(a-b)²

c² = 4· \frac{ab}{2} + (a-b)²\
c² = 2ab + a² -2ab +b²\
c² = a² + b²

Pythagoräischer Lehrsatz: Beweise

2. Beweis

c

a

b

a

b

c

c²

b

(a+b)^2 = c^2 + 4·\frac{ab}{2}\
a^2 + 2ab + b^2 = c^2 + 2ab\;\; | \; -2ab\
a^2+b^2=c^2

1.Beweis

Summe der Katheten-Quadrate ergibt das Hypotenusen-Quadrat

Begründung:

A = (0, 0)
B = (9, 0)
Vieleck1, a, b_3, c, d, C, D = Polygon(A, B, 4)
E = Midpoint(a)
e = Circle(E, A)
F = Point(e)
Vieleck2, b_1, a_1, f = Polygon(A, F, B)
g = Circle(B, Segment[A, F])
h = Circle(C, Segment[A, F])
k = Circle(D, Segment[A, F])
G = Intersect(g, a_1, 1)
Vieleck3, c_1, b_2, g_1 = Polygon(B, G, C)
H = Intersect(h, b_2, 1)
Vieleck4, d_1, c_2, h_1 = Polygon(C, H, D)
I = Intersect(k, c_2, 1)
Vieleck5, b, d_2, i = Polygon(D, I, A)
j = true
J = Intersect(xAxis, yAxis)
K = Point(xAxis)
Vieleck6, l, m, n, p, L, M = Polygon(J, K, 4)
N = Point(l)
q = Circle(L, Segment[K, N])
r = Circle(M, Segment[K, N])
s = Circle(J, Segment[K, N])
O = Intersect(q, m, 1)
P = Intersect(r, n, 1)
Q = Intersect(s, p, 1)
Vieleck7, n_1, o, p_1, q_1 = Polygon(N, O, P, Q)
Vieleck8, q_2, j_1, n_2 = Polygon(J, N, Q)
Vieleck9, o_1, n_3, k_1 = Polygon(N, K, O)
Vieleck10, p_2, o_2, l_1 = Polygon(O, L, P)
Vieleck11, q_3, p_3, m_1 = Polygon(P, M, Q)
t = false