Pythagore: découverte

Lis les consignes

Ensuite essaie d'écrire une égalité

Aire \;  du \; carré  \;de \; côté \left [ AB \right ]

=Aire \;  du \; carré  \;de \; côté \left [ BC \right ]

Interprétation

Aire \;  du \; carré  \;de \; côté \left [ AC \right ]

+

A = Intersect(xAxis, yAxis)
B = Point(xAxis)
C = Point(yAxis)
poly1, b, a, c = Polygon(A, C, B)
poly2, a_1, c_1, d, e, D, E = Polygon(A, C, 4)
poly3, c_2, b_1, f, g, F, G = Polygon(C, B, 4)
poly4, b_2, a_2, h, i, H, I = Polygon(B, A, 4)
J = Midpoint(A, I)
j = Line(J, a)
k = OrthogonalLine(J, a)
K = Intersect(j, a_2)
L = Intersect(j, i)
M = Intersect(k, c)
N = Intersect(k, h)
poly5, a_3, k_1, j_1, m = Polygon(A, K, J, M)
poly6, k_2, h_1, n_2, j_2 = Polygon(K, H, N, J)
poly7, i_1, n_1, j_3, l = Polygon(I, N, J, L)
poly8, l_1, b_3, m_1, j_4 = Polygon(L, B, M, J)
u = Vector(J, G)
v = Vector(J, C)
w = Vector(J, B)
z = Vector(J, F)
haut = 0 (slider from 0 to 1, step 0.01)
gauche = 0 (slider from 0 to 1, step 0.01)
droit = 0 (slider from 0 to 1, step 0.01)
bas = 0 (slider from 0 to 1, step 0.01)
I' = Translate(I, u)
N' = Translate(N, u)
J' = Translate(J, u)
L' = Translate(L, u)
L'_1 = Translate(L, v)
B' = Translate(B, v)
M' = Translate(M, v)
J'_1 = Translate(J, v)
K' = Translate(K, z)
H' = Translate(H, z)
N'_1 = Translate(N, z)
J'_2 = Translate(J, z)
p = (0, 0)
A' = Translate(A, p)
K'_1 = Translate(K, p)
J'_3 = Translate(J, p)
M'_1 = Translate(M, p)
poly5', a', k'_1, j'_3, m'_1 = Polygon(A', K'_1, J'_3, M'_1)
A'' = Translate(A', w)
O = Translate(K'_1, w)
P = Translate(J'_3, w)
Q = Translate(M'_1, w)
toppiece: (u * bas)
leftpiece: (v * droit)
rightpiece: (z * gauche)
K'_2 = Translate(K, rightpiece)
H'_1 = Translate(H, rightpiece)
N'_2 = Translate(N, rightpiece)
J'_4 = Translate(J, rightpiece)
gauche_2, k'_2, h'_1, n'_2, j'_4 = Polygon(K'_2, H'_1, N'_2, J'_4)
I'_1 = Translate(I, toppiece)
N'_3 = Translate(N, toppiece)
J'_5 = Translate(J, toppiece)
L'_2 = Translate(L, toppiece)
bas_2, i'_1, n'_3, j'_5, l'_2 = Polygon(I'_1, N'_3, J'_5, L'_2)
L'_3 = Translate(L, leftpiece)
B'_1 = Translate(B, leftpiece)
M'_2 = Translate(M, leftpiece)
J'_6 = Translate(J, leftpiece)
droit_2, l'_3, b'_1, m'_2, j'_6 = Polygon(L'_3, B'_1, M'_2, J'_6)
bottompiece: (w * haut)
A''_1 = Translate(A', bottompiece)
R = Translate(K'_1, bottompiece)
S = Translate(J'_3, bottompiece)
T = Translate(M'_1, bottompiece)
haut_2, a''_1, r, s, t = Polygon(A''_1, R, S, T)
U = Intersect(f, b_1)
V = Midpoint(C, U)
W = Intersect(d, e)
Z = Midpoint(C, W)
q = Vector(Z, V)
petit = 0 (slider from 0 to 1, step 0.01)
otherpiece: (q * petit)
petit_2 = Translate(poly2, otherpiece)
B'_2 = Rotate(B, 90°, C)
C' = Rotate(C, (-(90°)), B)
poly9, b'_2, c_3, b_4, c' = Polygon(B'_2, C, B, C')
A'_1 = Rotate(A, -90°, C)
C'_1 = Rotate(C, 90°, A)
poly10, a'_1, c'_1, a_4, c_4 = Polygon(A'_1, C'_1, A, C)
B'_3 = Rotate(B, -90°, A)
A'_2 = Rotate(A, 90°, B)
poly11, a_5, b'_3, a'_2, b_5 = Polygon(A, B'_3, A'_2, B)
α = Angle(B, A, C)
n = false
o = 0 (slider from 0 to 4, step 1)