T.M.Hughes
Author: 高一忠郭于瑄

B'=A  (3, 0)

11.3

 \frac{ 71 }{8 } 

T.M.Hughes胡格赫斯法   

求作一正方形其面積等於一已知圓

B_1 = (1.56, 3.96)
B'_1 = (2.686000000000001, 2.48)
c = Circle(B'_1, B_1)
A = Point(c)
B': A + (1.9, 0.0)
Q_1: A + (0.0, -(1.5))
u = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
v = Vector((0.0, y(Corner[2.0])), (0.0, y(Corner[4.0])))
D = Point(c)
B: A + (5.0, 0.0)
A_2 = Segment(A, B)
C = Point(c)
E = (2.84, 2.18)
w = Vector(C, E)
a = LineBisector(A, B'_1)
F = Intersect(a, A_2)
G = (2.4, 3.24)
d = Circle(F, G)
b = OrthogonalLine(A, u)
H = Point(b)
e = Segment(A, H)
f = OrthogonalLine(B'_1, u)
I: (x(B'), y(H))
g = Segment(B', I)
J = (-3.72, 4.8)
K = (-4.14, 3.34)
L = (-2.36, 2.88)
M = Point(e)
N = Point(g)
z = Vector(M, N)
X = Point(A_2)
h = OrthogonalLine(X, u)
Y = Intersect(d, h, 2.0)
P_1 = Intersect(d, h, 1.0)
i = Segment(Y, P_1)
j = Line(A, Y)
O = Point(j)
k = Segment(A, O)
Q = Point(e)
R = Point(i)
l = Vector(Q, R)
p = Semicircle(A, B'_1)
q = Semicircle(B'_1, A)
Y' = Intersect(c, k, 2.0)
S = Point(i)
T = Point(e)
m = Vector(S, T)
U = Point(z)
V_1 = Point(e)
n_2 = Vector(U, V_1)
distanceY'A = Distance(Y', A)
文字Y'A: "\overline{" + (Name[Y']) + (Name[A]) + "} \, = \, " + distanceY'A
r = OrthogonalLine(A, u)
W_1 = (0.78, 4.18)
Z = Intersect(c, k, 2.0)
s = Segment(W_1, Z)
t = OrthogonalLine(A, u)
A_1 = Point(t)
a_1 = Segment(A, A_1)
distanceA1A = Distance(A_1, A)
文字A1A: "\overline{" + (Name[A_1]) + (Name[A]) + "} \, = \, " + distanceA1A
b_1 = OrthogonalLine(Y', u)
C_1 = Intersect(b_1, A_2)
D_1 = Point(b_1)
c_1 = Segment(C_1, D_1)
distanceD1C1 = Distance(D_1, C_1)
文字D1C1: "\overline{" + (Name[D_1]) + (Name[C_1]) + "} \, = \, " + distanceD1C1
d_1 = Segment(A_1, D_1)
o = Distance(a_1, c_1)
e_1 = Distance(d_1, k)
distanceAY' = Distance(A, Y')
文字AY': "\overline{" + (Name[A]) + (Name[Y']) + "} \, = \, " + distanceAY'
E_1 = Point(a_1)
f_1 = Segment(A, E_1)
X' = Intersect(A_2, c_1)
G_1 = Point(c_1)
g_1 = Segment(X', G_1)
H_1 = Point(g_1)
i_1 = Segment(X', H_1)
I_1 = Point(f_1)
h_1 = Segment(A, I_1)
J_1 = Point(f_1)
j_1 = Segment(A, J_1)
K_1 = Point(j_1)
k_1 = Segment(A, K_1)
distanceF1A = Distance(X', A)
V = (0.8260000000000013, 5.079999999999999)
l_1 = Segment(A, V)
M_1 = (3.72, 5.38)
m_1 = Segment(X', M_1)
n_1 = Segment(V, M_1)
N_1 = Intersect(i_1, m_1)
O_1 = Intersect(i_1, m_1)
W_2 = Point(m_1)
p_1 = Segment(V, W_2)
q_1 = Line(V, v)
r_1 = Line(V, u)
s_1 = OrthogonalLine(Y', u)
W = Intersect(r_1, s_1)
t_1 = Segment(X', W)
a_2 = Segment(V, W)
P = Intersect(c, A_2, 2.0)
F_1: (x(A), y(P_1))
L_1: P_1
u_1 = Vector(F_1, L_1)
v_1 = Vector(L_1, F_1)
R_1: (x(B'), y(Q_1))
w_1 = Vector(Q_1, R_1)
z_1 = Vector(R_1, Q_1)
n = 4 (slider from 0 to 4, step 1)
S_1: A + (5.0, 0.0)
T_1: A + (3.0, 0.0)
U_1: A + (2.0, 0.0)
Z_1: A + (1.8, 0.0)