mirror of
https://github.com/3b1b/manim.git
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Grant Sanderson
GitHub
commit
c06ca048c6
3 changed files with 942 additions and 6 deletions
922
active_projects/pi_day.py
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922
active_projects/pi_day.py
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# -*- coding: utf-8 -*-
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from helpers import *
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from mobject.tex_mobject import TexMobject
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from mobject.vectorized_mobject import *
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from animation.animation import Animation
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from animation.transform import *
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from animation.simple_animations import *
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from animation.compositions import *
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from animation.playground import *
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from animation.continual_animation import *
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from topics.geometry import *
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from topics.characters import *
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from topics.functions import *
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from topics.fractals import *
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from topics.number_line import *
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from topics.combinatorics import *
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from topics.numerals import *
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from topics.three_dimensions import *
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from topics.objects import *
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from topics.probability import *
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from topics.complex_numbers import *
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from scene import Scene
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from scene.reconfigurable_scene import ReconfigurableScene
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from scene.zoomed_scene import *
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from scene.moving_camera_scene import *
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from camera import *
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from topics.graph_scene import *
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from topics.common_scenes import *
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RESOURCE_DIR = os.path.join(MEDIA_DIR, "3b1b_videos", "π Day 2018", "images")
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def get_image(name):
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return ImageMobject(os.path.join(RESOURCE_DIR, name))
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def get_circle_drawing_terms(radius = 1, positioning_func = lambda m : m.center()):
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circle = Circle(color = YELLOW, radius = 1.25)
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positioning_func(circle)
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radius = Line(circle.get_center(), circle.points[0])
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radius.highlight(WHITE)
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one = TexMobject("1")
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one.scale(0.75)
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one_update = UpdateFromFunc(
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one, lambda m : m.move_to(
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radius.get_center() + \
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0.25*rotate_vector(radius.get_vector(), TAU/4)
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),
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)
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decimal = DecimalNumber(0, num_decimal_points = 4, show_ellipsis = True)
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decimal.scale(0.75)
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def reposition_decimal(decimal):
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vect = radius.get_vector()
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unit_vect = vect/np.linalg.norm(vect)
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angle = radius.get_angle()
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alpha = (-np.cos(2*angle) + 1)/2
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interp_length = interpolate(decimal.get_width(), decimal.get_height(), alpha)
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buff = interp_length/2 + MED_SMALL_BUFF
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decimal.move_to(radius.get_end() + buff*unit_vect)
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decimal.shift(UP*decimal.get_height()/2)
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return decimal
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kwargs = {"run_time" : 3, "rate_func" : bezier([0, 0, 1, 1])}
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changing_decimal = ChangingDecimal(
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decimal, lambda a : a*TAU,
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position_update_func = reposition_decimal,
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**kwargs
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)
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terms = VGroup(circle, radius, one, decimal)
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generate_anims1 = lambda : [ShowCreation(radius), Write(one)]
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generate_anims2 = lambda : [
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ShowCreation(circle, **kwargs),
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Rotating(radius, about_point = radius.get_start(), **kwargs),
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changing_decimal,
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one_update,
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]
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return terms, generate_anims1, generate_anims2
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##
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class PiTauDebate(PiCreatureScene):
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def construct(self):
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pi, tau = self.pi, self.tau
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self.add(pi, tau)
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pi_value = TextMobject("3.1415...!")
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pi_value.highlight(BLUE)
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tau_value = TextMobject("6.2831...!")
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tau_value.highlight(GREEN)
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self.play(PiCreatureSays(
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pi, pi_value,
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target_mode = "angry",
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look_at_arg = tau.eyes,
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# bubble_kwargs = {"width" : 3}
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))
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self.play(PiCreatureSays(
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tau, tau_value,
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target_mode = "angry",
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look_at_arg = pi.eyes,
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bubble_kwargs = {"width" : 3, "height" : 2},
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))
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self.wait()
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# Show tau
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terms, generate_anims1, generate_anims2 = get_circle_drawing_terms(
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radius = 1.25,
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positioning_func = lambda m : m.to_edge(RIGHT, buff = 2).to_edge(UP, buff = 1)
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)
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circle, radius, one, decimal = terms
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self.play(
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RemovePiCreatureBubble(pi),
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RemovePiCreatureBubble(tau),
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*generate_anims1()
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)
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self.play(
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tau.change, "hooray",
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pi.change, "sassy",
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*generate_anims2()
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)
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self.wait()
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# Show pi
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circle = Circle(color = RED, radius = 1.25/2)
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circle.rotate(TAU/4)
