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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 *
XA, XB = 1.0, 7.4 # domain of 1/x
KX, KY = 1.00, 2.00 # scale to screen
X0S, CY = -3.75, 1.70
def sx(x):
return X0S + (x - XA) * KX
def sy(x):
return KY / x
def branch(next_one, n=160, **kw):
xs = np.linspace(XA, XB, n)
pts = [[sx(x), CY + next_one * sy(x), 0] for x in xs]
m = VMobject(**kw)
m.set_points_as_corners(pts)
return m
def body_obj(fill="#1E4E8C", op=0.55):
xs = np.linspace(XA, XB, 160)
up = [[sx(x), CY + sy(x), 0] for x in xs]
dn = [[sx(x), CY - sy(x), 0] for x in reversed(xs)]
m = VMobject(stroke_width=0, fill_color=fill, fill_opacity=op)
m.set_points_as_corners(up + dn + [up[0]])
return m
def hoops(n=9, col=C_SKY, op=0.55):
xs = np.linspace(XA + 0.35, XB, n)
return VGroup(*[
Ellipse(width=0.34, height=2 * sy(x), stroke_width=3, stroke_opacity=op,
color=col).move_to([sx(x), CY, 0]) for x in xs])
class Gabriel(TikTok):
NAME = "gabriel"
def construct(self):
self.prepare()
chip = self.chip("Paradoja del infinito", C_SKY)
with self.beat(0) as b:
b.play(FadeIn(chip, shift=DOWN * 0.3), run_time=0.45)
t = VGroup(
self.fit(Text("el cuerno de", font=FONT, font_size=50,
weight=BOLD, color=WHITE), 8.0),
self.fit(Text("GABRIEL", font=FONT, font_size=86,
weight=BOLD, color=AMBER), 8.0),
).arrange(DOWN, buff=0.25).move_to(UP * 2.6)
b.play(FadeIn(t[0], shift=UP * 0.15), run_time=0.5)
b.play(FadeIn(t[1], scale=0.7), run_time=0.8)
axis_obj = Line([sx(XA) - 0.5, CY, 0], [sx(XB) + 0.35, CY, 0],
stroke_width=3, color="#33405C")
with self.beat(1) as b:
b.play(t.animate.scale(0.5).move_to(UP * 5.3), run_time=0.5)
f = MathTex(r"y = \frac{1}{x}", color=AMBER).scale(1.35).move_to(DOWN * 2.4)
up = branch(+1, stroke_color=AMBER, stroke_width=6)
b.play(FadeIn(axis_obj), run_time=0.3)
b.play(Create(up), run_time=0.9)
b.play(Write(f), run_time=0.7)
body = body_obj()
low = branch(-1, stroke_color=AMBER, stroke_width=6)
ar = hoops()
mouth = Ellipse(width=0.42, height=2 * sy(XA), stroke_width=6,
color=AMBER).move_to([sx(XA), CY, 0])
with self.beat(2) as b:
b.play(Create(low), run_time=0.6)
b.play(FadeIn(body), FadeIn(mouth), run_time=0.5)
b.play(LaggedStart(*[Create(a) for a in ar], lag_ratio=0.15), run_time=0.9)
inf = MathTex(r"\cdots \infty", color=C_GRAY).scale(1.0)
inf.next_to([sx(XB), CY, 0], RIGHT, buff=0.2)
b.play(FadeIn(inf), run_time=0.4)
horn = VGroup(axis_obj, body, up, low, ar, mouth, inf)
with self.beat(3) as b:
b.play(FadeOut(f), run_time=0.25)
q = self.fit(Text("¿cuánta pintura entra?", font=FONT, font_size=52,
weight=BOLD, color=WHITE), 8.2).move_to(DOWN * 2.3)
b.play(FadeIn(q, shift=UP * 0.15), run_time=0.7)
with self.beat(4) as b:
b.play(FadeOut(q), run_time=0.25)
filled = body_obj(fill=C_GREEN, op=0.85)
b.play(FadeIn(filled), run_time=0.7)
v = MathTex(r"V = \pi\int_1^{\infty}\frac{dx}{x^2} = \pi",
color=C_GREEN).scale(1.15).move_to(DOWN * 2.05)
