def construct(self):
names = [
"Johann_Bernoulli2", "Jacob_Bernoulli",
"Gottfried_Wilhelm_von_Leibniz", "Newton"
]
guys = [ImageMobject(name, invert=False) for name in names]
johann = guys[0]
johann.scale(0.8)
pensive_johann = johann.copy()
pensive_johann.scale(0.25)
pensive_johann.to_corner(DOWN + LEFT)
comparitive_johann = johann.copy()
template = Square(side_length=2)
comparitive_johann.replace(template)
comparitive_johann.shift(UP + LEFT)
greater_than = TexMobject(">")
greater_than.next_to(comparitive_johann)
for guy, name in zip(guys, names)[1:]:
guy.replace(template)
guy.next_to(greater_than)
name_mob = TextMobject(name.replace("_", " "))
name_mob.scale(0.5)
name_mob.next_to(guy, DOWN)
guy.name_mob = name_mob
guy.sort_points(lambda p: np.dot(p, DOWN + RIGHT))
bubble = ThoughtBubble(initial_width=12)
bubble.stretch_to_fit_height(6)
bubble.ingest_submobjects()
bubble.pin_to(pensive_johann)
bubble.shift(DOWN)
point = Point(johann.get_corner(UP + RIGHT))
upper_point = Point(comparitive_johann.get_corner(UP + RIGHT))
lightbulb = ImageMobject("Lightbulb", invert=False)
lightbulb.scale(0.1)
lightbulb.sort_points(np.linalg.norm)
lightbulb.next_to(upper_point, RIGHT)
self.add(johann)
self.wait()
self.play(Transform(johann, pensive_johann),
Transform(point, bubble),
run_time=2)
self.remove(point)
self.add(bubble)
weakling = guys[1]
self.play(FadeIn(comparitive_johann), ShowCreation(greater_than),
FadeIn(weakling))
self.wait(2)
for guy in guys[2:]:
self.play(DelayByOrder(Transform(weakling, upper_point)))
self.play(FadeIn(guy), ShimmerIn(guy.name_mob))
self.wait(3)
self.remove(guy.name_mob)
weakling = guy
self.play(FadeOut(weakling), FadeOut(greater_than))
self.play(ShowCreation(lightbulb))
self.wait()
self.play(FadeOut(comparitive_johann), FadeOut(lightbulb))
self.play(ApplyMethod(Mobject(johann, bubble).scale, 10, run_time=3))
def construct(self):
self.bubble = ThoughtBubble().ingest_submobjects()
self.bubble.scale(1.5)
TransformOverIncreasingOrders.construct(self, FlowSnake, 7)
self.play(Transform(self.curve, self.bubble))
self.show_infinite_objects()
self.pose_question()
self.dither()
def construct(self):
johann, fermat = [
ImageMobject(name, invert=False)
for name in "Johann_Bernoulli2", "Pierre_de_Fermat"
]
johann.scale(0.2)
johann.to_corner(DOWN + LEFT)
bubble = ThoughtBubble(initial_width=12)
bubble.stretch_to_fit_height(6)
bubble.pin_to(johann)
bubble.shift(DOWN)
bubble.add_content(fermat)
fermat.scale_in_place(0.4)
self.add(johann, bubble)
self.wait()
self.play(FadeIn(fermat))
self.wait()
def construct(self):
johann, fermat = [
ImageMobject(name, invert = False)
for name in "Johann_Bernoulli2", "Pierre_de_Fermat"
]
johann.scale(0.2)
johann.to_corner(DOWN+LEFT)
bubble = ThoughtBubble(initial_width = 12)
bubble.stretch_to_fit_height(6)
bubble.pin_to(johann)
bubble.shift(DOWN)
bubble.add_content(fermat)
fermat.scale_in_place(0.4)
self.add(johann, bubble)
self.dither()
self.play(FadeIn(fermat))
self.dither()
def construct(self):
names = [
"Johann_Bernoulli2",
"Jacob_Bernoulli",
"Gottfried_Wilhelm_von_Leibniz",
"Newton"
]
guys = [
ImageMobject(name, invert = False)
for name in names
]
johann = guys[0]
johann.scale(0.8)
pensive_johann = johann.copy()
pensive_johann.scale(0.25)
pensive_johann.to_corner(DOWN+LEFT)
comparitive_johann = johann.copy()
