平方關係
Author: 藍邦偉  老師
Date: 31 12 月 2012

拉動A,B,C三點觀察

$ 平方關係 $

$ A $

$ B $

$ C $

A = (1.96, -1.36)
C = Point(Ray[A, A + (1, 0)])
B = Point(Ray[C, C + (0, 1)])
a = Segment(B, C)
c = Segment(B, A)
b = Segment(A, C)
α = Angle(B, C, A)
n = 0 (slider from 0 to 3, step 1)
θ = Angle(B, A, C)
a_0 = Distance(B, C)
t_a: "$ " + (LaTeX[If[n ≟ 3, "sinθ", If[n ≟ 1, "a"]]]) + " $"
t_b: "$ " + (LaTeX[If[n ≟ 1, "b", If[n ≟ 3, "cosθ"]]]) + " $"
t_c: "$ " + (LaTeX[If[n ≟ 1, "c", If[n ≟ 3, "1"]]]) + " $"
tc: "$ " + (LaTeX[a]) + " $"
tb: "$ " + (LaTeX[b]) + " $"
ta: "$ " + (LaTeX[c]) + " $"
t_{theta}: "$ " + (LaTeX[θ]) + " $"
t1: "$\;\;\;\;\;a^2+b^2 =c^2\;(畢氏定理)$
$⇒" + (LaTeX[a]) + "^2+" + (LaTeX[b]) + "^2=" + (LaTeX[a^(2) + b^(2)]) + "=" + (LaTeX[c]) + "^2$"
t3: "$\;\;\;\;sin^2\;" + (LaTeX[θ]) + "+cos^2\;" + (LaTeX[θ]) + "$
$=" + (LaTeX[sin(θ)]) + "^2+" + (LaTeX[cos(θ)]) + "^2$
$=" + (LaTeX[sin(θ)^(2)]) + "+" + (LaTeX[cos(θ)^(2)]) + "$
$⇒ sin^2θ+cos^2θ=1 $"
t2: "$\;\;\;\;\; \frac{a^2}{c^2}+\frac{b^2}{c^2}=1$
$⇒\frac{" + (LaTeX[a]) + "^2}{" + (LaTeX[c]) + "^2}+\frac{" + (LaTeX[b]) + "^2}{" + (LaTeX[c]) + "^2}=\frac{" + (LaTeX[a^(2) + b^(2)]) + "}{" + (LaTeX[c^(2)]) + "} =1$"
poly1, c_1, a_1, b_1 = Polygon(A, B, C)