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Finished pi day
This commit is contained in:
Grant Sanderson
parent
d6f8d5b0c4
commit
9ccc9fa8b4
3 changed files with 499 additions and 15 deletions
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@ -32,6 +32,7 @@ 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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@ -415,6 +416,488 @@ class HeroAndVillain(Scene):
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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)
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analysis.to_edge(LEFT, buff = 0)
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text = TextMobject(
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"``\\dots set the radius of",
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"the circle\\dots to be = 1, \\dots \\\\",
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"through approximations the",
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"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",
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"brevity, \\\\ I will write", "$\pi$\\dots''",
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alignment = ''
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)
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pi_formula = TexMobject(
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"\\pi", "=", "{ \\text{semicircumference}", "\\over", "\\text{radius}}"
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)
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text.scale_to_fit_width(SPACE_WIDTH)
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text.next_to(analysis, RIGHT, LARGE_BUFF)
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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({
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"semicircumference" : HIGHLIGHT_COLOR,
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"3.14" : HIGHLIGHT_COLOR,
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"\pi" : HIGHLIGHT_COLOR
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})
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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(text, DOWN, LARGE_BUFF)
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)
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terms[0].highlight(HIGHLIGHT_COLOR)
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terms[-1].highlight(HIGHLIGHT_COLOR)
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pi_formula.next_to(terms, DOWN, buff = 0)
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pi_formula.align_to(text, alignment_vect = RIGHT)
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pi_formula[0].scale(2, about_edge = RIGHT)
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self.add(analysis)
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self.play(*generate_anims2(), rate_func = lambda t : 0.5*smooth(t))
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self.play(LaggedStart(FadeIn,text), run_time = 5)
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self.play(FadeIn(pi_formula))
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self.wait()
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class QuarterTurn(Scene):
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def construct(self):
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terms, generate_anims1, generate_anims2 = get_circle_drawing_terms(
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radius = 2,
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positioning_func = lambda circ : circ.move_to(4*RIGHT)
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)
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circle, radius, one, decimal = terms
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circle_ghost = circle.copy().set_stroke(YELLOW_E, 1)
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radius_ghost = radius.copy().set_stroke(WHITE, 1)
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self.add(circle_ghost, radius_ghost)
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self.play(
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*generate_anims2(),
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rate_func = lambda t : 0.25*smooth(t)
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)
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self.wait()
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pi_halves = TexMobject("\\pi", "/2")
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pi_halves[0].highlight(RED)
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tau_fourths = TexMobject("\\tau", "/4")
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tau_fourths[0].highlight(GREEN)
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for mob in pi_halves, tau_fourths:
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mob.next_to(decimal, UP)
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self.play(FadeInFromDown(pi_halves))
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self.wait()
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self.play(
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pi_halves.shift, 0.75*UP,
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FadeInFromDown(tau_fourths)
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)
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self.wait()
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class UsingTheta(Scene):
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def construct(self):
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plane = NumberPlane(x_unit_size = 3, y_unit_size = 3)
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# plane.main_lines.fade(0.5)
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# plane.secondary_lines.fade(0.5)
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plane.fade(0.5)
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self.add(plane)
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circle = Circle(radius = 3)
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circle.set_stroke(YELLOW, 2)
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self.add(circle)
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radius = Line(ORIGIN, circle.get_right())
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arc = Arc(radius = 0.5, angle = TAU, num_anchors = 200)
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arc.highlight(GREEN)
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start_arc = arc.copy()
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theta = TexMobject("\\theta", "=")
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theta[0].match_color(arc)
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theta.add_background_rectangle()
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update_theta = ContinualUpdateFromFunc(
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theta, lambda m : m.shift(
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rotate_vector(0.9*RIGHT, radius.get_angle()/2) \
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- m[1][0].get_center()
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)
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)
