Juego de moneda  (Según Prof. Pau Atela, Smith College)
El triangulo verde representa un cono desenrollado en el plano.
La origen corresponde al vértice del cono, y los círculos concéntricos 
a niveles de altura constante en el cono. 
El parámetro “a” controla el ángulo del cono.
El parámetro “r” controla el radio de los discos que se empilan

Después de haber escogido unos parámetros “a” y “r”, 
empila los discos uno a uno siguiendo estas reglas:
- El nuevo disco se coloca al nivel mas bajo posible - es decir 
el mas cerca de la origen posible
- discos solo se pueden tocar tangencialmente

Es frecuentemente necesario de colocar copias de un disco en
las copias del cono marcadas en azul.

Analiza las configuraciones que resultan contando los vectores 
“sube” y “baja” de los frentes sucesivos

Explicación

a = 2.1 (slider from 0 to 4, step 0.05)
E_1 = Point(yAxis)
F_1 = Point(Circle[E_1, a])
F_2: ((-x(F_1)), y(F_1))
A = Intersect(xAxis, yAxis)
B = (0, 1)
c = Circle(A, B)
C = (0, 2)
d = Circle(A, C)
D = (0, 3)
e = Circle(A, D)
E = Point(yAxis)
f = Circle(A, E)
F = Point(yAxis)
g = Circle(A, F)
G = Point(yAxis)
h = Circle(A, G)
H = (0, 7)
k = Circle(A, H)
I = Point(yAxis)
p = Circle(A, I)
J = Intersect(xAxis, yAxis)
K: (x(F_2), y(F_2))
i = Segment(J, K)
j = Segment((0, 0), F_1)
L = Intersect(p, j, 1)
M = Intersect(p, i, 1)
N = Intersect(k, j, 1)
O' = Intersect(k, i, 1)
P = Intersect(h, j, 1)
Q = Intersect(h, i, 1)
R = Intersect(g, j, 1)
S = Intersect(g, i, 1)
T = Intersect(f, j, 1)
U = Intersect(f, i, 1)
V = Intersect(e, j, 1)
W = Intersect(e, i, 1)
Z = Intersect(d, j, 1)
A_1 = Intersect(d, i, 1)
B_1 = Intersect(c, j, 1)
C_1 = Intersect(c, i, 1)
r = 0.4 (slider from 0.05 to 1, step 0.01)
D_1 = (-0.6744459001816834, 1.9160117491694448)
D_2 = (2.444189656597023, 3.1099822452354493)
D_3 = (3.2941347554914673, 2.907614364546296)
D_4 = (3.830409639317724, 2.3814578747544974)
D_5 = (3.830409639317724, 1.6124599281357148)
D_6 = (3.6583969407319437, 0.9345275278270515)
D_7 = (2.818570235871957, 1.1166586204472895)
D_8 = (3.1322404509401447, 1.5112759877911384)
D_9 = (3.304253149525925, 2.158853205996429)
D_{10} = (2.4543080506314805, 2.54335217930582)
D_{11} = (2, 2)
l = Segment(E_1, F_1)
m = Segment(J, F_1)
b = Segment(E_1, F_2)
D_{12} = (-1.7522146837586963, 4.585077558823826)
r_2 = 0.35 (slider from 0.05 to 1, step 0.05)
D_{13} = (9.482211352094248, 4.934420416779891)
D_{14} = (0.6283105308229444, 1.9002652407520086)
D_{15} = (-0.030675473488433427, 2.4057850616462546)
D_{16} = (-0.4105941107446035, 3.124891520865725)
D_{17} = (-1.7939740234749755, 2.9893247560984175)
D_{18} = (1.554834837283264, 2.746026354180601)
D_{19} = (-1.88267497927339, 3.7965933257648667)
D_{20} = (1.4537105802286485, 1.942649512941532)
D_{21} = (1.1620394717181908, 3.4681460722157724)
D_{22} = (0.6916799781322894, 4.1416602144735775)
D_{23} = (-1.151910949010157, 3.4732914703992)
D_{24} = (1.762609586606514, 4.048895112914536)
D_{25} = (-0.649629243410308, 5.006966300300617)
D_{26} = (-1.0649177753658348, 2.6250633528476066)
D_{27} = (0.7265281605550228, 2.6998532908199193)
D_{28} = (0.3477777747561724, 3.406287241442461)
D_{29} = (1.2548024643063074, 4.682162225397203)
D_{30} = (4.857542529277701, 1.0532711476422962)
D_{31} = (6.6603549323490245, 0.8096478499299536)
D_{32} = (6.7090795918914905, 1.9059526896354944)
D_{33} = (4.760096700600504, 8.215548979517258)
D_{34} = (0.6526053532311096, 5.247989464197405)
D_{35} = (0.08586152668079161, 4.678672683541361)
D_{36} = (-0.25048950538971076, 3.9354541432076693)
D_{37} = (-0.9913485456318394, 4.27556079509827)
D_{38} = (5.568941472872771, 6.3703666888557615)
