Àrea del cercle

Move o esvarador " n " para modificar o número de lados do polígono
Move o esvarador " r " para modificar o radio da circunferencia
Move o esvarador " 1º movemento " para descompoñer o polígono en triángulos, e aparecerache outro esvarador 
Move o esvarador " 2º movemento " para descompoñer os triángulos nun rectángulo e aparecerache outro esvarador
Move o esvarador " 3º movemento " para dobrar o rectángulo e reducir a súa base a metade
Observa como se modifican os textos, e como a maior número de lados, a área círculo queda cuberta pola área do polígono en máis do 95 %

2º movemento

1º movemento

3º movemento

r

π ·r

mov2 = 0 (slider from 0 to 1, step 0.01)
A1 = 0
A2: A1 + 1
mov1 = 0 (slider from 0 to 1, step 0.01)
n = 9 (slider from 3 to 30, step 1)
α: (180 * ° / n)
r = 4 (slider from 1 to 4, step 0.5)
O: (0, r)
c = Circle(O, r)
A = Point(c)
B1: A
llista1 = Sequence(Rotate[A, ((2 * s) * α), O], s, 0, n, 1)
llista4 = Sequence(Vector[Midpoint[Element[llista1, s], Element[llista1, s + 1]], O], s, 1, n)
llista5 = Sequence(Vector[Rotate[Element[llista4, s], ((((-2 * s) + 1) * mov1) * α)]], s, 1, n)
llista2 = Sequence(Vector[Element[llista1, s], Element[llista1, s + 1]], s, 1, n)
llista3 = Sequence(Vector[Rotate[Element[llista2, s], ((((-2 * s) + 1) * mov1) * α)]], s, 1, n)
B2: B1 + Element[llista3, A2]
C1: Midpoint[B1, B2] + Element[llista5, A2]
I1 = Midpoint(C1, B2)
H1 = Midpoint(B1, C1)
J1 = Midpoint(H1, I1)
a = Segment(O, A)
base: ((2 * r) * sin((180 * ° / n)))
d = Circle(A, base)
k = OrthogonalLine(A, a)
A3: A2 + 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
A11: A10 + 1
A12: A11 + 1
A13: A12 + 1
A14: A13 + 1
A15: A14 + 1
A16: A15 + 1
A17: A16 + 1
A18: A17 + 1
A19: A18 + 1
A20: A19 + 1
A21: A20 + 1
A22: A21 + 1
A23: A22 + 1
A24: A23 + 1
A25: A24 + 1
A26: A25 + 1
B3: B2 + Element[llista3, A3]
B4: B3 + Element[llista3, A4]
B5: B4 + Element[llista3, A5]
B6: B5 + Element[llista3, A6]
B7: B6 + Element[llista3, A7]
B8: B7 + Element[llista3, A8]
B9: B8 + Element[llista3, A9]
B10: B9 + Element[llista3, A10]
B11: B10 + Element[llista3, A11]
B12: B11 + Element[llista3, A12]
B13: B12 + Element[llista3, A13]
B14: B13 + Element[llista3, A14]
B15: B14 + Element[llista3, A15]
B16: B15 + Element[llista3, A16]
B17: B16 + Element[llista3, A17]
B18: B17 + Element[llista3, A18]
B19: B18 + Element[llista3, A19]
B20: B19 + Element[llista3, A20]
B21: B20 + Element[llista3, A21]
B22: B21 + Element[llista3, A22]
B23: B22 + Element[llista3, A23]
B24: B23 + Element[llista3, A24]
B25: B24 + Element[llista3, A25]
B26: B25 + Element[llista3, A26]
