橢圓的內接正三角形的最大面積
Author: 藍邦偉  老師

x

y

$橢圓的內接三$
$角形最大面積$

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)
B = (0, 0)
α = 5.407030022678433 rad (slider from 0 to 6.283185307179586, step 0.003490658503988659)
a = 6 (slider from 1 to 10, step 1)
b = 2 (slider from 1 to 10, step 1)
c: x^(2) / a^(2) + y^(2) / b^(2) = 1
d: x^(2) + y^(2) = a^(2)
A_1: (a * cos(α), a * sin(α))
A_2: (a * cos(α + 120°), a * sin(α + 120°))
A_3: (a * cos(α + 240°), a * sin(α + 240°))
多邊形1, a_3, a_1, a_2 = Polygon(A_1, A_2, A_3)
e: x = x(A_1)
f: x = x(A_2)
g: x = x(A_3)
A = Intersect(c, f, 1)
C = Intersect(c, e, 1)
D = Intersect(c, g, 2)
多邊形2, c_1, a_4, d_1 = Polygon(A, D, C)
E = Intersect(c, e, 2)
F, G = Intersect(c, g)
H, I = Intersect(c, f)
Q_1: (x(A_1), 0)
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(A_3), 0)
多邊形5, g_2, c_4, i_2 = Polygon(C, I, G)
多邊形6, f_2, c_5, i_3 = Polygon(C, I, F)
多邊形7, i_4, f_3, e_1 = Polygon(F, E, I)
多邊形8, e_2, f_4, h = Polygon(F, H, E)
多邊形9, e_3, h_1, g_3 = Polygon(H, G, E)
text1: "$ \frac{x²}{" + (LaTeX[a^(2)]) + "} +\frac{y^2}{" + (LaTeX[b^(2)]) + "}=1$"
W_2: 0.2 * Corner[2] + 0.8 * Corner[1]
W_3: (x(W_2), y(Corner[4]))
poly1, i, w_2, w_3, j = Polygon(Corner[1], W_2, W_3, Corner[4])