根號n的作圖 (3)
Author: 藍邦偉老師

$ 根號\;n\;的作圖\;(3) $

$ 拉動\;m,\;n,\;k,\;t,\;s\;觀察 $

O = (0, 0)
m = 2 (slider from 1 to 10, step 1)
n = 1 (slider from 1 to 10, step 1)
P: (m, 0)
b_1: x = m
Q: (m, n)
e_1 = Ray(O, Q)
b_2 = OrthogonalLine(Q, e_1)
k = 2 (slider from 0 to 10, step 1)
c_2 = Circle(Q, k)
R = Intersect(c_2, b_2, 2)
e_2 = Ray(O, R)
b_3 = OrthogonalLine(R, e_2)
t = 2 (slider from 0 to 10, step 1)
c_5 = Circle(R, t)
S = Intersect(c_5, b_3, 2)
a_3 = Segment(O, P)
a_4 = Segment(Q, P)
a_5 = Segment(O, Q)
a_6 = Segment(Q, R)
a_7 = Segment(R, O)
a_8 = Segment(O, S)
a_9 = Segment(S, R)
t1: " \sqrt{ " + (m^(2) + n^(2)) + " } "
A = Midpoint(a_5)
B = Midpoint(a_7)
C = Midpoint(a_8)
t2: " \sqrt{ " + (m^(2) + n^(2) + k^(2)) + " } "
t3: " \sqrt{ " + (m^(2) + n^(2) + k^(2) + t^(2)) + " } "
s = 0 (slider from 0 to 10, step 1)
b_4 = OrthogonalLine(S, a_8)
c_1 = Circle(S, s)
T = Intersect(c_1, b_4, 2)
a_1 = Segment(T, S)
a_2 = Segment(T, O)
D = Midpoint(a_2)
t4: " \sqrt{ " + (m^(2) + n^(2) + k^(2) + t^(2) + s^(2)) + " } "
c_3 = Circle(O, T)
E = Intersect(c_3, xAxis, 2)
c_4 = Circle(O, S)
c_6 = Circle(O, R)
c_7 = Circle(O, Q)
F = Intersect(c_4, xAxis, 2)
G = Intersect(c_6, xAxis, 2)
H = Intersect(c_7, xAxis, 2)
s_1 = CircleArc(O, H, Q)
s_2 = CircleArc(O, G, R)
s_3 = CircleArc(O, F, S)
s_4 = CircleArc(O, E, T)
α = Angle(Q, P, O)
β = Angle(R, Q, O)
γ = Angle(S, R, O)
δ = Angle(T, S, O)
u = Vector((x(Corner[1]), 0), (x(Corner[2]), 0))