def scroll_through_patrons(self):
logo_box = Square(side_length=2.5)
logo_box.to_corner(DOWN + LEFT, buff=MED_LARGE_BUFF)
total_width = FRAME_X_RADIUS - logo_box.get_right()[0]
black_rect = Rectangle(
fill_color=BLACK,
fill_opacity=1,
stroke_width=0,
width=FRAME_WIDTH,
height=0.6 * FRAME_HEIGHT,
)
black_rect.to_edge(UP, buff=0)
line = DashedLine(FRAME_X_RADIUS * LEFT, FRAME_X_RADIUS * RIGHT)
line.move_to(ORIGIN)
self.add(line)
thanks = TextMobject("Funded by the community, with special thanks to:")
thanks.scale(0.9)
thanks.next_to(black_rect.get_bottom(), UP, SMALL_BUFF)
thanks.set_color(YELLOW)
underline = Line(LEFT, RIGHT)
underline.scale_to_fit_width(thanks.get_width() + MED_SMALL_BUFF)
underline.next_to(thanks, DOWN, SMALL_BUFF)
thanks.add(underline)
self.add(thanks)
patrons = VGroup(*map(TextMobject, self.specific_patrons))
patrons.scale(self.patron_scale_val)
for patron in patrons:
if patron.get_width() > self.max_patron_width:
patron.scale_to_fit_width(self.max_patron_width)
columns = VGroup(*[
VGroup(*patrons[i::self.n_patron_columns])
for i in range(self.n_patron_columns)
])
for column in columns:
for n, name in enumerate(column):
name.shift(n * self.name_y_spacing * DOWN)
columns.arrange_submobjects(
RIGHT, buff=LARGE_BUFF,
aligned_edge=UP,
)
columns.scale_to_fit_width(total_width - 1)
columns.next_to(black_rect, DOWN, 3 * LARGE_BUFF)
columns.to_edge(RIGHT)
thanks.align_to(columns, alignment_vect=RIGHT)
self.play(
columns.move_to, 2 * DOWN, DOWN,
columns.to_edge, RIGHT,
Animation(black_rect),
Animation(line),
Animation(thanks),
rate_func=None,
run_time=self.run_time,
)
def generate_symbol(self):
symbol = VGroup(*[
RegularPolygon(
n=3, stroke_width=0, fill_color=self.color, fill_opacity=1)
for i in range(2)
])
symbol.arrange_submobjects(RIGHT, buff=0)
symbol.set_height(self.inner_radius * 0.7)
return symbol
def construct(self):
author = TextMobject("@Solara570")
support = TextMobject("(Powered by @3Blue1Brown)")
author.scale(1.8)
support.match_width(author)
group = VGroup(author, support)
group.arrange_submobjects(DOWN)
group.to_corner(RIGHT+DOWN)
self.play(FadeIn(group))
self.wait(2)
def arrange_subparts(self, *subparts):
for i, piece in enumerate(subparts):
piece.rotate(i * np.pi / 12, about_point=ORIGIN)
p1, p2, p3, p4, p5, p6, p7 = subparts
center_row = VGroup(p1, p4, p7)
center_row.arrange_submobjects(RIGHT, buff=0)
for p in p2, p3, p5, p6:
p.set_width(p1.get_width())
p2.move_to(p1.get_top(), DOWN + LEFT)
p3.move_to(p1.get_bottom(), UP + LEFT)
p5.move_to(p4.get_top(), DOWN + LEFT)
p6.move_to(p4.get_bottom(), UP + LEFT)
def build_the_equation(self):
l_part = self.tower.copy()
r_part = TexMobject("=", "2")
r_part.match_height(l_part.get_base())
equation = VGroup(l_part, r_part)
equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
self.play(
ReplacementTransform(self.tower, l_part, run_time = 1),
Write(r_part, run_time = 2),
)
self.equation = equation
def arrange_subparts(self, *subparts):
for i, piece in enumerate(subparts):
piece.rotate(i * np.pi / 12, about_point=ORIGIN)
p1, p2, p3, p4, p5, p6, p7 = subparts