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circle.move_to(pi)
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circle.to_edge(UP, buff = MED_LARGE_BUFF)
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diameter = Line(circle.get_left(), circle.get_right())
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one = TexMobject("1")
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one.scale(0.75)
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one.next_to(diameter, UP, SMALL_BUFF)
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circum_line = diameter.copy().scale(np.pi)
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circum_line.match_style(circle)
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circum_line.next_to(circle, DOWN, buff = MED_LARGE_BUFF)
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# circum_line.to_edge(LEFT)
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brace = Brace(circum_line, DOWN, buff = SMALL_BUFF)
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decimal = DecimalNumber(np.pi, num_decimal_points = 4, show_ellipsis = True)
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decimal.scale(0.75)
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decimal.next_to(brace, DOWN, SMALL_BUFF)
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self.play(
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FadeIn(VGroup(circle, diameter, one)),
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tau.change, "confused",
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pi.change, "hooray"
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)
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self.add(circle.copy().fade(0.5))
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self.play(
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ReplacementTransform(circle, circum_line, run_time = 2)
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)
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self.play(GrowFromCenter(brace), Write(decimal))
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self.wait(3)
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# self.play()
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def create_pi_creatures(self):
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pi = self.pi = Randolph()
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pi.to_edge(DOWN).shift(4*LEFT)
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tau = self.tau = TauCreature(
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# mode = "angry",
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file_name_prefix = "TauCreatures",
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color = GREEN_E
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).flip()
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tau.to_edge(DOWN).shift(4*RIGHT)
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return VGroup(pi, tau)
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class HartlAndPalais(Scene):
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def construct(self):
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hartl_rect = ScreenRectangle(
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color = WHITE,
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stroke_width = 1,
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)
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hartl_rect.scale_to_fit_width(SPACE_WIDTH - 1)
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hartl_rect.to_edge(LEFT)
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palais_rect = hartl_rect.copy()
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palais_rect.to_edge(RIGHT)
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tau_words = TextMobject("$\\tau$ ``tau''")
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tau_words.next_to(hartl_rect, UP)
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hartl_words = TextMobject("Michael Hartl's \\\\ ``Tau manifesto''")
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hartl_words.next_to(hartl_rect, DOWN)
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palais_words = TextMobject("Robert Palais' \\\\ ``Pi is Wrong!''")
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palais_words.next_to(palais_rect, DOWN)
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for words in hartl_words, palais_words:
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words.scale(0.7, about_edge = UP)
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three_legged_creature = ThreeLeggedPiCreature(height = 1.5)
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three_legged_creature.next_to(palais_rect, UP)
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# self.add(hartl_rect, palais_rect)
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self.add(hartl_words)
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self.play(Write(tau_words))
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self.wait()
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self.play(FadeIn(palais_words))
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self.play(FadeIn(three_legged_creature))
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self.play(three_legged_creature.change_mode, "wave")
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self.play(Blink(three_legged_creature))
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self.play(Homotopy(
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lambda x, y, z, t : (x + 0.1*np.sin(2*TAU*t)*np.exp(-10*(t-0.5 - 0.5*(y-1.85))**2), y, z),
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three_legged_creature,
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run_time = 2,
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))
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self.wait()
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class ManyFormulas(Scene):
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def construct(self):
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formulas = VGroup(
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TexMobject("\\sin(x + \\tau) = \\sin(x)"),
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TexMobject("e^{\\tau i} = 1"),
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TexMobject("n! \\approx \\sqrt{\\tau n} \\left(\\frac{n}{e} \\right)^n"),
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TexMobject("c_n = \\frac{1}{\\tau} \\int_0^\\tau f(x) e^{inx}dx"),
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)
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formulas.arrange_submobjects(DOWN, buff = MED_LARGE_BUFF)
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formulas.to_edge(LEFT)
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self.play(LaggedStart(FadeIn, formulas, run_time = 3))
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circle = Circle(color = YELLOW, radius = 2)
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circle.to_edge(RIGHT)
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radius = Line(circle.get_center(), circle.get_right())
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radius.highlight(WHITE)
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angle_groups = VGroup()
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for denom in 5, 4, 3, 2:
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radius_copy = radius.copy()
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radius_copy.rotate(TAU/denom, about_point = circle.get_center())
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arc = Arc(
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angle = TAU/denom,
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stroke_color = RED,
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stroke_width = 4,
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radius = circle.radius,
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)
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arc.shift(circle.get_center())
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mini_arc = arc.copy()
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mini_arc.set_stroke(WHITE, 2)
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mini_arc.scale(0.15, about_point = circle.get_center())
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tau_tex = TexMobject("\\tau/%d"%denom)
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point = mini_arc.point_from_proportion(0.5)
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tau_tex.next_to(point, direction = point - circle.get_center())
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angle_group = VGroup(radius_copy, mini_arc, tau_tex, arc)
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angle_groups.add(angle_group)
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angle_group = angle_groups[0]
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self.play(*map(FadeIn, [circle, radius]))
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self.play(
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circle.set_stroke, {"width" : 1,},
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FadeIn(angle_group),
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)
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self.wait()
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for group in angle_groups[1:]:
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self.play(Transform(angle_group, group, path_arc = TAU/8))
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self.wait()
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class HistoryOfOurPeople(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Today: The history \\\\ of our people.",
