10GM16 Du polygone au disque
Author: Sandrine Rudaz

3

10

7

5

9

20

40

60

80

(a ; poly1)

13

17

21

25

Aire du polygone régulier =

nombre
de
côtés

aire du polygone
régulier

A = Intersect(xAxis, yAxis)
B = Point(yAxis)
c = Circle(A, B)
n = 4 (slider from 3 to 25, step 1)
b: 360.0 / n
B' = Rotate(B, b°, A)
poly1, b_1, b', a, d, C, J = Polygon(B, B', n)
U = Point(xAxis)
e_1 = OrthogonalLine(U, xAxis)
D = Point(c)
e = OrthogonalLine(D, yAxis)
E = Intersect(e_1, e)
f = Circle(E, 1.0)
F = Intersect(f, e_1, 2.0)
G = Intersect(f, e, 1.0)
H = Midpoint(E, G)
H'_1 = Mirror(H, G)
E' = Mirror(E, F)
F' = Mirror(F, E')
E'' = Mirror(E', F')
E''' = Mirror(E'', U)
U' = Mirror(U, E''')
I = Mirror(E''', U')
g = Circle(E, n / 4.0 - 0.75)
D_1 = Intersect(g, e, 1.0)
h_1 = OrthogonalLine(D_1, e)
k_1 = Circle(D_1, poly1 / 10.0)
E_1 = Intersect(k_1, h_1, 1.0)
H' = Mirror(H, H'_1)
G_1 = Mirror(H'_1, H')
H'' = Mirror(H', G_1)
H_1 = Mirror(G_1, H'')
F_1 = Point(e)
u = Vector(E, F_1)
I_1 = Point(e_1)
v = Vector(E, I_1)
i_1 = Segment(D_1, E_1)
j_1 = OrthogonalLine(E_1, v)
J_1 = Intersect(j_1, e_1)
l_1 = Segment(J_1, E_1)