center_row = VGroup(p1, p4, p7)
center_row.arrange_submobjects(RIGHT, buff=0)
for p in p2, p3, p5, p6:
p.scale_to_fit_width(p1.get_width())
p2.move_to(p1.get_top(), DOWN + LEFT)
p3.move_to(p1.get_bottom(), UP + LEFT)
p5.move_to(p4.get_top(), DOWN + LEFT)
p6.move_to(p4.get_bottom(), UP + LEFT)
def generate_symbol(self):
symbol = VGroup(*[
Rectangle(
length=2,
width=0.5,
stroke_width=0,
fill_color=self.color,
fill_opacity=1,
) for i in range(2)
])
symbol.arrange_submobjects(RIGHT, buff=0.5)
symbol.set_height(self.inner_radius)
return symbol
def add_words(self):
# Wallis product
product = TexMobject(*(["\\text{Wallis公式：}"] + [
"{%d \\over %d} \\," % (wallis_numer(n), wallis_denom(n))
for n in range(1, 8)
] + ["\\cdots = {\\pi \\over 2}"])).set_color(YELLOW)
rect = SurroundingRectangle(product, color=YELLOW, buff=0.25)
wallis_product = VGroup(product, rect)
wallis_product.set_width(6)
# All those steps
nums = [TextMobject("%d. " % k) for k in [1, 2, 3, 4]]
words = [
TextMobject(word) for word in [
"构造合适的矩形边长",
"同种颜色的矩形的面积之和恒为1",
"整个图形又像一个${1 \\over 4}$圆，半径是",
"比较${1 \\over 4}$圆与矩形的面积",
]
]
formulae = [
TextMobject(formula) for formula in [
"$a_0 = 1,\\, a_n = {1 \\over 2} \cdot {3 \\over 4} \cdots {2n-1 \\over 2n} (n \geq 1)$",
"$a_0 a_n + a_1 a_{n-1} + \\cdots + a_n a_0 = 1$",
"$\\begin{aligned} \
r_n & = a_0 + a_1 + \\cdots + a_{n-1} \\\\ \
& = \\textstyle{3 \\over 2} \cdot {5 \\over 4} \cdots {2n-1 \\over 2n-2} \
\\quad (n \geq 2) \
\\end{aligned}$",
"${1 \\over 4} \\pi {r_n}^2 \\approx n \\quad \\Rightarrow \\quad \\text{Wallis公式}$"
]
]
steps = VGroup()
for num, word, formula in zip(nums, words, formulae):
num.next_to(word, LEFT)
formula.next_to(word, DOWN, aligned_edge=LEFT)
steps.add(VGroup(num, word, formula))
steps.arrange_submobjects(DOWN, buff=0.6, aligned_edge=LEFT)
steps.set_width(6)
steps.next_to(wallis_product, DOWN)
VGroup(wallis_product, steps).center().to_edge(RIGHT, buff=0.15)
# Sep line and QED
sep_line = DashedLine(2 * TOP, 2 * BOTTOM, color=GREY, buff=0.5)
sep_line.next_to(steps, LEFT)
qed = QEDSymbol(height=0.570 / 2)
qed.next_to(steps[-1][-1][-1], RIGHT, aligned_edge=DOWN)
# Add everything
self.add(wallis_product, steps, sep_line, qed)
def scroll_through_patrons(self):
logo_box = Square(side_length=2.5)
logo_box.to_corner(DOWN + LEFT, buff=MED_LARGE_BUFF)
total_width = FRAME_X_RADIUS - logo_box.get_right()[0]
black_rect = Rectangle(fill_color=BLACK,
fill_opacity=1,
stroke_width=0,
width=FRAME_WIDTH,
height=1.1 * FRAME_Y_RADIUS)
black_rect.to_edge(UP, buff=0)
line = DashedLine(FRAME_X_RADIUS * LEFT, FRAME_X_RADIUS * RIGHT)
line.move_to(black_rect, DOWN)
line.shift(SMALL_BUFF * SMALL_BUFF * DOWN)
self.add(line)
patrons = VGroup(*map(TextMobject, self.specific_patrons))
patrons.scale(self.patron_scale_val)
for patron in patrons:
if patron.get_width() > self.max_patron_width:
patron.scale_to_fit_width(self.max_patron_width)
columns = VGroup(*[
VGroup(*patrons[i::self.n_patron_columns])
for i in range(self.n_patron_columns)
])
for column in columns:
for n, name in enumerate(column):