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bubble_kwargs = {"width" : 4, "height" : 3}
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)
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self.change_all_student_modes("hooray")
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self.wait()
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self.play(*[
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ApplyMethod(pi.change, "happy", self.screen)
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for pi in self.pi_creatures
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])
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self.wait(4)
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class TauFalls(Scene):
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def construct(self):
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tau = TauCreature()
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bottom = np.min(tau.body.points[:,1])*UP
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angle = -0.15*TAU
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tau.generate_target()
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tau.target.change("angry")
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tau.target.rotate(angle, about_point = bottom)
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self.play(Rotate(tau, angle, rate_func = rush_into, path_arc = angle, about_point = bottom))
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# self.play(MoveToTarget(tau, rate_func = rush_into, path_arc = angle))
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self.play(MoveToTarget(tau))
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self.wait()
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class EulerWrites628(Scene):
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CONFIG = {
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"camera_config" : {
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"background_alpha" : 255,
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}
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}
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def construct(self):
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image = ImageMobject(os.path.join(RESOURCE_DIR, "dalembert_zoom"))
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image.scale_to_fit_width(2*SPACE_WIDTH - 1)
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image.to_edge(UP, buff = MED_SMALL_BUFF)
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image.fade(0.15)
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rect = Rectangle(
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width = 12,
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height = 0.5,
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stroke_width = 0,
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fill_opacity = 0.3,
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fill_color = GREEN,
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)
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rect.insert_n_anchor_points(20)
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rect.apply_function(lambda p : np.array([p[0], p[1] - 0.005*p[0]**2, p[2]]))
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rect.rotate(0.012*TAU)
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rect.move_to(image)
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rect.shift(0.15*DOWN)
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words = TextMobject(
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"``Let", "$\\pi$", "be the", "circumference",
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"of a circle whose", "radius = 1''",
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)
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words.highlight_by_tex_to_color_map({
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"circumference" : YELLOW,
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"radius" : GREEN,
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})
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words.next_to(image, DOWN)
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pi = words.get_part_by_tex("\\pi").copy()
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terms, generate_anims1, generate_anims2 = get_circle_drawing_terms(
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radius = 1,
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positioning_func = lambda circ : circ.next_to(words, DOWN, buff = 1.25)
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)
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circle, radius, one, decimal = terms
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unwrapped_perimeter = Line(ORIGIN, TAU*RIGHT)
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unwrapped_perimeter.match_style(circle)
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unwrapped_perimeter.next_to(circle, DOWN)
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brace = Brace(unwrapped_perimeter, UP, buff = SMALL_BUFF)
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perimeter = TexMobject(
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"\\pi\\epsilon\\rho\\iota\\mu\\epsilon\\tau\\rho\\text{o}\\varsigma",
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"\\text{ (perimeter)}",
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"="
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)
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perimeter.next_to(brace, UP, submobject_to_align = perimeter[1], buff = SMALL_BUFF)
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perimeter[0][0].highlight(GREEN)
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self.play(FadeInFromDown(image))
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self.play(
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Write(words),
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GrowFromPoint(rect, rect.point_from_proportion(0.9))
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)
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self.wait()
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self.play(*generate_anims1())
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self.play(*generate_anims2())
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self.play(terms.shift, UP)
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self.play(
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pi.scale, 2,
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pi.shift, DOWN,
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pi.highlight, GREEN
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)
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self.wait()
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self.play(
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GrowFromCenter(brace),
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circle.set_stroke, YELLOW, 1,
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ReplacementTransform(circle.copy(), unwrapped_perimeter),
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decimal.scale, 1.25,
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decimal.next_to, perimeter[-1].get_right(), RIGHT,
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ReplacementTransform(pi, perimeter[0][0]),
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Write(perimeter),
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)
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self.wait()
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class HeroAndVillain(Scene):
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CONFIG = {
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"camera_config" : {
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"background_alpha" : 255,
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}
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}
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def construct(self):
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good_euler = get_image("Leonhard_Euler_by_Handmann")
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bad_euler_pixelated = get_image("Leonard_Euler_pixelated")
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bad_euler = get_image("Leonard_Euler_revealed")
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pictures = good_euler, bad_euler_pixelated, bad_euler
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for mob in pictures:
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mob.scale_to_fit_height(5)
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good_euler.move_to(SPACE_WIDTH*LEFT/2)
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bad_euler.move_to(SPACE_WIDTH*RIGHT/2)
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bad_euler_pixelated.move_to(bad_euler)
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good_euler_label = TextMobject("Leonhard Euler")
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good_euler_label.next_to(good_euler, DOWN)
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tau_words = TextMobject("Used 6.2831...")
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tau_words.next_to(good_euler, UP)
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tau_words.highlight(GREEN)
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bad_euler_label = TextMobject("Also Euler...")
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bad_euler_label.next_to(bad_euler, DOWN)
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pi_words = TextMobject("Used 3.1415...")
