橢圓的面積
Author: 藍邦偉  老師

x

y

橢圓的面積

圓面積

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h = -3.43 (slider from -a to a, step 0.01)
a = 5 (slider from 1 to 10, step 1)
A_0 = Corner(1)
B_0 = Corner(3)
C_0: (x(A_0), 0)
D_0: (x(B_0), 0)
u = Vector(C_0, D_0)
E_0: (0, y(A_0))
F_0: (0, y(B_0))
v = Vector(E_0, F_0)
A = Point(u)
B = (0, 0)
c: x^(2) + y^(2) = a^(2)
r = 0.4 (slider from 0 to 1, step 0.1)
d: x^(2) / a^(2) + y^(2) / (r * a)^(2) = 1
Q_1: (0, r * a)
O = (0, 0)
Q_2: (a, 0)
k: -a
Q_3: (0, a - (1 - r) * abs(k))
g: x = h
D = Intersect(c, g, 1)
D', E = Intersect(d, g)
H = Intersect(g, h_1)
i = Segment(D, H)
j = LineBisector(D, D')
l = LineBisector(D', H)
p = Circle(D, D')
q = Circle(D', H)
m = LineBisector(D, H)
s = Circle(D, H)
C = Intersect(s, m, 1)
a_1 = Segment(D', H)
b = LineBisector(D', H)
e = Circle(D', H)
F, G = Intersect(e, b)
f = CircleArc(G, D', H)
text1: " \frac{x²}{" + (a^(2)) + "}+\frac{y²}{" + ((r * a)^(2)) + "} =1"
text2: "即\frac{\overline{D'H}}{\overline{DH}}=" + r
ra: r * a
text4: "橢圓面積A_1=\pi×" + a + "×" + ra
text5: "將位於y軸的半徑壓縮" + r + "倍"
text3: "A=\pi×" + (LaTeX[a^(2)]) + "=\pi×" + (LaTeX[a]) + "×" + (LaTeX[a]) + ""
T_1 = Corner(1)
T_2: 0.7 * Corner[1] + 0.3 * Corner[2]
T_3: (x(T_2), y(Corner[4]))
T_4 = Corner(4)
poly1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
n = Segment(T_2, T_3)
C' = Mirror(C, g)
c_1 = CircleArc(C', H, D)