name.shift(n * self.name_y_spacing * DOWN)
columns.arrange_submobjects(
RIGHT,
buff=LARGE_BUFF,
aligned_edge=UP,
)
columns.scale_to_fit_width(total_width - 1)
columns.next_to(black_rect, DOWN, 3 * LARGE_BUFF)
columns.to_edge(RIGHT)
self.play(
columns.move_to,
2 * DOWN,
DOWN,
columns.to_edge,
RIGHT,
Animation(black_rect),
rate_func=None,
run_time=self.run_time,
)
def rewind_and_play_again(self):
watch_again = TextMobject("再看一遍...")
watch_again.set_color(YELLOW)
rewind, play = buttons = VGroup(*[
Button().get_symbol().set_color(YELLOW).set_height(1)
for Button in (RewindButton, PlayButton)
])
group = VGroup(watch_again, rewind)
group.arrange_submobjects(DOWN, aligned_edge = RIGHT)
group.to_corner(DOWN+RIGHT)
play.move_to(rewind, aligned_edge = RIGHT)
self.play(Write(watch_again), run_time = 0.5)
self.wait()
self.add(rewind)
self.words.reverse()
for word in self.words:
self.play(FadeOut(VGroup(word)), run_time = 0.2)
self.wait(0.1)
self.remove(rewind)
self.add(play)
self.play(FadeOut(watch_again), run_time = 0.5)
self.wait(0.5)
self.remove(play)
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VGroup(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(FRAME_WIDTH - 1)
self.add(everything)
def construct(self):
colors = ["#FF0000", "#FF8000", "#FFFF00", "#00FF00", "#0080FF"]
wallis_rects_4 = WallisRectangles(
order=5,
rect_colors=colors,
)
vert_lines = VGroup(*[
Line(3.5*UP, 3.5*DOWN, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(0, k), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [LEFT]*5+[RIGHT])
])
horiz_lines = VGroup(*[
Line(3.5*LEFT, 3.5*RIGHT, color = GREY, stroke_width = 3) \
.next_to(wallis_rects_4.get_rectangle(k, 0), direction, buff = 0)
for k, direction in zip(list(range(5))+[4], [DOWN]*5+[UP])
])
for vert_line in vert_lines:
vert_line.vertically_center()
for horiz_line in horiz_lines:
horiz_line.horizontally_center()
vert_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((vert_lines[k].get_center() + vert_lines[k+1].get_center())/2) \
.shift(3.5*DOWN)
for k in range(5)
])
horiz_labels = VGroup(*[
TexMobject("a_%d" % k) \
.move_to((horiz_lines[k].get_center() + horiz_lines[k+1].get_center())/2) \
.shift(3.5*LEFT)
for k in range(5)
])
area_texs = VGroup()
factors = [1.25, 1, 0.9, 0.7, 0.6]
for p in range(5):
for q in range(5 - p):
rect = wallis_rects_4.get_rectangle(p, q)
tex = TexMobject("{a_%d} {a_%d}" % (q, p))
tex.scale(factors[p + q])
tex.move_to(rect)
area_texs.add(tex)
figure = VGroup()
figure.add(wallis_rects_4, vert_lines, horiz_lines, vert_labels,
horiz_labels, area_texs)
figure.to_edge(LEFT)
self.add(figure)
tex_list = VGroup()
for p in range(5):
formula_string = (
" + ".join(["a_%d a_%d" % (q, p - q)
for q in range(p + 1)]) + "=1")
formula = TexMobject(formula_string)
tex_list.add(formula)
# tex_list.add(TexMobject("\\vdots"))
tex_factors = np.linspace(1, 0.7, 5)
for tex, color, factor in zip(tex_list, colors, tex_factors):
tex.set_color(color)
tex.scale(factor)
tex_list.arrange_submobjects(DOWN, aligned_edge=LEFT)
tex_list.to_edge(RIGHT)
self.add(tex_list)
self.wait()