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pi_words.highlight(RED)
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pi_words.next_to(bad_euler, UP)
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self.play(
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FadeInFromDown(good_euler),
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Write(good_euler_label)
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)
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self.play(LaggedStart(FadeIn, tau_words))
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self.wait()
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self.play(FadeInFromDown(bad_euler_pixelated))
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self.play(LaggedStart(FadeIn, pi_words))
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self.wait(2)
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self.play(
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FadeIn(bad_euler),
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Write(bad_euler_label),
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)
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self.remove(bad_euler_pixelated)
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self.wait(2)
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class AnalysisQuote(Scene):
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||||
def construct(self):
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analysis = get_image("Analysis_page_showing_pi")
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analysis.scale_to_fit_height(2*SPACE_HEIGHT)
|
||||
analysis.to_edge(LEFT, buff = 0)
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||||
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text = TextMobject(
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"``\\dots set the radius of",
|
||||
"the circle\\dots to be = 1, \\dots \\\\",
|
||||
"through approximations the",
|
||||
"semicircumference \\\\", "of said circle",
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||||
"has been found to be", "$= 3.14159\\dots$,\\\\",
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||||
"for which number, for the sake of",
|
||||
"brevity, \\\\ I will write", "$\pi$\\dots''",
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||||
alignment = ''
|
||||
)
|
||||
pi_formula = TexMobject(
|
||||
"\\pi", "=", "{ \\text{semicircumference}", "\\over", "\\text{radius}}"
|
||||
)
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||||
text.scale_to_fit_width(SPACE_WIDTH)
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||||
text.next_to(analysis, RIGHT, LARGE_BUFF)
|
||||
text.to_edge(UP)
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||||
|
||||
HIGHLIGHT_COLOR= GREEN
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for mob in text, pi_formula:
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||||
mob.highlight_by_tex_to_color_map({
|
||||
"semicircumference" : HIGHLIGHT_COLOR,
|
||||
"3.14" : HIGHLIGHT_COLOR,
|
||||
"\pi" : HIGHLIGHT_COLOR
|
||||
})
|
||||
|
||||
terms, generate_anims1, generate_anims2 = get_circle_drawing_terms(
|
||||
radius = 1,
|
||||
positioning_func = lambda circ : circ.next_to(text, DOWN, LARGE_BUFF)
|
||||
)
|
||||
terms[0].highlight(HIGHLIGHT_COLOR)
|
||||
terms[-1].highlight(HIGHLIGHT_COLOR)
|
||||
|
||||
pi_formula.next_to(terms, DOWN, buff = 0)
|
||||
pi_formula.align_to(text, alignment_vect = RIGHT)
|
||||
pi_formula[0].scale(2, about_edge = RIGHT)
|
||||
|
||||
self.add(analysis)
|
||||
self.play(*generate_anims2(), rate_func = lambda t : 0.5*smooth(t))
|
||||
self.play(LaggedStart(FadeIn,text), run_time = 5)
|
||||
self.play(FadeIn(pi_formula))
|
||||
self.wait()
|
||||
|
||||
class QuarterTurn(Scene):
|
||||
def construct(self):
|
||||
terms, generate_anims1, generate_anims2 = get_circle_drawing_terms(
|
||||
radius = 2,
|
||||
positioning_func = lambda circ : circ.move_to(4*RIGHT)
|
||||
)
|
||||
circle, radius, one, decimal = terms
|
||||
circle_ghost = circle.copy().set_stroke(YELLOW_E, 1)
|
||||
radius_ghost = radius.copy().set_stroke(WHITE, 1)
|
||||
|
||||
self.add(circle_ghost, radius_ghost)
|
||||
self.play(
|
||||
*generate_anims2(),
|
||||
rate_func = lambda t : 0.25*smooth(t)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
pi_halves = TexMobject("\\pi", "/2")
|
||||
pi_halves[0].highlight(RED)
