def rhs_could_be_any_number(self):
rhs_list = [
"2", # The journey starts here.
"3", # The first number that pops into your head when you hear "2".
"\\pi", # The good ol' pi.
"\\sqrt{2}", # The (most) famous irrational number.
"42", # The answer to everything.
"17.29", # TAXI.CAB
"-1", # A negative number, because why not?
"e", # The (most) famous mathematical constant.
"\\dfrac{3+\\sqrt{13}}{2}", # The bronze ratio... and a fraction.
"570", # 1/3 of the author.
"\\varphi", # The golden ratio.
"g_{64}", # Gigigigigigigigantic...
"0", # And... stop!
"N",
]
anything_text = TextMobject("等号右边似乎可以放任何数...")
anything_text.set_color(YELLOW)
anything_text.to_edge(UP)
equations = [
VGroup(ExpTower(order = 5), TexMobject("=", rhs).scale(0.8)).scale(2.5)
for rhs in rhs_list
]
init_equation = equations[0]
init_equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
init_equation.next_to(anything_text, DOWN, buff = self.tower_edge_buff)
init_equation.to_edge(LEFT, buff = self.tower_edge_buff)
for equation in equations:
equation[0].move_to(init_equation[0])
equation[1][0].move_to(init_equation[1][0])
equation[1][1].move_to(init_equation[1][1], aligned_edge = LEFT)
self.play(FadeIn(init_equation))
self.wait()
self.play(Write(anything_text), run_time = 1)
self.play(
ShowCreationThenDestruction(SurroundingRectangle(init_equation[1][1])),
run_time = 2
)
self.wait()
for k, equation in enumerate(equations):
if k > 0 and k != len(equations)-1:
equation[0].move_to(init_equation[0])
equation[1].move_to(init_equation[1], aligned_edge = LEFT)
self.remove(equations[k-1])
self.add(equations[k])
self.wait(1./3)
elif k == len(equations)-1:
self.wait()
self.play(ReplacementTransform(equations[k-1], equations[k]))
self.wait()
self.anything_text = anything_text
self.equation = equations[-1]
def generate_points(self):
rect = SurroundingRectangle(self.covered_mob)
rect.set_stroke(color = self.stroke_color, width = self.stroke_width)
rect.set_fill(color = self.fill_color, opacity = self.fill_opacity)
text = TextMobject(str(self.text))
text.set_color(self.text_color)
text.set_height(rect.get_height() * self.text_height_factor)
text.move_to(rect)
self.group = VGroup(rect, text)
self.add(self.group)
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 build_the_tower(self):
highest_order = 6
towers = [
ExpTower(order = k, is_infinite = False)
for k in range(1, highest_order + 1)
]
towers.append(ExpTower(order = highest_order, is_infinite = True))
heights = list(np.linspace(3, 4.5, highest_order + 2))
for tower, height in zip(towers, heights):
tower.set_height(height)
init_tower = towers[0]
final_tower = towers[-1]
self.play(Write(init_tower))
self.wait()
for k, tower in enumerate(towers):
if k < len(towers) - 2:
new_tower = towers[k+1]
new_exponent = new_tower.get_exponent()
new_base = new_tower.get_base()
self.play(
ReplacementTransform(tower, new_exponent),
Write(new_base),
)
self.wait()
else:
xs = final_tower.get_elements()
expdots = final_tower.get_expdots()
sur_rect = SurroundingRectangle(expdots)
self.play(
ReplacementTransform(tower, xs, run_time = 1),
Write(expdots, run_time = 2),
)
self.play(
Indicate(expdots, run_time = 1),
ShowCreationThenDestruction(sur_rect, run_time = 2),
)
self.wait()
break
self.tower = final_tower
self.highest_order = highest_order
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()
def add_display_frame(self, **kwargs):
config = dict(self.default_display_frame_config)
config.update(kwargs)
self.display_frame = SurroundingRectangle(self, **config)
self.add(self.display_frame)
return self
def __init__(self, mobject, **kwargs):
digest_config(self, kwargs)
rect = SurroundingRectangle(mobject,
**self.surrounding_rectangle_config)
AnimationGroup.__init__(self, self.rect_to_animation(rect, **kwargs))