def construct(self):
# Chart on the left
colors = [WHITE, ORANGE, GREEN]
titles = VGroup(*[
TexMobject(text).set_color(color)
for text, color in zip(["n", "p_n", "q_n"], colors)
])
contents = VGroup(*[
VGroup(*[
TexMobject("%d" % num) for num in
[k, central_binomial_coeff(k),
central_binomial_coeff(k)]
]) for k in range(8)
])
titles.arrange_submobjects(RIGHT, buff=1)
for num, line in enumerate(contents):
for k, element in enumerate(line):
buff = 0.6 + 0.8 * num
element.next_to(titles[k], DOWN, aligned_edge=LEFT, buff=buff)
element.set_color(colors[k])
sep_line = Line(ORIGIN, 4.5 * RIGHT, stroke_width=5)
sep_line.next_to(titles, DOWN)
chart = VGroup(titles, contents, sep_line)
chart.set_height(7)
chart.center().to_edge(LEFT)
self.add(chart)
# Figures on the right
std_zero_pos_axis = NumberLine(x_min=-2,
x_max=2,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_pos_axis.rotate(np.pi / 2)
std_nocross_pos_axis = NumberLine(x_min=-4,
x_max=4,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_nocross_pos_axis.rotate(np.pi / 2)
std_time_axis = NumberLine(x_min=0,
x_max=5.5,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_axes = VGroup(std_zero_pos_axis, std_time_axis)
std_nocross_axes = VGroup(std_nocross_pos_axis, std_time_axis)
zero_walks = VGroup()
for sequence in ["UUDD", "UDUD", "UDDU", "DDUU", "DUDU", "DUUD"]:
axes = std_zero_axes.copy()
zero_walk = RandomWalk1DArrow(sequence, step_size=0.25)
zero_walk.move_start_to(axes[0].number_to_point(0))
zero_walks.add(VGroup(axes, zero_walk))
zero_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
zero_rect = SurroundingRectangle(zero_walks, color=ORANGE, buff=0.4)
zero_walks.add(zero_rect)
nocross_walks = VGroup()
for sequence in ["DDDD", "DDUD", "DDDU", "UUUU", "UUDU", "UUUD"]:
axes = std_nocross_axes.copy()
nocross_walk = RandomWalk1DArrow(sequence, step_size=0.25)
nocross_walk.move_start_to(axes[0].number_to_point(0))
nocross_walks.add(VGroup(axes, nocross_walk))
nocross_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
nocross_rect = SurroundingRectangle(nocross_walks,
color=GREEN,
buff=0.4)
nocross_walks.add(nocross_rect)
relation = TexMobject("p_2", "=", "q_2", "=", "6")
relation[0].set_color(ORANGE)
relation[2].set_color(GREEN)
relation.scale(1.5)
figure = VGroup(zero_walks, relation, nocross_walks)
figure.arrange_submobjects(DOWN)
figure.set_height(7)
figure.center().to_edge(RIGHT)
self.add(figure)
self.wait()
class TeacherStudentsScene(PiCreatureScene):
CONFIG = {
"student_colors": [BLUE_D, BLUE_E, BLUE_C],
"student_scale_factor": 0.8,
"seconds_to_blink": 2,
"screen_height": 3,
}
def setup(self):
PiCreatureScene.setup(self)
self.screen = ScreenRectangle(height=self.screen_height)
self.screen.to_corner(UP + LEFT)
self.hold_up_spot = self.teacher.get_corner(UP +
LEFT) + MED_LARGE_BUFF * UP
def create_pi_creatures(self):
self.teacher = Mortimer(color=self.default_pi_creature_kwargs["color"])
self.teacher.to_corner(DOWN + RIGHT)
self.teacher.look(DOWN + LEFT)
self.students = VGroup(
*[Randolph(color=c) for c in self.student_colors])
self.students.arrange_submobjects(RIGHT)