|
||||
tau_fourths = TexMobject("\\tau", "/4")
|
||||
tau_fourths[0].highlight(GREEN)
|
||||
for mob in pi_halves, tau_fourths:
|
||||
mob.next_to(decimal, UP)
|
||||
|
||||
self.play(FadeInFromDown(pi_halves))
|
||||
self.wait()
|
||||
self.play(
|
||||
pi_halves.shift, 0.75*UP,
|
||||
FadeInFromDown(tau_fourths)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
class UsingTheta(Scene):
|
||||
def construct(self):
|
||||
plane = NumberPlane(x_unit_size = 3, y_unit_size = 3)
|
||||
# plane.main_lines.fade(0.5)
|
||||
# plane.secondary_lines.fade(0.5)
|
||||
plane.fade(0.5)
|
||||
self.add(plane)
|
||||
|
||||
circle = Circle(radius = 3)
|
||||
circle.set_stroke(YELLOW, 2)
|
||||
self.add(circle)
|
||||
|
||||
radius = Line(ORIGIN, circle.get_right())
|
||||
arc = Arc(radius = 0.5, angle = TAU, num_anchors = 200)
|
||||
arc.highlight(GREEN)
|
||||
start_arc = arc.copy()
|
||||
|
||||
theta = TexMobject("\\theta", "=")
|
||||
theta[0].match_color(arc)
|
||||
theta.add_background_rectangle()
|
||||
update_theta = ContinualUpdateFromFunc(
|
||||
theta, lambda m : m.shift(
|
||||
rotate_vector(0.9*RIGHT, radius.get_angle()/2) \
|
||||
- m[1][0].get_center()
|
||||
)
|
||||
)
|
||||
|
||||
angle = Integer(0, unit = "^\\circ")
|
||||
update_angle = ContinualChangingDecimal(
|
||||
angle, lambda a : radius.get_angle()*(360/TAU),
|
||||
position_update_func = lambda a : a.next_to(theta, RIGHT, SMALL_BUFF)
|
||||
)
|
||||
|
||||
self.add(update_theta, update_angle)
|
||||
last_frac = 0
|
||||
for frac in 1./4, 1./12, 3./8, 1./6, 5./6:
|
||||
self.play(
|
||||
Rotate(radius, angle = (frac-last_frac)*TAU, about_point = ORIGIN),
|
||||
UpdateFromAlphaFunc(
|
||||
arc,
|
||||
lambda m, a : m.pointwise_become_partial(
|
||||
start_arc, 0, interpolate(last_frac, frac, a)
|
||||
)
|
||||
),
|
||||
run_time = 3
|
||||
)
|
||||
last_frac = frac
|
||||
self.wait()
|
||||
|
||||
class ThingsNamedAfterEuler(Scene):
|
||||
def construct(self):
|
||||
group = VGroup(*map(TextMobject, [
|
||||
"Euler's formula (Complex analysis)",
|
||||
"Euler's formula (Graph theory)",
|
||||
"Euler's formula (Mechanical engineering)",
|
||||
"Euler's formula (Analytical number theory)",
|
||||
"Euler's formula (Continued fractions)",
|
||||
"Euler-Lagrance equations (mechanics)",
|
||||
"Euler number (topology)",
|
||||
"Euler equations (fluid dynamics)",
|
||||
"Euler angles (rigid-body mechanics)",
|
||||
"Euler totient function (number theory)",
|
||||
]))
|
||||
group.arrange_submobjects(DOWN, aligned_edge = LEFT)
|
||||
group.scale_to_fit_height(2*SPACE_HEIGHT - 1)
|
||||
|
||||
self.play(LaggedStart(FadeIn, group, lag_ratio = 0.2, run_time = 12))
|
||||
self.wait()
|
||||
|
||||
class EulerThinking(Scene):
|
||||
def construct(self):
|
||||
image = get_image("Leonhard_Euler_by_Handmann")
|
||||
image.scale_to_fit_height(4)
|
||||
image.to_edge(DOWN)
|
||||
image.shift(4*LEFT)
|
||||
bubble = ThoughtBubble(height = 4.5)
|
||||
bubble.next_to(image, RIGHT)
|
||||
bubble.to_edge(UP, buff = SMALL_BUFF)
|
||||
bubble.shift(0.8*LEFT)
|
||||
bubble.set_fill(BLACK, 0.3)
|
||||
|
||||
pi_vs_tau = TextMobject(
|
||||
"Should $\\pi$ represent \\\\", "3.1415...",
|
||||
"or", "6.2831...", "?"
|
||||
)
|
||||
pi_vs_tau.highlight_by_tex_to_color_map({
|
||||
"3.14" : GREEN,
|
||||
"6.28" : RED,
|
||||
})
|
||||
pi_vs_tau.move_to(bubble.get_bubble_center())
|
||||
|
||||
question = TexMobject(
|
||||
"\\frac{1}{1} + \\frac{1}{4} + \\frac{1}{9} + \\frac{1}{16} + \\cdots = ",
|
||||
"\\;???"
|
||||
)
|
||||
question[0].gradient_highlight(BLUE_C, BLUE_B)
|
||||
question.move_to(bubble.get_bubble_center())
|
||||
question.shift(2*SMALL_BUFF*UP)
|
||||
|
||||
cross = Cross(pi_vs_tau)
|
||||
cross.set_stroke(RED, 8)
|
||||
|
||||
self.add(image)
|
||||
self.play(
|
||||
ShowCreation(bubble),
|
||||
Write(pi_vs_tau)
|
||||
)
|
||||
self.play(ShowCreation(cross))
|
||||
self.wait()
|
||||
self.play(
|
||||
FadeOut(VGroup(pi_vs_tau, cross)),
|
||||
FadeIn(question),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class WhatIsRight(PiCreatureScene):
|
||||
CONFIG = {
|
||||
"default_pi_creature_kwargs" : {
|
||||
"color" : BLUE_D,
|
||||
"filp_at_start" : False,
|
||||
},
|
||||
"default_pi_creature_start_corner" : DOWN,
|
||||
}
|
||||
def construct(self):
|
||||
randy = self.pi_creature
|
||||
randy.scale(0.75, about_edge = DOWN)
|
||||
title = TextMobject("Which is ``right''?")
