Author: 藍邦偉  老師
Date: 24 12 月 2012

拉動θ與φ，使終邊重合，觀察同界角的關係

$O$

O: 0.5 * (Corner[1] + Corner[3])
u = Vector((x(Corner[1]), y(O)), (x(Corner[3]), y(O)))
v = Vector((x(O), y(Corner[1])), (x(O), y(Corner[3])))
θ = 0 (slider from 0 to 5, step 0.01)
a = CurveCartesian(x(O) + (t / 3 + 0.5) * cos(t * 2 * 3.141592653589793), y(O) + If[θ > 0, 1, -1] * (t / 3 + 0.5) * sin(2 * t * 3.141592653589793), t, 0, abs(θ))
b = Segment(O, (x(O) + (abs(θ) / 3 + 0.5) * cos(2 * θ * 3.141592653589793), y(O) + (abs(θ) / 3 + 0.5) * sin(2 * θ * 3.141592653589793)))
φ = 0 (slider from -5 to 0, step 0.01)
c = CurveCartesian(x(O) + (t / 3 + 0.5) * cos(t * 2 * 3.141592653589793), y(O) + If[φ > 0, 1, -1] * (t / 3 + 0.5) * sin(2 * t * 3.141592653589793), t, 0, abs(φ))
f = Segment(O, (x(O) + (abs(φ) / 3 + 0.5) * cos(2 * φ * 3.141592653589793), y(O) + (abs(φ) / 3 + 0.5) * sin(2 * φ * 3.141592653589793)))
text1: "$ 目前角度：\;" + (LaTeX[360 * θ]) + " °$"
text2: "$ 目前角度：\;" + (LaTeX[360 * φ]) + "° $"
Title: "$ 同界角 $
$定義：\;θ=360°\times n+θ$
$\;\;\;" + (LaTeX[360 * θ]) + "°=360°\times " + (LaTeX[floor(θ)]) + "+" + (LaTeX[360 * (θ - floor(θ))]) + "°$
$\;\;\;\fgcolor {red}{" + (LaTeX[360 * φ]) + "°=360°\times (" + (LaTeX[floor(φ)]) + ")+" + (LaTeX[360 * (φ - floor(φ))]) + "°}$"