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HeroAndVillain and EulerWrites628
This commit is contained in:
Grant Sanderson
parent
1acb718830
commit
d6f8d5b0c4
1 changed files with 212 additions and 39 deletions
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@ -33,7 +33,55 @@ 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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RESOURCE_DIR = os.path.join(MEDIA_DIR, "3b1b_videos", "π Day 2018")
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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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@ -45,7 +93,6 @@ class PiTauDebate(PiCreatureScene):
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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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@ -61,44 +108,21 @@ class PiTauDebate(PiCreatureScene):
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self.wait()
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# Show tau
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circle = Circle(color = YELLOW, radius = 1.25)
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circle.next_to(tau, UP, MED_LARGE_BUFF)
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circle.to_edge(RIGHT, buff = 2)
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circle.to_edge(UP)
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radius = Line(circle.get_center(), circle.get_right())
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radius.highlight(WHITE)
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one = TexMobject("1")
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kwargs = {"run_time" : 3, "rate_func" : bezier([0, 0, 1, 1])}
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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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**kwargs
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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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changing_decimal = ChangingDecimal(
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decimal, lambda a : a*TAU,
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position_update_func = lambda m : m.next_to(
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radius.get_end(), RIGHT,
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aligned_edge = DOWN,
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),
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**kwargs
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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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ShowCreation(radius), Write(one),
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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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Rotating(radius, about_point = radius.get_start(), **kwargs),
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ShowCreation(circle, **kwargs),
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changing_decimal,
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one_update,
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*generate_anims2()
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)
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self.wait()
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@ -181,6 +205,11 @@ class HartlAndPalais(Scene):
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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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@ -233,14 +262,158 @@ class ManyFormulas(Scene):
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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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