apotema: (r * cos((180 * ° / n)))
C2: Midpoint[B2, B3] + Element[llista5, A3]
C3: Midpoint[B3, B4] + Element[llista5, A4]
C4: Midpoint[B4, B5] + Element[llista5, A5]
C5: Midpoint[B5, B6] + Element[llista5, A6]
C6: Midpoint[B6, B7] + Element[llista5, A7]
C7: Midpoint[B7, B8] + Element[llista5, A8]
C8: Midpoint[B8, B9] + Element[llista5, A9]
C9: Midpoint[B9, B10] + Element[llista5, A10]
C10: Midpoint[B10, B11] + Element[llista5, A11]
C11: Midpoint[B11, B12] + Element[llista5, A12]
C12: Midpoint[B12, B13] + Element[llista5, A13]
C13: Midpoint[B13, B14] + Element[llista5, A14]
C14: Midpoint[B14, B15] + Element[llista5, A15]
C15: Midpoint[B15, B16] + Element[llista5, A16]
C16: Midpoint[B16, B17] + Element[llista5, A17]
C17: Midpoint[B17, B18] + Element[llista5, A18]
C18: Midpoint[B18, B19] + Element[llista5, A19]
C19: Midpoint[B19, B20] + Element[llista5, A20]
C20: Midpoint[B20, B21] + Element[llista5, A21]
C21: Midpoint[B21, B22] + Element[llista5, A22]
C22: Midpoint[B22, B23] + Element[llista5, A23]
C23: Midpoint[B23, B24] + Element[llista5, A24]
C24: Midpoint[B24, B25] + Element[llista5, A25]
C25: Midpoint[B25, B26] + Element[llista5, A26]
D1, E1, F1, G1 = Polygon(B1, B2, C1)
D2, E2, F2, G2 = Polygon(B2, B3, C2)
D3, E3, F3, G3 = Polygon(B3, B4, C3)
D4, E4, F4, G4 = Polygon(B4, B5, C4)
D5, E5, F5, G5 = Polygon(B5, B6, C5)
D6, E6, F6, G6 = Polygon(B6, B7, C6)
D7, E7, F7, G7 = Polygon(B7, B8, C7)
D8, E8, F8, G8 = Polygon(B8, B9, C8)
D9, E9, F9, G9 = Polygon(B9, B10, C9)
D10, E10, F10, G10 = Polygon(B10, B11, C10)
D11, E11, F11, G11 = Polygon(B11, B12, C11)
D12, E12, F12, G12 = Polygon(B12, B13, C12)
D13, E13, F13, G13 = Polygon(B13, B14, C13)
D14, E14, F14, G14 = Polygon(B14, B15, C14)
D15, E15, F15, G15 = Polygon(B15, B16, C15)
D16, E16, F16, G16 = Polygon(B16, B17, C16)
D17, E17, F17, G17 = Polygon(B17, B18, C17)
D18, E18, F18, G18 = Polygon(B18, B19, C18)
D19, E19, F19, G19 = Polygon(B19, B20, C19)
D20, E20, F20, G20 = Polygon(B20, B21, C20)
D21, E21, F21, G21 = Polygon(B21, B22, C21)
D22, E22, F22, G22 = Polygon(B22, B23, C22)
D23, E23, F23, G23 = Polygon(B23, B24, C23)
D24, E24, F24, G24 = Polygon(B24, B25, C24)
D25, E25, F25, G25 = Polygon(B25, B26, C25)
H2 = Midpoint(B2, C2)
H3 = Midpoint(B3, C3)
H4 = Midpoint(B4, C4)
H5 = Midpoint(B5, C5)
H6 = Midpoint(B6, C6)
H7 = Midpoint(B7, C7)
H8 = Midpoint(B8, C8)
H9 = Midpoint(B9, C9)
H10 = Midpoint(B10, C10)
H11 = Midpoint(B11, C11)
H12 = Midpoint(B12, C12)
H13 = Midpoint(B13, C13)
H14 = Midpoint(B14, C14)
H15 = Midpoint(B15, C15)
H16 = Midpoint(B16, C16)
H17 = Midpoint(B17, C17)
H18 = Midpoint(B18, C18)
H19 = Midpoint(B19, C19)
