扇形的弧長與面積
Author: 藍邦偉  老師

$r=%v$

$Case=%v$

$ O $

$ 扇形的弧長與面積 $

$θ=%v$

$ O $

$ A $

$ B $

r = 4 (slider from 1 to 4, step 1)
A_1 = (3.478716377344461, 1.3751516284560426)
n = 8 (slider from 1 to 24, step 1)
c = Circle(A_1, r)
A = Point(c)
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: 0.7 * Corner[1] + 0.3 * 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])
a = Segment(A_1, A)
B = Rotate(A, (n * 15)°, A_1)
b = Segment(A_1, B)
α = Angle(A, A_1, B)
d = CircleSector(A_1, A, B)
ϕ: α / (180°)
T_{angle}: "$ θ＝" + (LaTeX[α]) + " =\frac{" + (LaTeX[n]) + "}{12}π=" + (LaTeX[FractionText[n / 12]]) + "\pi$"
T_{Arc_Length}: "$s=rθ=" + (LaTeX[r]) + "×" + (LaTeX[FractionText[n / 12]]) + "π=" + (LaTeX[FractionText[n * r / 12]]) + "π$"
D = (-6.796056885291735, 2.84570467905639)
T_{Area}: "$ A=\frac{1}{2}r²θ$
$=\frac{1}{2}×" + (LaTeX[r]) + "² ×" + (LaTeX[FractionText[n / 12]]) + "\pi$
$=" + (LaTeX[FractionText[n * r * r / 24]]) + "π$"