self.students.scale(self.student_scale_factor)
self.students.to_corner(DOWN + LEFT)
self.teacher.look_at(self.students[-1].eyes)
for student in self.students:
student.look_at(self.teacher.eyes)
return [self.teacher] + list(self.students)
def get_teacher(self):
return self.teacher
def get_students(self):
return self.students
def teacher_says(self, *content, **kwargs):
return self.pi_creature_says(self.get_teacher(), *content, **kwargs)
def student_says(self, *content, **kwargs):
if "target_mode" not in kwargs:
target_mode = random.choice([
"raise_right_hand",
"raise_left_hand",
])
kwargs["target_mode"] = target_mode
student = self.get_students()[kwargs.get("student_index", 1)]
return self.pi_creature_says(student, *content, **kwargs)
def teacher_thinks(self, *content, **kwargs):
return self.pi_creature_thinks(self.get_teacher(), *content, **kwargs)
def student_thinks(self, *content, **kwargs):
student = self.get_students()[kwargs.get("student_index", 1)]
return self.pi_creature_thinks(student, *content, **kwargs)
def change_all_student_modes(self, mode, **kwargs):
self.change_student_modes(*[mode] * len(self.students), **kwargs)
def change_student_modes(self, *modes, **kwargs):
added_anims = kwargs.pop("added_anims", [])
self.play(self.get_student_changes(*modes, **kwargs), *added_anims)
def get_student_changes(self, *modes, **kwargs):
pairs = zip(self.get_students(), modes)
pairs = [(s, m) for s, m in pairs if m is not None]
start = VGroup(*[s for s, m in pairs])
target = VGroup(*[s.copy().change_mode(m) for s, m in pairs])
if "look_at_arg" in kwargs:
for pi in target:
pi.look_at(kwargs["look_at_arg"])
submobject_mode = kwargs.get("submobject_mode", "lagged_start")
return Transform(start,
target,
submobject_mode=submobject_mode,
run_time=2)
def zoom_in_on_thought_bubble(self,
bubble=None,
radius=FRAME_Y_RADIUS + FRAME_X_RADIUS):
if bubble is None:
for pi in self.get_pi_creatures():
if hasattr(pi, "bubble") and isinstance(
pi.bubble, ThoughtBubble):
bubble = pi.bubble
break
if bubble is None:
raise Exception("No pi creatures have a thought bubble")
vect = -bubble.get_bubble_center()
def func(point):
centered = point + vect
return radius * centered / np.linalg.norm(centered)
self.play(
*
[ApplyPointwiseFunction(func, mob) for mob in self.get_mobjects()])
def teacher_holds_up(self,
mobject,
target_mode="raise_right_hand",
**kwargs):
mobject.move_to(self.hold_up_spot, DOWN)
mobject.shift_onto_screen()
mobject_copy = mobject.copy()
mobject_copy.shift(DOWN)
mobject_copy.fade(1)
self.play(
ReplacementTransform(mobject_copy, mobject),
self.teacher.change,
target_mode,
)
class TeacherStudentsScene(PiCreatureScene):
CONFIG = {
"student_colors": [BLUE_D, BLUE_E, BLUE_C],
"teacher_color": GREY_BROWN,
"student_scale_factor": 0.8,
"seconds_to_blink": 2,
"screen_height": 3,
}
def setup(self):
PiCreatureScene.setup(self)
self.screen = ScreenRectangle(height=self.screen_height)
self.screen.to_corner(UP + LEFT)
self.hold_up_spot = self.teacher.get_corner(UP + LEFT) + MED_LARGE_BUFF * UP
def create_pi_creatures(self):
