def construct(self):
formula = TexMobject(*([
"{%d \\over %d} \\cdot" % (wallis_numer(n), wallis_denom(n))
for n in range(1, self.n_terms + 1)
] + ["\\cdots"]))
result = TexMobject("=", "{\\pi \\over 2}")
result.scale(2)
pi = result[-1][0]
pi.set_color(YELLOW)
circle = Circle(color=YELLOW)
circle.surround(pi)
question = TexMobject("?", color=YELLOW)
question.scale(2).next_to(circle, RIGHT, buff=0.4)
result_group = VGroup(result, circle, question)
result_group.next_to(formula, DOWN)
group = VGroup(formula, result_group)
group.center().set_width(10)
bg_rect = BackgroundRectangle(group, fill_opacity=0.5, buff=0.2)
random_walks = VGroup(*[
RandomWalk1DArrow(random_walk_string(30), step_size=0.5)
for k in range(self.n_walks)
])
for k, walk in enumerate(random_walks):
walk.shift(random.randrange(-5, 5) * 2 * walk.step_size * UP)
random_walks.center()
text = TextMobject(self.part).scale(3).set_color(YELLOW)
text.to_corner(RIGHT + DOWN)
self.add(random_walks)
self.add(FullScreenFadeRectangle())
self.add(bg_rect, group, text)
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_points(self):
body = Cube(side_length=1)
for dim, scale_factor in enumerate(self.body_dimensions):
body.stretch(scale_factor, dim=dim)
body.scale_to_fit_width(self.width)
body.set_fill(self.shaded_body_color, opacity=1)
body.sort_submobjects(lambda p: p[2])
body[-1].set_fill(self.body_color)
screen_plate = body.copy()
keyboard = VGroup(*[
VGroup(*[
Square(**self.key_color_kwargs)
for x in range(12 - y % 2)
]).arrange_submobjects(RIGHT, buff=SMALL_BUFF)
for y in range(4)
]).arrange_submobjects(DOWN, buff=MED_SMALL_BUFF)
keyboard.stretch_to_fit_width(
self.keyboard_width_to_body_width * body.get_width(),
)
keyboard.stretch_to_fit_height(
self.keyboard_height_to_body_height * body.get_height(),
)
keyboard.next_to(body, OUT, buff=0.1 * SMALL_BUFF)
keyboard.shift(MED_SMALL_BUFF * UP)
body.add(keyboard)
screen_plate.stretch(self.screen_thickness /
self.body_dimensions[2], dim=2)
screen = Rectangle(
stroke_width=0,
fill_color=BLACK,
fill_opacity=1,
)
screen.replace(screen_plate, stretch=True)
screen.scale_in_place(self.screen_width_to_screen_plate_width)
screen.next_to(screen_plate, OUT, buff=0.1 * SMALL_BUFF)
screen_plate.add(screen)
screen_plate.next_to(body, UP, buff=0)
screen_plate.rotate(
self.open_angle, RIGHT,
about_point=screen_plate.get_bottom()
)
self.screen_plate = screen_plate
self.screen = screen
axis = Line(
body.get_corner(UP + LEFT + OUT),
body.get_corner(UP + RIGHT + OUT),
color=BLACK,
stroke_width=2
)
self.axis = axis
self.add(body, screen_plate, axis)
self.rotate(5 * np.pi / 12, LEFT, about_point=ORIGIN)
self.rotate(np.pi / 6, DOWN, about_point=ORIGIN)
def generate_points(self):
body = Cube(side_length=1)
for dim, scale_factor in enumerate(self.body_dimensions):
body.stretch(scale_factor, dim=dim)
body.scale_to_fit_width(self.width)
body.set_fill(self.shaded_body_color, opacity=1)
body.sort_submobjects(lambda p: p[2])
body[-1].set_fill(self.body_color)
keyboard = VGroup(*[
VGroup(*[
Square(**self.key_color_kwargs)
for x in range(12 - y % 2)
]).arrange_submobjects(RIGHT, buff=SMALL_BUFF)
for y in range(4)
]).arrange_submobjects(DOWN, buff=MED_SMALL_BUFF)
keyboard.stretch_to_fit_width(
self.keyboard_width_to_body_width * body.get_width(),
)
keyboard.stretch_to_fit_height(
self.keyboard_height_to_body_height * body.get_height(),
)
keyboard.next_to(body, OUT, buff=0.1 * SMALL_BUFF)
keyboard.shift(MED_SMALL_BUFF * UP)
body.add(keyboard)
screen_plate = body.copy()
screen_plate.stretch(self.screen_thickness /
self.body_dimensions[2], dim=2)
screen = Rectangle(
stroke_width=0,
fill_color=BLACK,
fill_opacity=1,
)
screen.replace(screen_plate, stretch=True)
screen.scale_in_place(self.screen_width_to_screen_plate_width)
screen.next_to(screen_plate, OUT, buff=0.1 * SMALL_BUFF)
screen_plate.add(screen)
screen_plate.next_to(body, UP, buff=0)
screen_plate.rotate(
self.open_angle, RIGHT,
about_point=screen_plate.get_bottom()
)
self.screen_plate = screen_plate
self.screen = screen
axis = Line(
body.get_corner(UP + LEFT + OUT),
body.get_corner(UP + RIGHT + OUT),
color=BLACK,
stroke_width=2
)
self.axis = axis
self.add(body, screen_plate, axis)
self.rotate(5 * np.pi / 12, LEFT, about_point=ORIGIN)
self.rotate(np.pi / 6, DOWN, about_point=ORIGIN)
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,
)