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angle = Integer(0, unit = "^\\circ")
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update_angle = ContinualChangingDecimal(
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angle, lambda a : radius.get_angle()*(360/TAU),
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position_update_func = lambda a : a.next_to(theta, RIGHT, SMALL_BUFF)
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)
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self.add(update_theta, update_angle)
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last_frac = 0
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for frac in 1./4, 1./12, 3./8, 1./6, 5./6:
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self.play(
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Rotate(radius, angle = (frac-last_frac)*TAU, about_point = ORIGIN),
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UpdateFromAlphaFunc(
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arc,
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lambda m, a : m.pointwise_become_partial(
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start_arc, 0, interpolate(last_frac, frac, a)
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)
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),
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run_time = 3
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)
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last_frac = frac
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self.wait()
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class ThingsNamedAfterEuler(Scene):
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def construct(self):
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group = VGroup(*map(TextMobject, [
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"Euler's formula (Complex analysis)",
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"Euler's formula (Graph theory)",
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"Euler's formula (Mechanical engineering)",
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"Euler's formula (Analytical number theory)",
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"Euler's formula (Continued fractions)",
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"Euler-Lagrance equations (mechanics)",
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"Euler number (topology)",
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"Euler equations (fluid dynamics)",
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"Euler angles (rigid-body mechanics)",
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"Euler totient function (number theory)",
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]))
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group.arrange_submobjects(DOWN, aligned_edge = LEFT)
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group.scale_to_fit_height(2*SPACE_HEIGHT - 1)
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self.play(LaggedStart(FadeIn, group, lag_ratio = 0.2, run_time = 12))
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self.wait()
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class EulerThinking(Scene):
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def construct(self):
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image = get_image("Leonhard_Euler_by_Handmann")
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image.scale_to_fit_height(4)
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image.to_edge(DOWN)
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image.shift(4*LEFT)
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bubble = ThoughtBubble(height = 4.5)
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bubble.next_to(image, RIGHT)
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bubble.to_edge(UP, buff = SMALL_BUFF)
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bubble.shift(0.8*LEFT)
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bubble.set_fill(BLACK, 0.3)
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pi_vs_tau = TextMobject(
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"Should $\\pi$ represent \\\\", "3.1415...",
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"or", "6.2831...", "?"
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)
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pi_vs_tau.highlight_by_tex_to_color_map({
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"3.14" : GREEN,
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"6.28" : RED,
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})
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pi_vs_tau.move_to(bubble.get_bubble_center())
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question = TexMobject(
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"\\frac{1}{1} + \\frac{1}{4} + \\frac{1}{9} + \\frac{1}{16} + \\cdots = ",
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"\\;???"
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)
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question[0].gradient_highlight(BLUE_C, BLUE_B)
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question.move_to(bubble.get_bubble_center())
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question.shift(2*SMALL_BUFF*UP)
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cross = Cross(pi_vs_tau)
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cross.set_stroke(RED, 8)
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self.add(image)
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self.play(
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ShowCreation(bubble),
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Write(pi_vs_tau)
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)
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self.play(ShowCreation(cross))
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self.wait()
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self.play(
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FadeOut(VGroup(pi_vs_tau, cross)),
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FadeIn(question),
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)
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self.wait()
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class WhatIsRight(PiCreatureScene):
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CONFIG = {
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"default_pi_creature_kwargs" : {
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"color" : BLUE_D,
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"filp_at_start" : False,
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},
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"default_pi_creature_start_corner" : DOWN,
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}
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def construct(self):
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randy = self.pi_creature
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randy.scale(0.75, about_edge = DOWN)
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title = TextMobject("Which is ``right''?")