|
||||
title.scale(1.5)
|
||||
title.to_edge(UP)
|
||||
self.add(title)
|
||||
|
||||
sum_over_N_converges = TexMobject("1+2+3+\\cdots = -\\frac{1}{12}")
|
||||
sum_over_N_diverges = TexMobject("1+2+3+\\cdots \\text{ Diverges}")
|
||||
|
||||
literal_derivative = TexMobject(
|
||||
"f'(x) = \\frac{f(x+dx) - f(x)}{dx}"
|
||||
)
|
||||
limit_derivative = TexMobject(
|
||||
"f'(x) = \\lim_{h \\to 0}\\frac{f(x+h) - f(x)}{h}"
|
||||
)
|
||||
|
||||
divide_by_zero_definable = TexMobject(
|
||||
"\\frac{1}{0}", "\\text{ has meaning}"
|
||||
)
|
||||
divide_by_zero_undefinable = TexMobject(
|
||||
"\\frac{1}{0}", "\\text{ is undefined}"
|
||||
)
|
||||
|
||||
left_mobs = VGroup(
|
||||
sum_over_N_converges, literal_derivative,
|
||||
divide_by_zero_definable
|
||||
)
|
||||
right_mobs = VGroup(
|
||||
sum_over_N_diverges, limit_derivative,
|
||||
divide_by_zero_undefinable
|
||||
)
|
||||
|
||||
for mob in left_mobs:
|
||||
mob.next_to(randy, UP)
|
||||
mob.shift(3.5*LEFT)
|
||||
for mob in right_mobs:
|
||||
mob.next_to(randy, UP)
|
||||
mob.shift(3.5*RIGHT)
|
||||
|
||||
left_mobs.gradient_highlight(YELLOW_C, YELLOW_D)
|
||||
right_mobs.gradient_highlight(GREEN_C, GREEN_D)
|
||||
|
||||
self.play(randy.change, "pondering", title)
|
||||
self.wait()
|
||||
self.play(randy.change, "sassy", title)
|
||||
self.wait()
|
||||
|
||||
last_terms = VGroup()
|
||||
for left, right in zip(left_mobs, right_mobs)[:-1]:
|
||||
right.align_to(left)
|
||||
self.play(
|
||||
randy.change, "raise_right_hand",
|
||||
FadeInFromDown(left),
|
||||
last_terms.shift, 1.75*UP
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
randy.change, "raise_left_hand",
|
||||
FadeInFromDown(right)
|
||||
)
|
||||
self.play(randy.change, "plain", right)
|
||||
last_terms.add(left, right, title)
|
||||
self.play(
|
||||
randy.change, "shruggie",
|
||||
FadeInFromDown(left_mobs[-1]),
|
||||
FadeInFromDown(right_mobs[-1]),
|
||||
last_terms.shift, 1.75*UP,
|
||||
)
|
||||
self.wait(4)
|
||||
|
||||
class AskPuzzle(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
series = TexMobject(
|
||||
"\\frac{1}{1} + \\frac{1}{4} + \\frac{1}{9} + \\cdots + " +\
|
||||
"\\frac{1}{n^2} + \\cdots = ", "\\,???"
|
||||
)
|
||||
series[0].gradient_highlight(BLUE_C, BLUE_B)
|
||||
series[1].highlight(YELLOW)
|
||||
|
||||
question = TextMobject(
|
||||
"How should we think about\\\\",
|
||||
"$\\displaystyle \\sum_{n=1}^\\infty \\frac{1}{n^s}$",
|
||||
"for arbitrary $s$?"
|
||||
)
|
||||
question[1].highlight(BLUE)
|
||||
question[0].shift(SMALL_BUFF*UP)
|
||||
|
||||
response = TextMobject(
|
||||
"What do you mean by ",
|
||||
"$\\displaystyle \\sum_{n = 1}^{\\infty}$",
|
||||
"?"
|
||||
)
|
||||
response[1].highlight(BLUE)
|
||||
|
||||
self.teacher_says(series)
|
||||
self.change_all_student_modes("pondering", look_at_arg = series)
|
||||
self.wait(3)
|
||||
self.play(
|
||||
FadeOut(self.teacher.bubble),
|
||||
self.teacher.change, "happy",
|
||||
series.scale, 0.5,
|
||||
series.to_corner, UP+LEFT,
|
||||
PiCreatureSays(
|
||||
self.students[0], question,
|
||||
target_mode = "raise_left_hand"
|
||||
)
|
||||
)
|
||||
self.change_student_modes(
|
||||
None, "confused", "confused",
|
||||
added_anims = [self.students[0].look_at, question]
|
||||
)
|
||||
self.wait(2)
|
||||
|
||||
self.students[0].bubble.content = VGroup()
|
||||
self.play(
|
||||
RemovePiCreatureBubble(self.students[0]),
|
||||
question.scale, 0.5,
|
||||
question.next_to, series, DOWN, MED_LARGE_BUFF, LEFT,
|
||||
PiCreatureSays(self.teacher, response)
|
||||
)
|
||||
self.change_all_student_modes("erm")
|
||||
self.wait(3)
|
||||
|
||||
class ChangeTopic(PiCreatureScene):
|
||||
def construct(self):
|
||||
pi, tau = self.pi_creatures
|
||||
title = TextMobject("Happy $\\pi$ day!")
