
C28: ((A28 * sqrt((r / cos((B28 / 2)°))^(2) - (r * r))) * r)
M_8: (A2, C2)
N_8: (A3, C3)
O_8: (A4, C4)
P_8: (A5, C5)
Q_8: (A6, C6)
R_8: (A7, C7)
S_8: (A8, C8)
T_8: (A9, C9)
U_8: (A10, C10)
V_8: (A11, C11)
W_8: (A12, C12)
Z_8: (A13, C13)
A_9: (A14, C14)
B_9: (A15, C15)
C_9: (A16, C16)
F_9: (A17, C17)
G_9: (A18, C18)
H_9: (A19, C19)
I_9: (A20, C20)
J_9: (A21, C21)
K_9: (A22, C22)
L_9: (A23, C23)
M_9: (A24, C24)
N_9: (A25, C25)
O_9: (A26, C26)
P_9: (A27, C27)
Q_9: (A28, C28)
lista2: {M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9}
R_9: (A2, D2)
S_9: (A3, D3)
U_9: (A4, D4)
V_9: (A5, D5)
W_9: (A6, D6)
Z_9: (A7, D7)
A_{10}: (A8, D8)
B_{10}: (A9, D9)
C_{10}: (A10, D10)
D_{10}: (A11, D11)
E_{10}: (A12, D12)
F_{10}: (A13, D13)
G_{10}: (A14, D14)
H_{10}: (A15, D15)
I_{10}: (A16, D16)
J_{10}: (A17, D17)
K_{10}: (A18, D18)
L_{10}: (A19, D19)
M_{10}: (A20, D20)
N_{10}: (A21, D21)
O_{10}: (A22, D22)
P_{10}: (A23, D23)
Q_{10}: (A24, D24)
R_{10}: (A25, D25)
S_{10}: (A26, D26)
T_{10}: (A27, D27)
U_{10}: (A28, D28)
lista3: {R_9, S_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}}
V_{10} = Point(a_{11})
szöveg11: "" + o + ""
szöveg2_1: "Beírt " + n + "-szög területe: " + o_1 + ""
szöveg3_1: "Körülírt " + n + "-szög területe: " + o_2 + ""
szöveg7_1: "Beírt szabályos " + n_9 + "-szög területe: " + t0 + ""
szöveg9_1: "Körülírt szabályos " + n_9 + "-szög területe: " + w + ""

Tool: fixpont
szam,szam
Input: u, v
Output: P

P: (x(Corner[4]) + (u / x(Corner[5]) * (x(Corner[3]) - x(Corner[4]))), y(Corner[4]) - (v / y(Corner[5]) * (y(Corner[4]) - y(Corner[1]))))

Tool: panelfent
szam
Input: a
Output: poligon, s

A = fixpont(0, a)
B = fixpont(x(Corner[5]), a)
s = Segment(A, B)
poligon, b, c, a_1, b_1 = Polygon(Corner[3], Corner[4], A, B)

Tool: fixpont (command fixpont1)
szam,szam
Input: u, v
Output: P

P: (x(Corner[4]) + (u / x(Corner[5]) * (x(Corner[3]) - x(Corner[4]))), y(Corner[4]) - (v / y(Corner[5]) * (y(Corner[4]) - y(Corner[1]))))

Tool: panelfent (command panelfent1)
szam
Input: a
Output: poligon, s

A = fixpont(0, a)
B = fixpont(x(Corner[5]), a)
s = Segment(A, B)
poligon, b, c, a_1, b_1 = Polygon(Corner[3], Corner[4], A, B)