Area del cerchio
Author: Spinelli

Animazione per "vedere" che un cerchio ha l'area uguale a quella di un triangolo che ha per base la circonferenza e per altezza il raggio del cerchio.

L'area quindi è uguale a       (2 π r *r) / 2  =  π r²

r

2 π r

AREA DEL CERCHIO

(muovi il punto h )

Area cerchio   =

2 π r * r

2

= π r²

h = 2 (slider from 2 to 50, step 0.1)
z = If(h < 48.0, h, 1000.0)
B = Point(yAxis)
E: (0.0, z + 1.0)
A = Point(yAxis)
d: y(A) - y(B)
B'_1 = Rotate(B, 360.0 * 2.0 * 3.141592653589793 / (3.141592653589793 * 2.0 * z)°, E)
α = Angle(B, A, B'_1)
B' = Rotate(B, -(360.0 * 2.0 * 3.141592653589793 / (3.141592653589793 * 2.0 * z)°), E)
c = CircleArc(E, B, B'_1)
β = Angle(B', A, B)
a, j = Tangent(B, c)
C = (-6.283185307179586, 1)
D = (6.283185307179586, 1)
b = Segment(C, D)
h_1: d
f = Segment(A, D)
g = Segment(A, C)
e = CircleArc(E, B', B)
B_2 = Rotate((0.0, 1.2), 360.0 * 1.8 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.2))°, E)
c1 = CircleArc(E, (0.0, 1.2), B_2)
B_3 = Rotate((0.0, 1.2), -(360.0) * 1.8 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.2))°, E)
c3 = CircleArc(E, B_3, (0.0, 1.2))
B_4 = Rotate((0.0, 1.4), 360.0 * 1.6 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.4))°, E)
c2 = CircleArc(E, (0.0, 1.4), B_4)
B_5 = Rotate((0.0, 1.4), -(360.0) * 1.6 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.4))°, E)
c5 = CircleArc(E, B_5, (0.0, 1.4))
B_6 = Rotate((0.0, 1.6), 360.0 * 1.4 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.6))°, E)
B_8 = Rotate((0.0, 1.8), 360.0 * 1.2 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.8))°, E)
c4 = CircleArc(E, (0.0, 1.6), B_6)
c8 = CircleArc(E, (0.0, 1.8), B_8)
B_10 = Rotate((0.0, 2.0), 360.0 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.0))°, E)
B_12 = Rotate((0.0, 2.2), 360.0 * 0.8 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.2))°, E)
c10 = CircleArc(E, (0.0, 2.0), B_10)
c12 = CircleArc(E, (0.0, 2.2), B_12)
B_14 = Rotate((0.0, 2.4), 360.0 * 0.6 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.4))°, E)
B_16 = Rotate((0.0, 2.6), 360.0 * 0.4 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.6))°, E)
B_18 = Rotate((0.0, 2.8), 360.0 * 0.2 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.8))°, E)
c14 = CircleArc(E, (0.0, 2.4), B_14)
c16 = CircleArc(E, (0.0, 2.6), B_16)
c18 = CircleArc(E, (0.0, 2.8), B_18)
B_7 = Rotate((0.0, 1.6), -(360.0) * 1.4 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.6))°, E)
B_9 = Rotate((0.0, 1.8), -(360.0) * 1.2 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 0.8))°, E)
B_11 = Rotate((0.0, 2.0), -(360.0) * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.0))°, E)
B_13 = Rotate((0.0, 2.2), -(360.0) * 0.8 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.2))°, E)
B_15 = Rotate((0.0, 2.4), -(360.0) * 0.6 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.4))°, E)
B_19 = Rotate((0.0, 2.8), -(360.0) * 0.2 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.8))°, E)
B_17 = Rotate((0.0, 2.6), -(360.0) * 0.4 * 3.141592653589793 / (3.141592653589793 * 2.0 * (z - 1.6))°, E)
c7 = CircleArc(E, B_7, (0.0, 1.6))
c9 = CircleArc(E, B_9, (0.0, 1.8))
c11 = CircleArc(E, B_11, (0.0, 2.0))
c13 = CircleArc(E, B_13, (0.0, 2.2))
c15 = CircleArc(E, B_15, (0.0, 2.4))
c17 = CircleArc(E, B_17, (0.0, 2.6))
c19 = CircleArc(E, B_19, (0.0, 2.8))
i = Segment(A, B)
poli1, d_1, c_1, a_1 = Polygon(C, A, D)
F = (-0.2, 5.7)
G = (0.8, 5.7)
k = Segment(F, G)