H20 = Midpoint(B20, C20)
H21 = Midpoint(B21, C21)
H22 = Midpoint(B22, C22)
H23 = Midpoint(B23, C23)
H24 = Midpoint(B24, C24)
H25 = Midpoint(B25, C25)
I2 = Midpoint(C2, B3)
I3 = Midpoint(C3, B4)
I4 = Midpoint(C4, B5)
I5 = Midpoint(C5, B6)
I6 = Midpoint(C6, B7)
I7 = Midpoint(C7, B8)
I8 = Midpoint(C8, B9)
I9 = Midpoint(C9, B10)
I10 = Midpoint(C10, B11)
I11 = Midpoint(C11, B12)
I12 = Midpoint(C12, B13)
I13 = Midpoint(C13, B14)
I14 = Midpoint(C14, B15)
I15 = Midpoint(C15, B16)
I16 = Midpoint(C16, B17)
I17 = Midpoint(C17, B18)
I18 = Midpoint(C18, B19)
I19 = Midpoint(C19, B20)
I20 = Midpoint(C20, B21)
I21 = Midpoint(C21, B22)
I22 = Midpoint(C22, B23)
I23 = Midpoint(C23, B24)
I24 = Midpoint(C24, B25)
I25 = Midpoint(C25, B26)
J2 = Midpoint(H2, I2)
J3 = Midpoint(H3, I3)
J4 = Midpoint(H4, I4)
J5 = Midpoint(H5, I5)
J6 = Midpoint(H6, I6)
J7 = Midpoint(H7, I7)
J8 = Midpoint(H8, I8)
J9 = Midpoint(H9, I9)
J10 = Midpoint(H10, I10)
J11 = Midpoint(H11, I11)
J12 = Midpoint(H12, I12)
J13 = Midpoint(H13, I13)
J14 = Midpoint(H14, I14)
J15 = Midpoint(H15, I15)
J16 = Midpoint(H16, I16)
J17 = Midpoint(H17, I17)
J18 = Midpoint(H18, I18)
J19 = Midpoint(H19, I19)
J20 = Midpoint(H20, I20)
J21 = Midpoint(H21, I21)
J22 = Midpoint(H22, I22)
J23 = Midpoint(H23, I23)
J24 = Midpoint(H24, I24)
J25 = Midpoint(H25, I25)
K1, L1, M1, N1, O1 = Polygon(B1, H1, I1, B2)
K2, L2, M2, N2, O2 = Polygon(B2, H2, I2, B3)
K3, L3, M3, N3, O3 = Polygon(B3, H3, I3, B4)
K4, L4, M4, N4, O4 = Polygon(B4, H4, I4, B5)
K5, L5, M5, N5, O5 = Polygon(B5, H5, I5, B6)
K6, L6, M6, N6, O6 = Polygon(B6, H6, I6, B7)
K7, L7, M7, N7, O7 = Polygon(B7, H7, I7, B8)
K8, L8, M8, N8, O8 = Polygon(B8, H8, I8, B9)
K9, L9, M9, N9, O9 = Polygon(B9, H9, I9, B10)
K10, L10, M10, N10, O10 = Polygon(B10, H10, I10, B11)
K11, L11, M11, N11, O11 = Polygon(B11, H11, I11, B12)
K12, L12, M12, N12, O12 = Polygon(B12, H12, I12, B13)
K13, L13, M13, N13, O13 = Polygon(B13, H13, I13, B14)
K14, L14, M14, N14, O14 = Polygon(B14, H14, I14, B15)
K15, L15, M15, N15, O15 = Polygon(B15, H15, I15, B16)
K16, L16, M16, N16, O16 = Polygon(B16, H16, I16, B17)
K17, L17, M17, N17, O17 = Polygon(B17, H17, I17, B18)
K18, L18, M18, N18, O18 = Polygon(B18, H18, I18, B19)
K19, L19, M19, N19, O19 = Polygon(B19, H19, I19, B20)
K20, L20, M20, N20, O20 = Polygon(B20, H20, I20, B21)
K21, L21, M21, N21, O21 = Polygon(B21, H21, I21, B22)
K22, L22, M22, N22, O22 = Polygon(B22, H22, I22, B23)
K23, L23, M23, N23, O23 = Polygon(B23, H23, I23, B24)
K24, L24, M24, N24, O24 = Polygon(B24, H24, I24, B25)
K25, L25, M25, N25, O25 = Polygon(B25, H25, I25, B26)
