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 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 construct(self):
# Setup
axes_group = self.axes_group
pos_axis, time_axis = axes_group[:2]
title_pq = self.title_pq
walk_q = self.walk_q
parts_q = self.parts_q
l_arrow = self.l_arrow
self.add(axes_group, title_pq, walk_q, l_arrow)
walk_q_copy = walk_q.copy()
# Q_4 -> P_4
steps_qp = VGroup(*[
TextMobject(text) for text in [
"1. 找到路径终点的位置坐标$h$", "2. 找到最晚一次穿过$\\frac{h}{2}$的时刻",
"3. 在这个时刻上进行分割", "4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_qp:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_qp, step2_qp, step3_qp, step4_qp, step5_qp = steps_qp
# 1. Find the endpoint
step1_qp.next_to(time_axis.number_to_point(4.5), UP)
end_horiz_line = DashedLine(LEFT_SIDE, RIGHT_SIDE, color=YELLOW)
end_horiz_line.move_to(pos_axis.number_to_point(-4))
end_horiz_line.horizontally_center()
end_brace_line = DashedLine(time_axis.number_to_point(8),
walk_q.get_end_point())
end_brace = Brace(end_brace_line, direction=RIGHT, color=YELLOW)
h = TexMobject("h").set_color(YELLOW)
end_brace.put_at_tip(h)
self.play(Write(step1_qp), ShowCreation(end_horiz_line), run_time=1)
self.play(GrowFromCenter(end_brace), GrowFromCenter(h))
self.wait(1.5)
self.play(FadeOut(step1_qp))
# 2. Find the last time it GOES THROUGH half its final value
half_point = walk_q.get_arrow_end_point(3)
step2_qp.next_to(time_axis.number_to_point(4.5), UP)
half_horiz_line = end_horiz_line.copy().shift(2 * UP)
half_brace_line = DashedLine(time_axis.number_to_point(4), half_point)
half_brace = Brace(half_brace_line, direction=RIGHT, color=YELLOW)
half_h = TexMobject("\\frac{h}{2}").set_color(YELLOW)
half_brace.put_at_tip(half_h)
half_dot = Dot(half_point, color=YELLOW)
self.play(FadeIn(step2_qp), run_time=1)
self.wait(0.5)
self.play(
ReplacementTransform(end_brace, half_brace),
ReplacementTransform(end_horiz_line, half_horiz_line),
ReplacementTransform(h, half_h[0]),
Write(half_h[1:]),
)
self.play(DrawBorderThenFill(half_dot))
self.wait(1.5)
self.play(
FadeOut(VGroup(step2_qp, half_horiz_line, half_brace, half_h)))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(half_point)
step3_qp.next_to(vert_line, UP)
left_part_q, right_part_q = parts_q
self.play(ShowCreation(vert_line), Write(step3_qp), run_time=1)
self.play(
FadeOut(half_dot),
left_part_q.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_q.shift,
0.5 * UP + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_qp))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_q)
step4_qp.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_qp),
run_time=1,
)
self.play(
left_part_q.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_qp), FadeOut(flip_axis))
# 5. Put the pieces together
step5_qp.shift(2.5 * DOWN)
flip_arrow_anims = walk_q.get_flip_arrows_animation(3, color=ORANGE)
self.play(Write(step5_qp), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_q.set_color, ORANGE)
self.wait(0.5)
self.play(
left_part_q.shift,
2.5 * UP + 0.5 * RIGHT,
right_part_q.shift,
3.5 * UP + 0.5 * LEFT,
Animation(step5_qp),
)
self.wait(0.5)
self.play(FadeOut(step5_qp))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_q))
self.play(FadeIn(walk_q_copy))
self.wait()
def construct(self):
# Setup
axes_group = self.axes_group
title_pq = self.title_pq
walk_p = self.walk_p
parts_p = self.parts_p
r_arrow = self.r_arrow
self.add(axes_group, title_pq, walk_p, r_arrow)
walk_p_copy = walk_p.copy()
# P_4 -> Q_4
steps_pq = VGroup(*[
TextMobject(text) for text in [
"1. 第一步是沿着正方向走的", "2. 找到第一次到达最大值的时刻", "3. 在这个时刻上进行分割",
"4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_pq:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_pq, step2_pq, step3_pq, step4_pq, step5_pq = steps_pq
# 1. Check the first step of the walk
step1_circle = Circle(color=YELLOW)
first_arrow = walk_p.get_arrow_by_number(0)
step1_circle.surround(first_arrow)