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title.scale(1.5)
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title.to_edge(UP)
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self.add(title)
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sum_over_N_converges = TexMobject("1+2+3+\\cdots = -\\frac{1}{12}")
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sum_over_N_diverges = TexMobject("1+2+3+\\cdots \\text{ Diverges}")
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literal_derivative = TexMobject(
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"f'(x) = \\frac{f(x+dx) - f(x)}{dx}"
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)
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limit_derivative = TexMobject(
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"f'(x) = \\lim_{h \\to 0}\\frac{f(x+h) - f(x)}{h}"
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)
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divide_by_zero_definable = TexMobject(
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"\\frac{1}{0}", "\\text{ has meaning}"
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)
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divide_by_zero_undefinable = TexMobject(
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"\\frac{1}{0}", "\\text{ is undefined}"
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)
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left_mobs = VGroup(
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sum_over_N_converges, literal_derivative,
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divide_by_zero_definable
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)
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right_mobs = VGroup(
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sum_over_N_diverges, limit_derivative,
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divide_by_zero_undefinable
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)
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for mob in left_mobs:
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mob.next_to(randy, UP)
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mob.shift(3.5*LEFT)
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for mob in right_mobs:
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mob.next_to(randy, UP)
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mob.shift(3.5*RIGHT)
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left_mobs.gradient_highlight(YELLOW_C, YELLOW_D)
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right_mobs.gradient_highlight(GREEN_C, GREEN_D)
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self.play(randy.change, "pondering", title)
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self.wait()
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self.play(randy.change, "sassy", title)
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self.wait()
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last_terms = VGroup()
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for left, right in zip(left_mobs, right_mobs)[:-1]:
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right.align_to(left)
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self.play(
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randy.change, "raise_right_hand",
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FadeInFromDown(left),
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last_terms.shift, 1.75*UP
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)
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self.wait()
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self.play(
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randy.change, "raise_left_hand",
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FadeInFromDown(right)
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)
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self.play(randy.change, "plain", right)
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last_terms.add(left, right, title)
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self.play(
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randy.change, "shruggie",
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FadeInFromDown(left_mobs[-1]),
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FadeInFromDown(right_mobs[-1]),
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last_terms.shift, 1.75*UP,
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)
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self.wait(4)
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class AskPuzzle(TeacherStudentsScene):
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def construct(self):
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series = TexMobject(
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"\\frac{1}{1} + \\frac{1}{4} + \\frac{1}{9} + \\cdots + " +\
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"\\frac{1}{n^2} + \\cdots = ", "\\,???"
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)
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series[0].gradient_highlight(BLUE_C, BLUE_B)
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series[1].highlight(YELLOW)
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question = TextMobject(
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"How should we think about\\\\",
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"$\\displaystyle \\sum_{n=1}^\\infty \\frac{1}{n^s}$",
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"for arbitrary $s$?"
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)
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question[1].highlight(BLUE)
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question[0].shift(SMALL_BUFF*UP)
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response = TextMobject(
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"What do you mean by ",
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"$\\displaystyle \\sum_{n = 1}^{\\infty}$",
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"?"
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)
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response[1].highlight(BLUE)
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self.teacher_says(series)
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self.change_all_student_modes("pondering", look_at_arg = series)
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self.wait(3)
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self.play(
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FadeOut(self.teacher.bubble),
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self.teacher.change, "happy",
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series.scale, 0.5,
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series.to_corner, UP+LEFT,
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PiCreatureSays(
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self.students[0], question,
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target_mode = "raise_left_hand"
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)
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)
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self.change_student_modes(
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None, "confused", "confused",
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added_anims = [self.students[0].look_at, question]
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)
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self.wait(2)
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self.students[0].bubble.content = VGroup()
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self.play(
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RemovePiCreatureBubble(self.students[0]),
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question.scale, 0.5,
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question.next_to, series, DOWN, MED_LARGE_BUFF, LEFT,
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PiCreatureSays(self.teacher, response)
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)
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self.change_all_student_modes("erm")
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self.wait(3)
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class ChangeTopic(PiCreatureScene):
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def construct(self):
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pi, tau = self.pi_creatures
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title = TextMobject("Happy $\\pi$ day!")
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title.scale(1.5)
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title.to_edge(UP, buff = MED_SMALL_BUFF)
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self.add(title)
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question = TextMobject(
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"Have you ever seen why \\\\",
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"$\\displaystyle \\frac{2}{1} \\cdot \\frac{2}{3} \\cdots"+ \
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"\\frac{4}{3} \\cdot \\frac{4}{5} \\cdot" + \
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"\\frac{6}{5} \\cdot \\frac{6}{7} \\cdots = \\frac{\\pi}{2}$", "?"