|
||||
title.scale(1.5)
|
||||
title.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||
self.add(title)
|
||||
|
||||
question = TextMobject(
|
||||
"Have you ever seen why \\\\",
|
||||
"$\\displaystyle \\frac{2}{1} \\cdot \\frac{2}{3} \\cdots"+ \
|
||||
"\\frac{4}{3} \\cdot \\frac{4}{5} \\cdot" + \
|
||||
"\\frac{6}{5} \\cdot \\frac{6}{7} \\cdots = \\frac{\\pi}{2}$", "?"
|
||||
)
|
||||
question[0].shift(MED_SMALL_BUFF*UP)
|
||||
question[1].gradient_highlight(YELLOW, GREEN)
|
||||
|
||||
self.play(
|
||||
PiCreatureSays(
|
||||
tau, "We should \\emph{really} celebrate \\\\ on 6/28!",
|
||||
target_mode = "angry",
|
||||
),
|
||||
pi.change, "guilty",
|
||||
)
|
||||
self.wait(2)
|
||||
self.play(
|
||||
PiCreatureSays(pi, question),
|
||||
RemovePiCreatureBubble(
|
||||
tau, target_mode = "pondering", look_at_arg = question,
|
||||
)
|
||||
)
|
||||
self.play(pi.change, "pondering", question)
|
||||
self.wait(4)
|
||||
|
||||
|
||||
def create_pi_creatures(self):
|
||||
tau = TauCreature(color = GREEN_E)
|
||||
pi = Randolph().flip()
|
||||
VGroup(pi, tau).scale(0.75)
|
||||
tau.to_edge(DOWN).shift(3*LEFT)
|
||||
pi.to_edge(DOWN).shift(3*RIGHT)
|
||||
return pi, tau
|
||||
|
||||
class SpecialThanks(Scene):
|
||||
def construct(self):
|
||||
title = TextMobject("Special thanks to:")
|
||||
title.to_edge(UP, LARGE_BUFF)
|
||||
title.scale(1.5)
|
||||
title.highlight(BLUE)
|
||||
h_line = Line(LEFT, RIGHT).scale(4)
|
||||
h_line.next_to(title, DOWN)
|
||||
h_line.set_stroke(WHITE, 1)
|
||||
|
||||
people = VGroup(*map(TextMobject, [
|
||||
"Ben Hambrecht",
|
||||
"University Library Basel",
|
||||
"Martin Mattmüller",
|
||||
"Library of the Institut de France",
|
||||
]))
|
||||
people.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = MED_LARGE_BUFF)
|
||||
people.next_to(h_line, DOWN)
|
||||
|
||||
self.add(title, h_line, people)
|
||||
|
||||
class EndScene(PatreonEndScreen):
|
||||
CONFIG = {
|
||||
"camera_config" : {
|
||||
"background_alpha" : 255,
|
||||
}
|
||||
}
|
||||
def construct(self):
|
||||
self.add_title()
|
||||
title = self.title
|
||||
basel_screen = ScreenRectangle(height = 2.35)
|
||||
basel_screen.next_to(title, DOWN)
|
||||
watch_basel = TextMobject(
|
||||
"One such actual piece of math", "(quite pretty!)",
|
||||
)
|
||||
watch_basel[0].highlight(YELLOW)
|
||||
watch_basel.next_to(basel_screen, DOWN, submobject_to_align = watch_basel[0])
|
||||
|
||||
self.add(watch_basel)
|
||||
# self.add(basel_screen)
|
||||
|
||||
line = DashedLine(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
|
||||
line.next_to(watch_basel, DOWN)
|
||||
self.add(line)
|
||||
|
||||
plushie_square = Square(side_length = 2)
|
||||
plushie_square.to_corner(DOWN+LEFT, buff = MED_LARGE_BUFF)
|
||||
plushie_square.shift(UP)
|
||||
|
||||
plushie_words = TextMobject(
|
||||
"Plushie pi \\\\ creatures \\\\ now available.",
|
||||
alignment = ""
|
||||
)
|
||||
plushie_words.next_to(plushie_square, RIGHT)
|
||||
|
||||
self.add(plushie_words)
|
||||
# self.add(plushie_square)
|
||||
|
||||
instagram_line = TextMobject(
|
||||
"randy\\_the\\_pi"
|
||||
)
|
||||
instagram_logo = ImageMobject("instagram_logo")
|
||||
instagram_logo.match_height(instagram_line)
|
||||
instagram_logo.next_to(instagram_line, LEFT, SMALL_BUFF)
|
||||
instagram = Group(instagram_logo, instagram_line)
|
||||
instagram.next_to(line, DOWN)
|
||||
instagram.shift(SPACE_WIDTH*RIGHT/2)
|
||||
self.add(instagram)
|
||||
|
||||
|
||||
pictures = Group(*[
|
||||
ImageMobject("randy/randy_%s"%name)
|
||||
for name in [
|
||||
"science",
|
||||
"cooking",
|
||||
"in_a_can",
|
||||
"sandwhich",
|
||||
"lab",
|
||||
"fractal",
|
||||
"flowers",
|
||||
"group",
|
||||
"labcoat",
|
||||
"tennis",
|
||||
]
|
||||
])
|
||||
for i, picture in enumerate(pictures):
|
||||
picture.scale_to_fit_height(2)
|
||||
picture.next_to(instagram, DOWN, aligned_edge = RIGHT)
|
||||
if i%3 != 0:
|
||||
picture.next_to(last_picture, LEFT, buff = 0)
|
||||
self.play(FadeIn(picture, run_time = 2))
|
||||
last_picture = picture
|
||||
|
||||
class Thumbnail(Scene):
|
||||
def construct(self):
|
||||
pi, eq, num = formula = TexMobject(
|
||||
"\\pi", "=", "6.283185\\dots"
|
||||
)
|
||||
formula.scale(2)
|
||||
pi.scale(1.5, about_edge = RIGHT)
|
||||
formula.set_stroke(BLUE, 1)
|
||||
formula.scale_to_fit_width(2*SPACE_WIDTH - 2)
|
||||
# formula.shift(0.5*RIGHT)
|
||||
self.add(formula)
|
||||
|
||||
words = TextMobject("...according to Euler.")