b.play(Write(v), run_time=1.1)
with self.beat(5) as b:
lt = self.fit(Text("≈ 3,14 litros y te sobra", font=FONT, font_size=48,
weight=BOLD, color=C_GREEN), 8.2).move_to(DOWN * 2.90)
b.play(FadeIn(lt, shift=UP * 0.15), run_time=0.7)
with self.beat(6) as b:
b.play(FadeOut(VGroup(v, lt, filled)), run_time=0.4)
q2 = self.fit(Text("¿y pintarlo por fuera?", font=FONT, font_size=52,
weight=BOLD, color=WHITE), 8.2).move_to(DOWN * 2.3)
b.play(up.animate.set_stroke(C_PINK, 8), low.animate.set_stroke(C_PINK, 8),
run_time=0.6)
b.play(FadeIn(q2, shift=UP * 0.15), run_time=0.6)
with self.beat(7) as b:
b.play(FadeOut(q2), run_time=0.25)
a = MathTex(r"A > 2\pi\int_1^{\infty}\frac{dx}{x} = \infty",
color=C_PINK).scale(1.15).move_to(DOWN * 2.15)
b.play(Write(a), run_time=1.1)
b.play(Flash(a, color=C_PINK, line_length=0.5, num_lines=18,
flash_radius=2.4), run_time=0.7)
with self.beat(8) as b:
b.play(FadeOut(VGroup(a, horn)), run_time=0.45)
def row(txt, val, col):
t1 = Text(txt, font=FONT, font_size=44, weight=BOLD, color=WHITE)
t2 = Text(val, font=FONT, font_size=56, weight=BOLD, color=col)
return VGroup(t1, t2).arrange(DOWN, buff=0.18)
cmp = VGroup(row("volumen", "π (finito)", C_GREEN),
row("superficie", "∞ (infinita)", C_PINK)
).arrange(DOWN, buff=0.75).move_to(UP * 2.4)
self.fit(cmp, 8.2)
b.play(FadeIn(cmp[0], shift=UP * 0.15), run_time=0.55)
b.play(FadeIn(cmp[1], shift=UP * 0.15), run_time=0.55)
impact = VGroup(
self.fit(Text("lo llenás de pintura", font=FONT, font_size=48,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("pero no lo podés pintar", font=FONT, font_size=48,
weight=BOLD, color=AMBER), 8.2),
).arrange(DOWN, buff=0.3).move_to(DOWN * 0.6)
b.play(FadeIn(impact, scale=0.85), run_time=0.8)
with self.beat(9) as b:
b.play(FadeOut(VGroup(cmp, impact)), run_time=0.4)
tr = VGroup(
self.fit(Text("la trampa:", font=FONT, font_size=48,
weight=BOLD, color=C_PINK), 8.2),
self.fit(Text("la pintura real tiene", font=FONT, font_size=46,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("espesor. El cuerno", font=FONT, font_size=46,
weight=BOLD, color=WHITE), 8.2),
self.fit(Text("se hace más fino que eso.", font=FONT, font_size=46,
weight=BOLD, color=WHITE), 8.2),
).arrange(DOWN, buff=0.3).move_to(UP * 1.8)
for k in range(4):
b.play(FadeIn(tr[k], shift=UP * 0.12), run_time=0.45)
with self.beat(10) as b:
b.play(FadeOut(tr), run_time=0.35)
count_txt = VGroup(
self.fit(Text("con el infinito", font=FONT, font_size=52,
weight=BOLD, color=WHITE), 8.0),
self.fit(Text("la intuición se rompe", font=FONT, font_size=56,
weight=BOLD, color=AMBER), 8.0),
).arrange(DOWN, buff=0.35).move_to(UP * 1.4)
b.play(FadeIn(count_txt[0], shift=UP * 0.15), run_time=0.55)
b.play(Write(count_txt[1]), run_time=0.9)
b.play(Circumscribe(count_txt[1], color=AMBER, buff=0.25, stroke_width=6),
run_time=0.8)
self.finish()
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