$\textcolor{}\Huge{a}$

$\textcolor{}\Huge{c}$

$\textcolor{}\Huge{b}$

演示

\Huge{a}

b = 3.3 (slider from 1 to 5)
a = 2 (slider from 0.9 to b)
A: (0, 0)
B: A + (a, 0)
C: A + (0, b)
t1, c, a_1, b_1 = Polygon(A, B, C)
D: B + (0, b)
E: B + (b, 0)
F: E + (0, a)
G: B + (0, a)
H: G + (b - a, 0)
I: D + (b - a, 0)
t2, b_2, c_1, d = Polygon(C, D, B)
t3, f, b_3, e = Polygon(B, E, F)
t4, f_1, b_4, g = Polygon(B, G, F)
q1, g_1, h, i, d_1 = Polygon(G, H, I, D)
α = 0 rad (slider from 0° to 90°)
A' = Rotate(A, α, C)
B' = Rotate(B, α, C)
C' = Rotate(C, α, C)
t1', c', a', b' = Polygon(A', B', C')
B'_1 = Rotate(B, (-α), F)
E' = Rotate(E, (-α), F)
F' = Rotate(F, (-α), F)
t3', f', b'_1, e' = Polygon(B'_1, E', F')
J: B + (b - a, 0)
j = Segment(H, J)
k = PolyLine(H, J, E, F, H)
l = PolyLine(C, A, J, I, C)
n = 1 (slider from 0 to 8, step 1)
text1 = LaTeX(If[3 ≤ n < 5, "\textcolor{blue}{a^2}", n ≟ 5, "\textcolor{blue}{a^2}+\textcolor{#006400}{b^2}", n ≟ 7, "\textcolor{red}{c^2}", n ≟ 8, "\textcolor{blue}{a^2}+\textcolor{#006400}{b^2}=\textcolor{red}{c^2}"])

Tool: 坐标系
x最小、最大，y最小、最大，0.23
Input: m, n, q, p, a
Output: A, B, O, l1, l2, list3, list4, list5, list6, u, v

$\huge\textcolor{}{x}$

$\huge\textcolor{}{y}$

$\Large{O}$

u = Vector((m - 1, 0), (n + 1, 0))
l1 = Sequence(Segment[(k, 0), (k, a)], k, m, n)
A: (n + 1, 0)
list4 = Sequence(Text[k, Element[Sequence[(t - 0.15, 0), t, 1, n], k], true, true], k, 1, n)
list3 = Sequence(Text[k, Element[Sequence[(t - 0.5, 0), t, m, -1], k + abs(m) + 1], true, true], k, m, -1)
l2 = Sequence(Segment[(0, k), (a, k)], k, q, p)
list5 = Sequence(Text[k, Element[Sequence[(-0.9, t + 0.2), t, q, -1], k + abs(q) + 1], true, true], k, q, -1)
v = Vector((0, q - 1), (0, p + 1))
B: (0, p + 1)
list6 = Sequence(Text[k, Element[Sequence[(-0.6, t + 0.2), t, 1, p], k], true, true], k, 1, p)
O: B - (0, p + 1)