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)
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question[0].shift(MED_SMALL_BUFF*UP)
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question[1].gradient_highlight(YELLOW, GREEN)
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self.play(
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PiCreatureSays(
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tau, "We should \\emph{really} celebrate \\\\ on 6/28!",
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target_mode = "angry",
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),
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pi.change, "guilty",
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)
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self.wait(2)
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self.play(
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PiCreatureSays(pi, question),
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RemovePiCreatureBubble(
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tau, target_mode = "pondering", look_at_arg = question,
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)
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)
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self.play(pi.change, "pondering", question)
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self.wait(4)
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def create_pi_creatures(self):
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tau = TauCreature(color = GREEN_E)
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pi = Randolph().flip()
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VGroup(pi, tau).scale(0.75)
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tau.to_edge(DOWN).shift(3*LEFT)
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pi.to_edge(DOWN).shift(3*RIGHT)
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return pi, tau
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class SpecialThanks(Scene):
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def construct(self):
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title = TextMobject("Special thanks to:")
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title.to_edge(UP, LARGE_BUFF)
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title.scale(1.5)
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title.highlight(BLUE)
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h_line = Line(LEFT, RIGHT).scale(4)
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h_line.next_to(title, DOWN)
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h_line.set_stroke(WHITE, 1)
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people = VGroup(*map(TextMobject, [
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"Ben Hambrecht",
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"University Library Basel",
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"Martin Mattmüller",
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"Library of the Institut de France",
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]))
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people.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = MED_LARGE_BUFF)
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people.next_to(h_line, DOWN)
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self.add(title, h_line, people)
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class EndScene(PatreonEndScreen):
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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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self.add_title()
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title = self.title
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basel_screen = ScreenRectangle(height = 2.35)
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basel_screen.next_to(title, DOWN)
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watch_basel = TextMobject(
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"One such actual piece of math", "(quite pretty!)",
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)
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watch_basel[0].highlight(YELLOW)
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watch_basel.next_to(basel_screen, DOWN, submobject_to_align = watch_basel[0])
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self.add(watch_basel)
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# self.add(basel_screen)
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line = DashedLine(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
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line.next_to(watch_basel, DOWN)
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self.add(line)
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plushie_square = Square(side_length = 2)
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plushie_square.to_corner(DOWN+LEFT, buff = MED_LARGE_BUFF)
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plushie_square.shift(UP)
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plushie_words = TextMobject(
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"Plushie pi \\\\ creatures \\\\ now available.",
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alignment = ""
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)
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plushie_words.next_to(plushie_square, RIGHT)
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self.add(plushie_words)
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# self.add(plushie_square)
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instagram_line = TextMobject(
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"randy\\_the\\_pi"
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)
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instagram_logo = ImageMobject("instagram_logo")
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instagram_logo.match_height(instagram_line)
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instagram_logo.next_to(instagram_line, LEFT, SMALL_BUFF)
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instagram = Group(instagram_logo, instagram_line)
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instagram.next_to(line, DOWN)
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instagram.shift(SPACE_WIDTH*RIGHT/2)
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self.add(instagram)
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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)
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -46,19 +46,19 @@ class PiCreature(SVGMobject):
|
|||
def __init__(self, mode = "plain", **kwargs):
|
||||
digest_config(self, kwargs)
|
||||
self.parts_named = False
|
||||
# try:
|
||||
svg_file = os.path.join(
|
||||
PI_CREATURE_DIR,
|
||||
"%s_%s.svg"%(self.file_name_prefix, mode)
|
||||
)
|
||||
SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
# except:
|
||||
# warnings.warn("No %s design with mode %s"%(self.file_name_prefix, mode))
|
||||
# svg_file = os.path.join(
|
||||
# FILE_DIR,
|
||||
# "PiCreatures_plain.svg",
|
||||
# )
|
||||
# SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
try:
|
||||
svg_file = os.path.join(
|
||||
PI_CREATURE_DIR,
|
||||
"%s_%s.svg"%(self.file_name_prefix, mode)
|
||||
)
|
||||
SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
except:
|
||||
warnings.warn("No %s design with mode %s"%(self.file_name_prefix, mode))
|
||||
svg_file = os.path.join(
|
||||
FILE_DIR,
|
||||
"PiCreatures_plain.svg",
|
||||
)
|
||||
SVGMobject.__init__(self, file_name = svg_file, **kwargs)
|
||||
|
||||
if self.flip_at_start:
|
||||
self.flip()
|
||||
|
|
|
|||
|
|
@ -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