P1, b, e, f = Polygon(Rotate[H1, ((mov2 * 180))°, H1], Rotate[C1, ((mov2 * 180))°, H1], Rotate[J1, ((mov2 * 180))°, H1])
P2, g, h, i = Polygon(Rotate[H2, ((mov2 * 180))°, H2], Rotate[C2, ((mov2 * 180))°, H2], Rotate[J2, ((mov2 * 180))°, H2])
P3, j, l, m = Polygon(Rotate[H3, ((mov2 * 180))°, H3], Rotate[C3, ((mov2 * 180))°, H3], Rotate[J3, ((mov2 * 180))°, H3])
P4, p, q, s = Polygon(Rotate[H4, ((mov2 * 180))°, H4], Rotate[C4, ((mov2 * 180))°, H4], Rotate[J4, ((mov2 * 180))°, H4])
P5, t, a_1, b_1 = Polygon(Rotate[H5, ((mov2 * 180))°, H5], Rotate[C5, ((mov2 * 180))°, H5], Rotate[J5, ((mov2 * 180))°, H5])
P6, c_1, d_1, e_1 = Polygon(Rotate[H6, ((mov2 * 180))°, H6], Rotate[C6, ((mov2 * 180))°, H6], Rotate[J6, ((mov2 * 180))°, H6])
P7, f_1, g_1, h_1 = Polygon(Rotate[H7, ((mov2 * 180))°, H7], Rotate[C7, ((mov2 * 180))°, H7], Rotate[J7, ((mov2 * 180))°, H7])
P8, i_1, j_1, k_1 = Polygon(Rotate[H8, ((mov2 * 180))°, H8], Rotate[C8, ((mov2 * 180))°, H8], Rotate[J8, ((mov2 * 180))°, H8])
P9, l_1, m_1, n_1 = Polygon(Rotate[H9, ((mov2 * 180))°, H9], Rotate[C9, ((mov2 * 180))°, H9], Rotate[J9, ((mov2 * 180))°, H9])
P10, p_1, q_1, r_1 = Polygon(Rotate[H10, ((mov2 * 180))°, H10], Rotate[C10, ((mov2 * 180))°, H10], Rotate[J10, ((mov2 * 180))°, H10])
P11, s_1, t_1, a_2 = Polygon(Rotate[H11, ((mov2 * 180))°, H11], Rotate[C11, ((mov2 * 180))°, H11], Rotate[J11, ((mov2 * 180))°, H11])
P12, b_2, c_2, d_2 = Polygon(Rotate[H12, ((mov2 * 180))°, H12], Rotate[C12, ((mov2 * 180))°, H12], Rotate[J12, ((mov2 * 180))°, H12])
P13, e_2, f_2, g_2 = Polygon(Rotate[H13, ((mov2 * 180))°, H13], Rotate[C13, ((mov2 * 180))°, H13], Rotate[J13, ((mov2 * 180))°, H13])
P14, h_2, i_2, j_2 = Polygon(Rotate[H14, ((mov2 * 180))°, H14], Rotate[C14, ((mov2 * 180))°, H14], Rotate[J14, ((mov2 * 180))°, H14])
P15, k_2, l_2, m_2 = Polygon(Rotate[H15, ((mov2 * 180))°, H15], Rotate[C15, ((mov2 * 180))°, H15], Rotate[J15, ((mov2 * 180))°, H15])
P16, n_2, p_2, q_2 = Polygon(Rotate[H16, ((mov2 * 180))°, H16], Rotate[C16, ((mov2 * 180))°, H16], Rotate[J16, ((mov2 * 180))°, H16])
P17, r_2, s_2, t_2 = Polygon(Rotate[H17, ((mov2 * 180))°, H17], Rotate[C17, ((mov2 * 180))°, H17], Rotate[J17, ((mov2 * 180))°, H17])
P18, a_3, b_3, c_3 = Polygon(Rotate[H18, ((mov2 * 180))°, H18], Rotate[C18, ((mov2 * 180))°, H18], Rotate[J18, ((mov2 * 180))°, H18])
P19, d_3, e_3, f_3 = Polygon(Rotate[H19, ((mov2 * 180))°, H19], Rotate[C19, ((mov2 * 180))°, H19], Rotate[J19, ((mov2 * 180))°, H19])
P20, g_3, h_3, i_3 = Polygon(Rotate[H20, ((mov2 * 180))°, H20], Rotate[C20, ((mov2 * 180))°, H20], Rotate[J20, ((mov2 * 180))°, H20])