self.teacher = Mortimer(color=self.teacher_color)
self.teacher.to_corner(DOWN + RIGHT)
self.teacher.look(DOWN + LEFT)
self.students = VGroup(*[
Randolph(color=c)
for c in self.student_colors
])
self.students.arrange_submobjects(RIGHT)
self.students.scale(self.student_scale_factor)
self.students.to_corner(DOWN + LEFT)
self.teacher.look_at(self.students[-1].eyes)
for student in self.students:
student.look_at(self.teacher.eyes)
return [self.teacher] + list(self.students)
def get_teacher(self):
return self.teacher
def get_students(self):
return self.students
def teacher_says(self, *content, **kwargs):
return self.pi_creature_says(
self.get_teacher(), *content, **kwargs
)
def student_says(self, *content, **kwargs):
if "target_mode" not in kwargs:
target_mode = random.choice([
"raise_right_hand",
"raise_left_hand",
])
kwargs["target_mode"] = target_mode
student = self.get_students()[kwargs.get("student_index", 1)]
return self.pi_creature_says(
student, *content, **kwargs
)
def teacher_thinks(self, *content, **kwargs):
return self.pi_creature_thinks(
self.get_teacher(), *content, **kwargs
)
def student_thinks(self, *content, **kwargs):
student = self.get_students()[kwargs.get("student_index", 1)]
return self.pi_creature_thinks(student, *content, **kwargs)
def change_all_student_modes(self, mode, **kwargs):
self.change_student_modes(*[mode] * len(self.students), **kwargs)
def change_student_modes(self, *modes, **kwargs):
added_anims = kwargs.pop("added_anims", [])
self.play(
self.get_student_changes(*modes, **kwargs),
*added_anims
)
def get_student_changes(self, *modes, **kwargs):
pairs = zip(self.get_students(), modes)
pairs = [(s, m) for s, m in pairs if m is not None]
start = VGroup(*[s for s, m in pairs])
target = VGroup(*[s.copy().change_mode(m) for s, m in pairs])
if "look_at_arg" in kwargs:
for pi in target:
pi.look_at(kwargs["look_at_arg"])
submobject_mode = kwargs.get("submobject_mode", "lagged_start")
return Transform(
start, target,
submobject_mode=submobject_mode,
run_time=2
)
def zoom_in_on_thought_bubble(self, bubble=None, radius=FRAME_Y_RADIUS + FRAME_X_RADIUS):
if bubble is None:
for pi in self.get_pi_creatures():
if hasattr(pi, "bubble") and isinstance(pi.bubble, ThoughtBubble):
bubble = pi.bubble
break
if bubble is None:
raise Exception("No pi creatures have a thought bubble")
vect = -bubble.get_bubble_center()
def func(point):
centered = point + vect
return radius * centered / np.linalg.norm(centered)
self.play(*[
ApplyPointwiseFunction(func, mob)
for mob in self.get_mobjects()
])
def teacher_holds_up(self, mobject, target_mode="raise_right_hand", added_anims=None, **kwargs):
mobject.move_to(self.hold_up_spot, DOWN)
mobject.shift_onto_screen()
mobject_copy = mobject.copy()
mobject_copy.shift(DOWN)
mobject_copy.fade(1)
added_anims = added_anims or []
self.play(
ReplacementTransform(mobject_copy, mobject),
self.teacher.change, target_mode,
*added_anims
)
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VGroup(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(FRAME_WIDTH - 1)
self.add(everything)