template = Square(side_length = 2)
comparitive_johann.replace(template)
comparitive_johann.shift(UP+LEFT)
greater_than = TexMobject(">")
greater_than.next_to(comparitive_johann)
for guy, name in zip(guys, names)[1:]:
guy.replace(template)
guy.next_to(greater_than)
name_mob = TextMobject(name.replace("_", " "))
name_mob.scale(0.5)
name_mob.next_to(guy, DOWN)
guy.name_mob = name_mob
guy.sort_points(lambda p : np.dot(p, DOWN+RIGHT))
bubble = ThoughtBubble(initial_width = 12)
bubble.stretch_to_fit_height(6)
bubble.ingest_submobjects()
bubble.pin_to(pensive_johann)
bubble.shift(DOWN)
point = Point(johann.get_corner(UP+RIGHT))
upper_point = Point(comparitive_johann.get_corner(UP+RIGHT))
lightbulb = ImageMobject("Lightbulb", invert = False)
lightbulb.scale(0.1)
lightbulb.sort_points(np.linalg.norm)
lightbulb.next_to(upper_point, RIGHT)
self.add(johann)
self.dither()
self.play(
Transform(johann, pensive_johann),
Transform(point, bubble),
run_time = 2
)
self.remove(point)
self.add(bubble)
weakling = guys[1]
self.play(
FadeIn(comparitive_johann),
ShowCreation(greater_than),
FadeIn(weakling)
)
self.dither(2)
for guy in guys[2:]:
self.play(DelayByOrder(Transform(
weakling, upper_point
)))
self.play(
FadeIn(guy),
ShimmerIn(guy.name_mob)
)
self.dither(3)
self.remove(guy.name_mob)
weakling = guy
self.play(FadeOut(weakling), FadeOut(greater_than))
self.play(ShowCreation(lightbulb))
self.dither()
self.play(FadeOut(comparitive_johann), FadeOut(lightbulb))
self.play(ApplyMethod(
Mobject(johann, bubble).scale, 10,
run_time = 3
))
class AboutSpaceFillingCurves(TransformOverIncreasingOrders):
@staticmethod
def args_to_string():
return ""
@staticmethod
def string_to_args(arg_str):
return ()
def construct(self):
self.bubble = ThoughtBubble().ingest_submobjects()
self.bubble.scale(1.5)
TransformOverIncreasingOrders.construct(self, FlowSnake, 7)
self.play(Transform(self.curve, self.bubble))
self.show_infinite_objects()
self.pose_question()
self.dither()
def show_infinite_objects(self):
sigma, summand, equals, result = TexMobject([
"\\sum_{n = 1}^{\\infty}",
"\\dfrac{1}{n^2}",
"=",
"\\dfrac{\pi^2}{6}"
]).split()
alt_summand = TexMobject("n").replace(summand)
alt_result = TexMobject("-\\dfrac{1}{12}").replace(result)
rationals, other_equals, naturals = TexMobject([
"|\\mathds{Q}|",
"=",
"|\\mathds{N}|"
]).scale(2).split()
infinity = TexMobject("\\infty").scale(2)
local_mobjects = filter(
lambda m : isinstance(m, Mobject),
locals().values(),
)
for mob in local_mobjects:
mob.sort_points(np.linalg.norm)
self.play(ShimmerIn(infinity))
self.dither()
self.play(
ShimmerIn(summand),
ShimmerIn(equals),
ShimmerIn(result),
DelayByOrder(Transform(infinity, sigma))
)
self.dither()
self.play(
Transform(summand, alt_summand),
Transform(result, alt_result),
)
self.dither()
self.remove(infinity)
self.play(*[
CounterclockwiseTransform(
Mobject(summand, equals, result, sigma),
Mobject(rationals, other_equals, naturals)
)
])
self.dither()
self.clear()
self.add(self.bubble)
def pose_question(self):
infinity, rightarrow, N = TexMobject([
"\\infty", "\\rightarrow", "N"
]).scale(2).split()
question_mark = TextMobject("?").scale(2)
self.add(question_mark)
self.dither()
self.play(*[
ShimmerIn(mob)
for mob in infinity, rightarrow, N
] + [
ApplyMethod(question_mark.next_to, rightarrow, UP),
])
self.dither()