P21, j_3, k_3, l_3 = Polygon(Rotate[H21, ((mov2 * 180))°, H21], Rotate[C21, ((mov2 * 180))°, H21], Rotate[J21, ((mov2 * 180))°, H21])
P22, m_3, n_3, p_3 = Polygon(Rotate[H22, ((mov2 * 180))°, H22], Rotate[C22, ((mov2 * 180))°, H22], Rotate[J22, ((mov2 * 180))°, H22])
P23, q_3, r_3, s_3 = Polygon(Rotate[H23, ((mov2 * 180))°, H23], Rotate[C23, ((mov2 * 180))°, H23], Rotate[J23, ((mov2 * 180))°, H23])
P24, t_3, a_4, b_4 = Polygon(Rotate[H24, ((mov2 * 180))°, H24], Rotate[C24, ((mov2 * 180))°, H24], Rotate[J24, ((mov2 * 180))°, H24])
P25, c_4, d_4, e_4 = Polygon(Rotate[H25, ((mov2 * 180))°, H25], Rotate[C25, ((mov2 * 180))°, H25], Rotate[J25, ((mov2 * 180))°, H25])
T1, e_8, f_8, g_8 = Polygon(Rotate[C1, (((-mov2) * 180))°, I1], Rotate[J1, (((-mov2) * 180))°, I1], Rotate[I1, (((-mov2) * 180))°, I1])
T2, h_8, i_8, j_8 = Polygon(Rotate[C2, (((-mov2) * 180))°, I2], Rotate[J2, (((-mov2) * 180))°, I2], Rotate[I2, (((-mov2) * 180))°, I2])
T3, k_8, l_8, m_8 = Polygon(Rotate[C3, (((-mov2) * 180))°, I3], Rotate[J3, (((-mov2) * 180))°, I3], Rotate[I3, (((-mov2) * 180))°, I3])
T4, n_8, p_8, q_8 = Polygon(Rotate[C4, (((-mov2) * 180))°, I4], Rotate[J4, (((-mov2) * 180))°, I4], Rotate[I4, (((-mov2) * 180))°, I4])
T5, r_8, s_8, t_8 = Polygon(Rotate[C5, (((-mov2) * 180))°, I5], Rotate[J5, (((-mov2) * 180))°, I5], Rotate[I5, (((-mov2) * 180))°, I5])
T6, a_9, b_9, c_9 = Polygon(Rotate[C6, (((-mov2) * 180))°, I6], Rotate[J6, (((-mov2) * 180))°, I6], Rotate[I6, (((-mov2) * 180))°, I6])
T7, d_9, e_9, f_9 = Polygon(Rotate[C7, (((-mov2) * 180))°, I7], Rotate[J7, (((-mov2) * 180))°, I7], Rotate[I7, (((-mov2) * 180))°, I7])
T8, g_9, h_9, i_9 = Polygon(Rotate[C8, (((-mov2) * 180))°, I8], Rotate[J8, (((-mov2) * 180))°, I8], Rotate[I8, (((-mov2) * 180))°, I8])
T9, j_9, k_9, l_9 = Polygon(Rotate[C9, (((-mov2) * 180))°, I9], Rotate[J9, (((-mov2) * 180))°, I9], Rotate[I9, (((-mov2) * 180))°, I9])
T10, m_9, n_9, p_9 = Polygon(Rotate[C10, (((-mov2) * 180))°, I10], Rotate[J10, (((-mov2) * 180))°, I10], Rotate[I10, (((-mov2) * 180))°, I10])
T11, q_9, r_9, s_9 = Polygon(Rotate[C11, (((-mov2) * 180))°, I11], Rotate[J11, (((-mov2) * 180))°, I11], Rotate[I11, (((-mov2) * 180))°, I11])
T12, t_9, a_{10}, b_{10} = Polygon(Rotate[C12, (((-mov2) * 180))°, I12], Rotate[J12, (((-mov2) * 180))°, I12], Rotate[I12, (((-mov2) * 180))°, I12])
T13, c_{10}, d_{10}, e_{10} = Polygon(Rotate[C13, (((-mov2) * 180))°, I13], Rotate[J13, (((-mov2) * 180))°, I13], Rotate[I13, (((-mov2) * 180))°, I13])
T14, f_{10}, g_{10}, h_{10} = Polygon(Rotate[C14, (((-mov2) * 180))°, I14], Rotate[J14, (((-mov2) * 180))°, I14], Rotate[I14, (((-mov2) * 180))°, I14])