H_1 = (7.0991206157515405, 3.1896407639689675)
d_1 = Circle(H_1, r)
I_1 = (5.723012627991244, 3.4436914694016387)
f_1 = Circle(I_1, r)
J_1 = (5.0243731880514, 3.4436914694016387)
g_1 = Circle(J_1, r)
K_1 = (6.675702773363756, 2.575684892506678)
h_1 = Circle(K_1, r)
L_1 = (4.982031403812622, 4.756286780803775)
k_1 = Circle(L_1, r)
M_1 = (6.985671810288116, 7.372501700563063)
p_1 = Circle(M_1, r)
N_1 = (5.419759776275695, 7.4014370402190295)
q_1 = Circle(N_1, r)
O_1 = (5.490132814677962, 2.5333431082678994)
s_1 = Circle(O_1, r)
P_1 = (4.643297129902395, 2.8932482742975174)
t_1 = Circle(P_1, r)
Q_1 = (5.384278354081016, 5.7936604946538495)
c_2 = Circle(Q_1, r)
R_1 = (6.84506991031887, 4.967995701997667)
d_2 = Circle(R_1, r)
S_1 = (6.188772254617805, 4.7774576729231635)
e_2 = Circle(S_1, r)
T_1 = (7.247316860587264, 3.9306219881475926)
f_2 = Circle(T_1, r)
U_1 = (6.527506528528032, 3.6130586063567534)
g_2 = Circle(U_1, r)
V_1 = (6.96732920220819, 6.2352599996076945)
h_2 = Circle(V_1, r)
W_1 = (7.683922887253131, 6.548498881974102)
k_2 = Circle(W_1, r)
Z_1 = (5.490132814677962, 5.1373628389527815)
p_2 = Circle(Z_1, r)
A_2 = (4.6221262377830055, 3.8671093117894246)
q_2 = Circle(A_2, r)
B_2 = (6.362023135570657, 7.4091869167229145)
s_2 = Circle(B_2, r)
C_2 = (6.2311140388565835, 6.132394768564078)
t_2 = Circle(C_2, r)
H_2 = (5.595987275274908, 4.544577859609881)
d_3 = Circle(H_2, r)
H_3 = (7.247316860587264, 5.476097112863011)
d_4 = Circle(H_3, r)
H_4 = (5.257253001364681, 4.015305556625149)
d_5 = Circle(H_4, r)
H_5 = (5.998234225543302, 5.4337553286242315)
d_6 = Circle(H_5, r)
H_6 = (7.040699634527892, 6.712167809685752)
d_7 = Circle(H_6, r)
H_7 = (6.633360989124978, 5.603122465579346)
d_8 = Circle(H_7, r)
H_8 = (5.977063333423914, 2.8720773821781282)
d_9 = Circle(H_8, r)
H_9 = (4.4315882087085035, 4.502236075371103)
d_{10} = Circle(H_9, r)
H_{10} = (8.269654375882885, 7.427529524802839)
d_{11} = Circle(H_{10}, r)
H_{11} = (6.380365743650581, 6.730510417765678)
d_{12} = Circle(H_{11}, r)
distanceJH10 = Distance(J, H_{10})
H_{12} = (7.621891021198954, 5.86614835537816)
d_{13} = Circle(H_{12}, r)
H_{13} = (8.36136741628251, 6.822223458165304)
d_{14} = Circle(H_{13}, r)
H_{14} = (7.957830038524155, 8.216261672239627)
d_{15} = Circle(H_{14}, r)
r_1 = 0.4 (slider from 0.05 to 1, step 0.05)
H_{15} = (4.876176943215676, 2.4063177555515636)
d_{16} = Circle(H_{15}, r_1)
r_3 = 0.4 (slider from 0.05 to 1, step 0.05)
H_{16} = (5.320765677722849, 1.8982163446862208)
d_{17} = Circle(H_{16}, r_3)
H_{17} = (4.862454277465875, 8.152261211402433)
d_{18} = Circle(H_{17}, r_1)
H_{18} = (6.4851647442892535, 3.1049571954914104)
d_{19} = Circle(H_{18}, r_1)
H_{19} = (6.019405117662692, 4.099989125102707)
d_{20} = Circle(H_{19}, r_1)
H_{20} = (5.476997402359636, 8.101049284327951)
d_{21} = Circle(H_{20}, r_1)
H_{21} = (7.3531713211842105, 2.5333431082678994)
d_{22} = Circle(H_{21}, r_1)
H_{22} = (6.633360989124978, 4.2905271541772105)
d_{23} = Circle(H_{22}, r_1)
H_{23} = (6.040576009782081, 2.1734379422382815)
d_{24} = Circle(H_{23}, r_1)
H_{24} = (7.572635268845724, 7.354159092483139)
d_{25} = Circle(H_{24}, r_1)
H_{25} = (7.132412674927518, 8.069520807600226)
d_{26} = Circle(H_{25}, r_1)
H_{26} = (6.006187315462596, 8.186402496118752)
d_{27} = Circle(H_{26}, r_1)
n = Segment(J, E_1)
J' = Mirror(J, j)
G_1 = Mirror(E_1, j)
n' = Segment(J', G_1)
j' = Mirror(j, n')
j'' = Mirror(j', n)
O = Mirror(J', n)
E_2 = Mirror(G_1, n)
n'' = Segment(O, E_2)
poly4, j_1, f_3, f_4 = Polygon(F_2, F_1, J)
G_2 = Intersect(d, j, 1)
q = Circle(G_2, r)
I_2 = Intersect(d, i, 1)
s = Circle(I_2, r)
o = true