Il Teorema di Pitagora si generalizza cosruendo sui lati qualsiasi poligono regolare.
Sposta la slider bar per cambiare il numero dei lati del poligono da 3 a 10.

A = (-6.044482972618012, -3.942551991330423)
B = (-0.723501433751143, -3.994212006270878)
a = Segment(A, B)
b = OrthogonalLine(A, a)
C = Point(b)
poly1, c, a_1, b_1 = Polygon(A, B, C)
m = 3 (slider from 3 to 10, step 1)
poly2, d, e, f, D = Polygon(C, B, m)
poly3, g, h, i, E = Polygon(A, C, m)
poly4, j, k, l, F = Polygon(B, A, m)
Testopoly2: "Area = " + poly2
Testopoly3: "Area = " + poly3
Testopoly4: "Area = " + poly4
text2: poly3 + " + " + poly4 + " = " + poly2
pp: poly3 + poly4

Tool: Circocerchio
Clicca sul triangolo
Input: poly1
Output: p, T

A = (-4.666277570350066, -0.6659276849718916)
B = (-6.154342751259048, -2.671580754892693)
C = (-1.5306066234247662, -3.3810584720750883)
poly1, c, a, b = Polygon(A, B, C)
j = LineBisector(a)
l = LineBisector(c)
T = Intersect(j, l)
p = Circle(T, B)

Tool: Circonferenza inscrita (command Circonferenzainscrita)
Clicca sui vertici del triangolo
Input: N, P, Q
Output: c_1, R

poly2, q_1, n_1, p_1 = Polygon(N, P, Q)
r = AngularBisector(N, Q, P)
s = AngularBisector(P, N, Q)
R = Intersect(r, s)
t = OrthogonalLine(R, p_1)
S = Intersect(t, p_1)
c_1 = Circle(R, S)

Tool: Ortocentro
Clicca sui vertici del triangolo
Input: E_1, F_1, G_1
Output: H_1

j_1 = Line(F_1, G_1)
l_1 = Line(G_1, E_1)
m_1 = OrthogonalLine(F_1, l_1)
n_1 = OrthogonalLine(E_1, j_1)
H_1 = Intersect(m_1, n_1)

Tool: Excerchi
Clicca su 3 rette che determinano un triangolo
Input: b, c, a
Output: p, E, D, F, q, r

d, e = AngularBisector(a, c)
f, g = AngularBisector(b, c)
h, i = AngularBisector(a, b)
D = Intersect(h, d)
E = Intersect(d, f)
F = Intersect(f, h)
j = OrthogonalLine(D, a)
k = OrthogonalLine(E, c)
l = OrthogonalLine(F, b)
G = Intersect(b, l)
H = Intersect(k, c)
I = Intersect(j, a)
p = Circle(E, H)
q = Circle(F, G)
r = Circle(D, I)

Tool: Tr. Equil. su lato (command Treqlato)
Clicca sugli estremi in verso orario
Input: A, C
Output: poly2, a_1, c_1, D, d_1

d = Circle(C, A)
e = Circle(A, C)
D = Intersect(d, e, 2)
poly2, c_1, a_1, d_1 = Polygon(A, D, C)

Tool: Rapporto aureo (command Rapportoaureo)
Clicca sugli estremi del segmento
Input: A, B
Output: E

a = Segment(A, B)
b = OrthogonalLine(B, a)
M = Midpoint(a)
c = Circle(B, M)
C = Intersect(c, b, 2)
d = Segment(C, A)
e = Circle(C, B)
D = Intersect(e, d, 1)
f = Circle(A, D)
E = Intersect(f, a, 1)

Tool: Quadrato su segmento (command Quadratosusegmento)
Clicca sugli estremi e sul segmento
Input: A, B, a_1
Output: poly2, e_1, d_1, b_2

a = Line(A, B)
b = OrthogonalLine(A, a)
C = Point(b)
poly1, c, a_1, b_1 = Polygon(A, B, C)
d = OrthogonalLine(C, a_1)
e = OrthogonalLine(B, a_1)
f = Circle(B, C)
D = Intersect(f, e, 1)
g = OrthogonalLine(D, e)
E = Intersect(d, g)
poly2, c_1, b_2, d_1, e_1 = Polygon(C, B, D, E)