T15, i_{10}, j_{10}, k_{10} = Polygon(Rotate[C15, (((-mov2) * 180))°, I15], Rotate[J15, (((-mov2) * 180))°, I15], Rotate[I15, (((-mov2) * 180))°, I15])
T16, l_{10}, m_{10}, n_{10} = Polygon(Rotate[C16, (((-mov2) * 180))°, I16], Rotate[J16, (((-mov2) * 180))°, I16], Rotate[I16, (((-mov2) * 180))°, I16])
T17, p_{10}, q_{10}, r_{10} = Polygon(Rotate[C17, (((-mov2) * 180))°, I17], Rotate[J17, (((-mov2) * 180))°, I17], Rotate[I17, (((-mov2) * 180))°, I17])
T18, s_{10}, t_{10}, a_{11} = Polygon(Rotate[C18, (((-mov2) * 180))°, I18], Rotate[J18, (((-mov2) * 180))°, I18], Rotate[I18, (((-mov2) * 180))°, I18])
T19, b_{11}, c_{11}, d_{11} = Polygon(Rotate[C19, (((-mov2) * 180))°, I19], Rotate[J19, (((-mov2) * 180))°, I19], Rotate[I19, (((-mov2) * 180))°, I19])
T20, e_{11}, f_{11}, g_{11} = Polygon(Rotate[C20, (((-mov2) * 180))°, I20], Rotate[J20, (((-mov2) * 180))°, I20], Rotate[I20, (((-mov2) * 180))°, I20])
T21, h_{11}, i_{11}, j_{11} = Polygon(Rotate[C21, (((-mov2) * 180))°, I21], Rotate[J21, (((-mov2) * 180))°, I21], Rotate[I21, (((-mov2) * 180))°, I21])
T22, k_{11}, l_{11}, m_{11} = Polygon(Rotate[C22, (((-mov2) * 180))°, I22], Rotate[J22, (((-mov2) * 180))°, I22], Rotate[I22, (((-mov2) * 180))°, I22])
T23, n_{11}, p_{11}, q_{11} = Polygon(Rotate[C23, (((-mov2) * 180))°, I23], Rotate[J23, (((-mov2) * 180))°, I23], Rotate[I23, (((-mov2) * 180))°, I23])
T24, r_{11}, s_{11}, t_{11} = Polygon(Rotate[C24, (((-mov2) * 180))°, I24], Rotate[J24, (((-mov2) * 180))°, I24], Rotate[I24, (((-mov2) * 180))°, I24])
T25, a_{12}, b_{12}, c_{12} = Polygon(Rotate[C25, (((-mov2) * 180))°, I25], Rotate[J25, (((-mov2) * 180))°, I25], Rotate[I25, (((-mov2) * 180))°, I25])
mov3 = 0 (slider from 0 to 1, step 0.01)
Polígon1, a_{17}, c_{16}, d_{16}, e_{16} = Polygon(A, ((n * base / 2), 0), ((n * base / 2), apotema / 2), (0, apotema / 2))
Polígon2 = Rotate(Polygon[((n * base), 0), ((n * base / 2), 0), ((n * base / 2), apotema / 2), ((n * base), apotema / 2)], ((mov3 * 180))°, ((n * base / 2), apotema / 2))
Polígon3, a_{18}, f_{16}, g_{16}, o = Polygon(A, ((π * r), 0), ((π * r), r), O)
u: (base * apotema / 2)
texto3: "A área de cada un dos  " + n + "  triángulos é " + base + " ·" + apotema + " ÷2 =  " + u + ""
v: (n * u)
texto4: "Área polígono = Área dos " + n + " triángulos = " + v + ""
w: (π * r^(2))
texto5: "A área do circulo sería: π·r² = " + w + " "
o_1: (100 * v / w)
texto6: "A superficie do círculo que cubren os polígonos é = " + o_1 + " %"
texto1: "Polígono inscrito de  " + n + " lados nunha circunferencia de radio " + r + ", dividido en triángulos isósceles de base " + base + " e altura " + apotema + " "