step1_pq.next_to(step1_circle, RIGHT + DOWN)
self.play(ShowCreation(step1_circle), Write(step1_pq), run_time=1)
self.wait(1.5)
self.play(FadeOut(step1_circle), FadeOut(step1_pq))
# 2. Find the first time it reaches the maximum
peak = walk_p.get_arrow_end_point(3)
horiz_line = DashedLine(2.5 * LEFT, 2.5 * RIGHT, color=YELLOW)
horiz_line.move_to(peak)
dot = Dot(color=YELLOW)
dot.move_to(peak)
step2_pq.next_to(horiz_line, UP)
self.play(ShowCreation(horiz_line),
DrawBorderThenFill(dot),
Write(step2_pq),
run_time=1)
self.wait(1.5)
self.play(FadeOut(horiz_line), FadeOut(step2_pq))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(peak)
step3_pq.next_to(vert_line, DOWN)
left_part_p, right_part_p = parts_p
self.play(ShowCreation(vert_line), Write(step3_pq), run_time=1)
self.play(
FadeOut(dot),
left_part_p.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_p.shift,
DOWN + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_pq))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_p)
step4_pq.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_pq),
run_time=1,
)
self.play(
left_part_p.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_pq), FadeOut(flip_axis))
# 5. Put the pieces together
step5_pq.move_to(dot)
flip_arrow_anims = walk_p.get_flip_arrows_animation(3, color=GREEN)
self.play(Write(step5_pq), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_p.set_color, GREEN)
self.wait(0.5)
self.play(
left_part_p.shift,
1.5 * DOWN + 0.5 * RIGHT,
right_part_p.shift,
3 * DOWN + 0.5 * LEFT,
Animation(step5_pq),
)
self.wait(0.5)
self.play(FadeOut(step5_pq))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_p))
self.play(FadeIn(walk_p_copy))
self.wait()
def construct(self):
# Setup
pos_axis = NumberLine(x_min=-3.5, x_max=3.5, color=WHITE)
pos_axis.rotate(np.pi / 2)
pos_axis.add_tip()
time_axis = NumberLine(x_min=0, x_max=9.5, color=WHITE)
time_axis.add_tip()
pos_text = TextMobject("位置")
pos_text.next_to(pos_axis.number_to_point(3.5), LEFT)
time_text = TextMobject("时间")
time_text.next_to(time_axis.number_to_point(9.5), DOWN)
group = VGroup(pos_axis, time_axis, pos_text, time_text)
group.to_edge(LEFT, buff=2)
self.add(group)
# Some preparations
sequences = [
"UDDDUDUD", "DUUDDDUD", "DDUUUDUD", "UUUDDUDU", "UDDDUDUD"
]
nums = [1, 3, 7, -1, 1]
walks = [
RandomWalk1DArrow(sequence).move_start_to(
pos_axis.number_to_point(0)) for sequence in sequences
]
parts = [walk.split_at(num) for walk, num in zip(walks, nums)]
split_lines = [
DashedLine(TOP, BOTTOM, color = GREY) \
.move_to(time_axis.number_to_point(num+1))
for num in nums
]
zero_words = [
TextMobject("“正点到家” \\\\ $P_%s$" % str((num+1)//2)) \
.next_to(line, LEFT).shift(2.8 * DOWN).set_color(ORANGE)
for num, line in zip(nums, split_lines)
]
nocross_words = [
TextMobject("“不经过家门” \\\\ $Q_%s$" % str(4-(num+1)//2)) \
.next_to(line, RIGHT).shift(2.8 * DOWN).set_color(GREEN)
for num, line in zip(nums, split_lines)
]
for words, direction in zip([zero_words, nocross_words],
[RIGHT, LEFT]):
for word in words:
text, symbol = VGroup(word[:-2]), VGroup(word[-2:])
symbol.scale(1.5)
symbol.next_to(text, DOWN, aligned_edge=direction)
word.add_background_rectangle()
# Demonstrate how to split
self.add(walks[0], split_lines[0], zero_words[0], nocross_words[0])
l = len(walks)
for k in range(l - 1):
cur_walk = walks[k]
cur_line = split_lines[k]
cur_zero_word = zero_words[k]
cur_nocross_word = nocross_words[k]
next_walk = walks[k + 1]
next_line = split_lines[k + 1]
next_zero_word = zero_words[k + 1]
next_nocross_word = nocross_words[k + 1]
part1, part2 = parts[k]
cur_walk.save_state()
self.play(
part1.set_color,
ORANGE,
part2.set_color,
GREEN,
)
self.wait()
self.play(cur_walk.restore)
self.wait()
self.play(
ReplacementTransform(cur_walk, next_walk),
ReplacementTransform(cur_line, next_line),
ReplacementTransform(cur_zero_word, next_zero_word),
ReplacementTransform(cur_nocross_word, next_nocross_word),
)
self.wait()