Pitagores
Author: Enric Brasó

Comprovació del Teorema de pitagores bla

bb

Quina propietat té el triangle ABC quan les àrees 
 verda i groga sumades són iguals a l'àrea blava?

Moveu els punts A, B i C i investigueu:

Suma de les àrees
verda i groga

C = (1.5049582958048462, 3.070736474294921)
B = (2.0375851125208264, -0.04986508842607774)
a = Segment(B, C)
A = (-0.8770223221658747, -0.044161256897560314)
c = Segment(A, B)
G: (x(B) + 5 + c, y(B) - c)
J: (x(G) + 1, y(G))
M: (x(J), y(J) + a a / c)
K: (x(J) + c, y(G))
b = Segment(A, C)
A' = Rotate(A, 1.5707963267948966, B)
d = Segment(B, A')
B' = Rotate(B, -1.5707963267948966, A)
e = Segment(B', A)
f = Segment(B', A')
poly1, a_1, b', a', b_1 = Polygon(A, B', A', B)
B'_1 = Rotate(B, 1.57, C)
C' = Rotate(C, -1.57, B)
poly2, c_1, b'_1, c', b_2 = Polygon(C, B'_1, C', B)
A'_1 = Rotate(A, -1.57, C)
C'_1 = Rotate(C, 90°, A)
poly3, c'_1, a_2, c_2, a'_1 = Polygon(C'_1, A, C, A'_1)
Textpoly3: "Àrea =b² =" + poly3
Textpoly2: "Àrea = a² =" + poly2
Textpoly1: "Àrea= c² = " + poly1
α = Angle(B, A, C)
E: (x(B) + 5, y(B))
D: (x(B) + 5 + c, y(B))
F: (x(B) + 5, y(B) - c)
H: (x(B) + 5, y(B) + b b / c)
I: (x(D), y(H))
poly4, e_1, f_1, g, d_1 = Polygon(E, F, G, D)
poly5, h, e_2, d_2, i = Polygon(H, E, D, I)
L: (x(K), y(M))
poly6, m, j, k, l = Polygon(M, J, K, L)
N = Midpoint(B'_1, B)
O = Midpoint(A'_1, A)
P = Intersect(d, a')
Q = Intersect(f, b')
R = Intersect(d, a')
S = Intersect(f, b')
T = Midpoint(A, A')
U = Midpoint(H, D)
V = Midpoint(D, F)
W = Midpoint(M, K)
text1: "Àrea =b² =" + poly3
text4: "Àrea =c² =" + poly1
text5: "Àrea =a² =" + poly2
Z = Midpoint(H, I)
A_1 = Midpoint(F, G)
text7: "= " + (poly1 + poly3)