|
||||
words.scale(1.5)
|
||||
words.next_to(formula, DOWN, MED_LARGE_BUFF)
|
||||
self.add(words)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -29,6 +29,7 @@ MOUTH_INDEX = 5
|
|||
class PiCreature(SVGMobject):
|
||||
CONFIG = {
|
||||
"color" : BLUE_E,
|
||||
"file_name_prefix" : "PiCreatures",
|
||||
"stroke_width" : 0,
|
||||
"stroke_color" : BLACK,
|
||||
"fill_opacity" : 1.0,
|
||||
|
|
@ -43,18 +44,19 @@ class PiCreature(SVGMobject):
|
|||
"left_arm_range" : [.34, .462],
|
||||
}
|
||||
def __init__(self, mode = "plain", **kwargs):
|
||||
digest_config(self, kwargs)
|
||||
self.parts_named = False
|
||||
try:
|
||||
svg_file = os.path.join(
|
||||
PI_CREATURE_DIR,
|
||||
"PiCreatures_%s.svg"%mode
|
||||
"%s_%s.svg"%(self.file_name_prefix, mode)
|
||||
)
|
||||
SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
except:
|
||||
warnings.warn("No PiCreature design with mode %s"%mode)
|
||||
warnings.warn("No %s design with mode %s"%(self.file_name_prefix, mode))
|
||||
svg_file = os.path.join(
|
||||
FILE_DIR,
|
||||
"PiCreatures_plain.svg"
|
||||
"PiCreatures_plain.svg",
|
||||
)
|
||||
SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
|
||||
|
|
@ -210,7 +212,7 @@ class PiCreature(SVGMobject):
|
|||
|
||||
def get_all_pi_creature_modes():
|
||||
result = []
|
||||
prefix = "PiCreatures_"
|
||||
prefix = "%s_"%PiCreature.CONFIG["file_name_prefix"]
|
||||
suffix = ".svg"
|
||||
for file in os.listdir(PI_CREATURE_DIR):
|
||||
if file.startswith(prefix) and file.endswith(suffix):
|
||||
|
|
@ -253,6 +255,17 @@ class BabyPiCreature(PiCreature):
|
|||
pupil.scale_in_place(self.pupil_scale_factor)
|
||||
self.look(looking_direction)
|
||||
|
||||
class TauCreature(PiCreature):
|
||||
CONFIG = {
|
||||
"file_name_prefix" : "TauCreatures"
|
||||
}
|
||||
|
||||
class ThreeLeggedPiCreature(PiCreature):
|
||||
CONFIG = {
|
||||
"file_name_prefix" : "ThreeLeggedPiCreatures"
|
||||
}
|
||||
|
||||
|
||||
class Blink(ApplyMethod):
|
||||
CONFIG = {
|
||||
"rate_func" : squish_rate_func(there_and_back)
|
||||
|
|
|
|||
|
|
@ -3,7 +3,8 @@ from helpers import *
|
|||
|
||||
from scene.scene import Scene
|
||||
from animation import Animation
|
||||
from animation.simple_animations import Write, DrawBorderThenFill, LaggedStart
|
||||
from animation.simple_animations import Write, DrawBorderThenFill
|
||||
from animation.compositions import LaggedStart
|
||||
from animation.transform import FadeIn, FadeOut, ApplyMethod
|
||||
from mobject.vectorized_mobject import VGroup
|
||||
from mobject.tex_mobject import TexMobject, TextMobject
|
||||
|
|
@ -132,7 +133,7 @@ class PatreonEndScreen(PatreonThanks):
|
|||
self.scroll_through_patrons()
|
||||
|
||||
def add_title(self):
|
||||
title = TextMobject("Clicky Stuffs")
|
||||
title = self.title = TextMobject("Clicky Stuffs")
|
||||
title.scale(1.5)
|
||||
title.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue