def generate_points(self):
hollow_tri = HollowTriangle(**self.triangle_config)
bang = TexMobject("!")
bang.set_height(hollow_tri.inner_height * 0.7)
bang.move_to(hollow_tri.get_center_of_mass())
self.add(hollow_tri, bang)
self.set_color(self.color)
def construct(self):
wallis_rects_570 = WallisRectangles(order=570)
quarter_circle = Sector(
outer_radius=wallis_rects_570.get_height(),
stroke_color=GREY,
stroke_width=5.70,
fill_opacity=0,
)
quarter_circle.move_arc_center_to(wallis_rects_570.get_bottom_left())
text = TexMobject("n = 570")
text.scale(1.5)
text.move_to(wallis_rects_570.get_top_right())
self.add(wallis_rects_570, quarter_circle, text)
self.wait()
def construct(self):
wallis_rects_5 = WallisRectangles(rect_colors=[
"#FF0000", "#FF8000", "#FFFF00", "#00FF00", "#0080FF"
],
order=5)
quarter_circle = Sector(
outer_radius=wallis_rects_5.get_height(),
stroke_color=GREY,
stroke_width=5.70,
fill_opacity=0,
)
quarter_circle.move_arc_center_to(wallis_rects_5.get_bottom_left())
text = TexMobject("n = 5")
text.scale(1.5)
text.move_to(wallis_rects_5.get_top_right())
self.add(wallis_rects_5, quarter_circle, text)
self.wait()
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 add_figure(self):
# Main figure
wallis_rects = WallisRectangles(order=10)
order = wallis_rects.get_order()
# Variables and braces on the left
left_rects = [
wallis_rects.get_rectangle(k, 0) for k in [0, 1, 2, 3, -1]
]
left_braces = [
Brace(rect, direction=LEFT, buff=0.1) for rect in left_rects
]
left_lengths = [
TexMobject(symbol)
for symbol in ["a_0", "a_1", "a_2", "a_3", "a_{n-1}"]
]
left_lengths[-1].scale(0.7)
for brace, length in zip(left_braces, left_lengths):
brace.put_at_tip(length, buff=0.15)
left_vdots = TexMobject("\\vdots")
left_vdots.scale(2)
left_vdots.move_to(
(left_braces[-1].get_center() + left_braces[-2].get_center()) / 2)
# Variables and braces on the bottom
down_rects = [
wallis_rects.get_rectangle(0, k) for k in [0, 1, 2, 3, -1]
]
down_braces = [
Brace(rect, direction=DOWN, buff=0.1) for rect in down_rects
]
down_lengths = [
TexMobject(symbol)
for symbol in ["a_0", "a_1", "a_2", "a_3", "a_{n-1}"]
]
down_lengths[-1].scale(0.7)
for brace, length in zip(down_braces, down_lengths):
brace.put_at_tip(length, buff=0.15)
down_cdots = TexMobject("\\cdots")
down_cdots.scale(2)
down_cdots.move_to(
(down_braces[-1].get_center() + down_braces[-2].get_center()) / 2)
# The quarter circle
quarter_circle = Sector(
outer_radius=wallis_rects.get_height(),
stroke_color=GREY,
stroke_width=5.70,
fill_opacity=0,
)
quarter_circle.move_arc_center_to(wallis_rects.get_bottom_left())
# Add everthing
figure_group = VGroup(
wallis_rects,
VGroup(*left_braces),
VGroup(*left_lengths),
left_vdots,
VGroup(*down_braces),
VGroup(*down_lengths),
down_cdots,
quarter_circle,
)
figure_group.center().to_edge(LEFT, buff=0.15)
self.add(figure_group)
def show_the_solution(self):
# Prepare for the solution
pre_solve = VGroup(*self.question[::2])
self.play(
ReplacementTransform(pre_solve, self.solve),
FadeOut(self.question[1]),
run_time = 1,
)
self.wait()
# Manipulate LHS
old_l_part, r_part = self.equation
new_l_part = ExpTower(order = self.highest_order+1, is_infinite = True)
new_l_part.match_height(old_l_part)
new_l_part.next_to(r_part, LEFT, aligned_edge = DOWN)
old_rect, new_rect = rects = [
CoverRectangle(part, text = "2")
for part in (old_l_part, new_l_part.get_exponent())
]
old_two, new_two = twos = [
rect.get_text_mob()
for rect in rects
]
self.play(DrawBorderThenFill(old_rect, run_time = 1))
self.wait()
self.play(
ReplacementTransform(old_l_part, new_l_part),
ReplacementTransform(old_rect, new_rect),
)
self.wait()
new_equation = VGroup(new_l_part, r_part, new_rect)
new_equation.generate_target()
new_equation.target.scale(0.8)
new_equation.target.shift(UP)
self.play(MoveToTarget(new_equation))
self.wait()
# A little bit clean-up
source_eq = VGroup(*[
mob.copy()
for mob in (new_l_part.get_base(), new_two, r_part[0], r_part[1])
])
source_eq.generate_target()
target_eq = TexMobject("x", "^2", "=", "2")
target_eq.scale(3).next_to(source_eq, DOWN, buff = 1)
for k, (old_part, new_part) in enumerate(zip(source_eq.target, target_eq)):
old_part.move_to(new_part)
if k == 1:
old_part.scale(0.5)
old_part.shift(RIGHT/4)
self.play(
FadeOut(new_rect),
MoveToTarget(source_eq),
)
self.wait()
# Reveal the final answer
result = TexMobject("x", "=", "\\sqrt", "2")
result.set_height(source_eq.get_height() * 0.7)
result.move_to(source_eq)
self.play(*[
ReplacementTransform(source_eq[m], result[n], path_arc = angle)
for m, n, angle in [(0, 0, 0), (1, 2, -TAU/3), (2, 1, 0), (3, 3, 0)]
])
self.wait()
qed = QEDSymbol()
qed.next_to(result, RIGHT, aligned_edge = DOWN, buff = 1.5)
self.play(FadeIn(qed))
self.wait()
