根號n的作圖(2)
Author: 藍邦偉  老師

$ O $

$Step=%v$

$ 2.\;在數線上取B(-1) $

$ 3.\;以\overline{AB}為直徑，\;作一半圓  $

$ 4.\;過原點O作鉛直線交半圓於C $

$ B(-1) $

$ C $

$ 1.\;連\overline{AC}，\;\overline{BC} $

1

3

4

2

$ 2.\;∵∠1+∠2=∠1+∠3=∠2+∠4=90° $

$ 3.\;∴\Delta BOC≈\Delta COA $

$ 證明： $

Reset

$ 作法： $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.8 * Corner[1] + 0.2 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
n = 5 (slider from 1 to 10, step 1)
s = 0 (slider from 0 to 9, step 1)
A: (n, 0)
B = (-1, 0)
M = Midpoint(A, B)
α = 0 rad (slider from 0*° to 180*°, step 0.1*°)
A' = Rotate(B, -α, M)
d = Semicircle(B, A)
a = 0 (slider from 0 to 4, step 0.01)
b = Segment(O, O + (0, a))
C = Intersect(d, b)
t_A: "$ A(" + (LaTeX[n]) + ") $"
β = 0 rad (slider from 0*° to 90*°, step 0.1*°)
C' = Rotate(C, -β, O)
e = CircleArc(O, C', C)
Title: "$  在數線上求作\sqrt{" + (LaTeX[n]) + "}$"
text1: "$1.\;在數線上取一點A(" + (LaTeX[n]) + ") $"
t_D: "$ D(\sqrt{" + (LaTeX[n]) + "}) $"
f = Segment(C, B)
g = Segment(C, A)
γ = Angle(O, B, C)
δ = Angle(B, C, O)
ε = Angle(O, C, A)
ζ = Angle(C, A, O)
c = CircleArc(M, A', B)
text5: "$ 5.\;以O為圓心，\;\overline{OC}\;為半徑畫弧，\;交數$
$\;\;\;\;線於D\;點，\;則D\;點座標即為D(\sqrt{" + (LaTeX[n]) + "}) $"
D = (2.5637441723074117, 6.957002936224774)
text9_1: "$ 4.\;∴\;\frac{\overline{OC}}{\overline{OB}}=\frac{\overline{OA}}{\overline{OC}} ⇒\overline{OC}^2=\overline{OA}×\overline{OB}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=n^2=" + (LaTeX[n]) + "×1⇒\overline{OC}=\sqrt{" + (LaTeX[n]) + "}$"