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# -*- coding: utf-8 -*-
import sys, os, math
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from manim import *
from tiktok import *
D = 1.1 # line spacing = needle length
Y0 = 0.35 # lowest line
NLIN = 5
SEED, N1, N2 = 36, 60, 200
def throw(n):
rng = np.random.default_rng(SEED)
x = rng.uniform(-3.9, 3.9, n)
y = rng.uniform(Y0 + 0.1, Y0 + (NLIN - 1) * D - 0.1, n)
th = rng.uniform(0, PI, n)
dx, dy = D / 2 * np.cos(th), D / 2 * np.sin(th)
p1 = np.stack([x - dx, y - dy, np.zeros(n)], axis=1)
p2 = np.stack([x + dx, y + dy, np.zeros(n)], axis=1)
crosses = np.floor((p1[:, 1] - Y0) / D) != np.floor((p2[:, 1] - Y0) / D)
return p1, p2, crosses
class Buffon(TikTok):
NAME = "buffon"
def construct(self):
self.prepare()
chip = self.chip("π sin círculos", C_PINK)
p1, p2, crosses = throw(N2)
stripes = VGroup(*[Line([-4.2, Y0 + k * D, 0], [4.2, Y0 + k * D, 0],
stroke_width=4, color="#33405C") for k in range(NLIN)])
with self.beat(0) as b:
hook = VGroup(
self.fit(Text("tiro agujas al piso", font=FONT, font_size=52,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("y sale π", font=FONT, font_size=64,
weight=BOLD, color=AMBER), 8.2),
).arrange(DOWN, buff=0.32).move_to(UP * 2.4)
b.play(FadeIn(chip, shift=DOWN * 0.3), run_time=0.45)
b.play(FadeIn(hook[0], shift=UP * 0.15), run_time=0.6)
b.play(Write(hook[1]), run_time=0.8)
with self.beat(1) as b:
b.play(FadeOut(hook), run_time=0.35)
b.play(LaggedStart(*[Create(r) for r in stripes], lag_ratio=0.12), run_time=0.9)
demo = Line([-1.0, Y0 + D, 0], [-1.0, Y0 + 2 * D, 0],
stroke_width=9, color=AMBER)
med = DoubleArrow([0.2, Y0 + D, 0], [0.2, Y0 + 2 * D, 0], buff=0,
color=C_GREEN, stroke_width=6, tip_length=0.2)
lab = Text("mismo largo", font=FONT, font_size=32, weight=BOLD, color=C_GREEN)
lab.next_to(med, RIGHT, buff=0.25)
b.play(Create(demo), run_time=0.5)
b.play(GrowArrow(med), FadeIn(lab), run_time=0.6)
needles = VGroup(*[Line(p1[i], p2[i], stroke_width=4.5, color="#7C8AA8")
for i in range(N2)])
with self.beat(2) as b:
b.play(FadeOut(VGroup(demo, med, lab)), run_time=0.3)
b.play(LaggedStart(*[FadeIn(needles[i]) for i in range(N1)],
lag_ratio=0.012), run_time=max(1.1, b.floor - 0.5))
with self.beat(3) as b:
hit = [needles[i] for i in range(N1) if crosses[i]]
miss = [needles[i] for i in range(N1) if not crosses[i]]
b.play(*[a.animate.set_stroke(AMBER, 6) for a in hit],
*[a.animate.set_stroke("#46526E", 3.5) for a in miss], run_time=1.0)
c1 = int(crosses[:N1].sum())
def marker(n, c, y=-0.75):
g = VGroup(
VGroup(Text("tiradas", font=FONT, font_size=30, color=C_GRAY),
Text(str(n), font=FONT, font_size=62, weight=BOLD, color=WHITE)
).arrange(DOWN, buff=0.1),
VGroup(Text("cruzan", font=FONT, font_size=30, color=C_GRAY),
Text(str(c), font=FONT, font_size=62, weight=BOLD, color=AMBER)
).arrange(DOWN, buff=0.1),
).arrange(RIGHT, buff=1.5).move_to([0, y, 0])
return g
marker_m = marker(N1, c1)
with self.beat(4) as b:
b.play(FadeIn(marker_m, shift=UP * 0.15), run_time=0.8)
with self.beat(5) as b:
f = MathTex(r"\frac{2 \times \text{tiradas}}{\text{cruces}}",
color=C_SKY).scale(1.25).move_to(DOWN * 2.45)
b.play(Write(f), run_time=1.1)
with self.beat(6) as b:
estimate = 2 * N1 / c1
res = MathTex(r"= %s" % f"{estimate:.4f}".replace(".", "{,}"),
color=C_GREEN).scale(1.45)
res.next_to(f, RIGHT, buff=0.4)
grp = VGroup(f, res)
b.play(Write(res), run_time=0.8)
b.play(grp.animate.move_to(DOWN * 2.45), run_time=0.4)
b.play(Flash(res, color=C_GREEN, line_length=0.5, num_lines=16,
flash_radius=1.4), run_time=0.6)
c2 = int(crosses.sum())
with self.beat(7) as b:
hit = [needles[i] for i in range(N1, N2) if crosses[i]]
miss = [needles[i] for i in range(N1, N2) if not crosses[i]]
for a in hit:
a.set_stroke(AMBER, 6)
for a in miss:
a.set_stroke("#46526E", 3.5)
b.play(LaggedStart(*[FadeIn(needles[i]) for i in range(N1, N2)],
lag_ratio=0.004), run_time=max(1.0, b.floor - 1.3))
est2 = 2 * N2 / c2
nm = marker(N2, c2)
nres = MathTex(r"= %s" % f"{est2:.4f}".replace(".", "{,}"),
color=C_GREEN).scale(1.45).next_to(f, RIGHT, buff=0.4)
b.play(Transform(marker_m, nm), Transform(res, nres), run_time=0.9)
with self.beat(8) as b:
pi = MathTex(r"\pi = 3{,}14159\ldots", color=AMBER).scale(1.5)
pi.move_to(UP * 5.5)
b.play(Write(pi), run_time=1.0)
b.play(Circumscribe(pi, color=AMBER, buff=0.25, stroke_width=6), run_time=0.8)
with self.beat(9) as b:
b.play(FadeOut(VGroup(marker_m, pi, f, res)), run_time=0.45)
t = VGroup(
self.fit(Text("no hay ningún círculo", font=FONT, font_size=48,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("y π aparece igual", font=FONT, font_size=48,
weight=BOLD, color=AMBER), 8.2),
).arrange(DOWN, buff=0.35).move_to(DOWN * 1.5)
b.play(FadeIn(t[0], shift=UP * 0.15), run_time=0.6)
b.play(FadeIn(t[1], shift=UP * 0.15), run_time=0.7)
with self.beat(10) as b:
b.play(FadeOut(t), run_time=0.35)
count_txt = VGroup(
self.fit(Text("aguja de Buffon", font=FONT, font_size=58,
weight=BOLD, color=AMBER), 8.0),
self.fit(Text("hacelo con fósforos", font=FONT, font_size=44,
weight=BOLD, color=WHITE), 8.0),
).arrange(DOWN, buff=0.35).move_to(DOWN * 1.5)
b.play(Write(count_txt[0]), run_time=0.8)
b.play(FadeIn(count_txt[1], shift=UP * 0.15), run_time=0.6)
self.finish()
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