mirror of
https://github.com/3b1b/manim.git
synced 2025-08-05 16:49:03 +00:00
InitialFiveChooseThreeExample of eop/combinations
This commit is contained in:
Grant Sanderson
parent
d585cc8edf
commit
1e8b10edb0
1 changed files with 325 additions and 119 deletions
|
|
@ -110,7 +110,6 @@ class PascalsTraingle(VGroup):
|
||||||
|
|
||||||
######################
|
######################
|
||||||
|
|
||||||
|
|
||||||
class ExperienceProblemSolver(PiCreatureScene):
|
class ExperienceProblemSolver(PiCreatureScene):
|
||||||
def construct(self):
|
def construct(self):
|
||||||
self.add_equation()
|
self.add_equation()
|
||||||
|
|
@ -226,32 +225,38 @@ class ExperienceProblemSolver(PiCreatureScene):
|
||||||
self.randy, self.jenny = randy, jenny
|
self.randy, self.jenny = randy, jenny
|
||||||
return randy, jenny
|
return randy, jenny
|
||||||
|
|
||||||
class Introduction(Scene):
|
class InitialFiveChooseThreeExample(Scene):
|
||||||
CONFIG = {
|
CONFIG = {
|
||||||
"start_n" : 4,
|
"n" : 5,
|
||||||
|
"zero_color" : BLUE,
|
||||||
|
"one_color" : PINK,
|
||||||
}
|
}
|
||||||
def construct(self):
|
def construct(self):
|
||||||
self.write_n_choose_k()
|
self.add_title()
|
||||||
self.show_binomial_coefficients()
|
self.show_all_stacks()
|
||||||
self.perform_shift()
|
self.show_binomial_name()
|
||||||
|
self.issolate_single_stack()
|
||||||
|
self.count_chosen_stack()
|
||||||
|
self.count_ways_to_fill_slots()
|
||||||
|
self.walk_though_notation()
|
||||||
|
self.emphasize_pattern_over_number()
|
||||||
|
|
||||||
def write_n_choose_k(self):
|
def add_title(self):
|
||||||
symbol = TexMobject("n \\choose k")
|
symbol = TexMobject("n \\choose k")
|
||||||
words = TextMobject("``n choose k''")
|
words = TextMobject("``n choose k''")
|
||||||
group = VGroup(symbol, words)
|
group = VGroup(symbol, words)
|
||||||
group.arrange_submobjects(RIGHT)
|
group.arrange_submobjects(RIGHT)
|
||||||
|
group.to_edge(UP)
|
||||||
|
|
||||||
self.play(
|
self.add(group)
|
||||||
FadeIn(symbol),
|
self.n_choose_k = symbol
|
||||||
Write(words)
|
self.n_choose_k_words = words
|
||||||
)
|
|
||||||
self.dither()
|
|
||||||
|
|
||||||
self.set_variables_as_attrs(n_choose_k_group = group)
|
def show_all_stacks(self):
|
||||||
|
n = self.n
|
||||||
|
n_choose_k = self.n_choose_k
|
||||||
|
n_choose_k_words = self.n_choose_k_words
|
||||||
|
|
||||||
def show_binomial_coefficients(self):
|
|
||||||
n = self.start_n
|
|
||||||
n_choose_k, n_choose_k_words = self.n_choose_k_group
|
|
||||||
binomials = VGroup(*[
|
binomials = VGroup(*[
|
||||||
TexMobject("%d \\choose %d"%(n, k))
|
TexMobject("%d \\choose %d"%(n, k))
|
||||||
for k in range(n+1)
|
for k in range(n+1)
|
||||||
|
|
@ -265,138 +270,339 @@ class Introduction(Scene):
|
||||||
equation.highlight(YELLOW)
|
equation.highlight(YELLOW)
|
||||||
equation[1].highlight(WHITE)
|
equation[1].highlight(WHITE)
|
||||||
binomial_equations.add(equation)
|
binomial_equations.add(equation)
|
||||||
new_words = TextMobject("``Binomial coefficients''")
|
|
||||||
|
|
||||||
stacks = get_stacks(
|
stacks = get_stacks(
|
||||||
TexMobject("x").highlight(BLUE),
|
self.get_obj1(), self.get_obj2(), n,
|
||||||
TexMobject("y").highlight(RED),
|
vertical_buff = SMALL_BUFF
|
||||||
n
|
|
||||||
)
|
)
|
||||||
stacks.to_edge(DOWN, buff = LARGE_BUFF)
|
stacks.to_edge(DOWN, buff = MED_LARGE_BUFF)
|
||||||
for stack, eq in zip(stacks, binomial_equations):
|
for stack, eq in zip(stacks, binomial_equations):
|
||||||
eq.scale_to_fit_width(0.9*stack.get_width())
|
eq.scale_to_fit_width(0.9*stack.get_width())
|
||||||
eq.next_to(stack, UP)
|
eq.next_to(stack, UP)
|
||||||
|
|
||||||
self.play(
|
mover = VGroup()
|
||||||
FadeIn(stacks, run_time = 2, submobject_mode = "lagged_start"),
|
|
||||||
self.n_choose_k_group.to_edge, UP
|
|
||||||
)
|
|
||||||
new_words.move_to(n_choose_k_words, LEFT)
|
|
||||||
self.play(Transform(n_choose_k_words, new_words))
|
|
||||||
for eq in binomial_equations:
|
for eq in binomial_equations:
|
||||||
point = VectorizedPoint(n_choose_k.get_center())
|
point = VectorizedPoint(n_choose_k.get_center())
|
||||||
self.play(ReplacementTransform(
|
group = VGroup(n_choose_k, point, point).copy()
|
||||||
VGroup(n_choose_k, point, point).copy(),
|
group.target = eq
|
||||||
eq
|
mover.add(group)
|
||||||
|
|
||||||
|
self.play(FadeIn(
|
||||||
|
stacks,
|
||||||
|
run_time = 2,
|
||||||
|
submobject_mode = "lagged_start"
|
||||||
))
|
))
|
||||||
|
self.play(LaggedStart(
|
||||||
|
MoveToTarget, mover,
|
||||||
|
run_time = 3,
|
||||||
|
))
|
||||||
|
self.remove(mover)
|
||||||
|
self.add(binomial_equations)
|
||||||
self.dither()
|
self.dither()
|
||||||
|
|
||||||
self.set_variables_as_attrs(stacks, binomial_equations)
|
self.set_variables_as_attrs(stacks, binomial_equations)
|
||||||
|
|
||||||
def perform_shift(self):
|
def show_binomial_name(self):
|
||||||
n = self.start_n
|
new_words = TextMobject("``Binomial coefficients''")
|
||||||
to_fade = VGroup(
|
new_words.move_to(self.n_choose_k_words, LEFT)
|
||||||
self.n_choose_k_group,
|
|
||||||
self.binomial_equations
|
|
||||||
)
|
|
||||||
stacks = self.stacks
|
|
||||||
top_stacks = stacks.copy()
|
|
||||||
top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
|
|
||||||
|
|
||||||
line = Line(LEFT, RIGHT, color = WHITE)
|
self.play(Transform(self.n_choose_k_words, new_words))
|
||||||
line.scale(SPACE_WIDTH)
|
self.dither(2)
|
||||||
line.next_to(top_stacks, DOWN)
|
|
||||||
|
|
||||||
x = TexMobject("x").highlight(BLUE)
|
def issolate_single_stack(self):
|
||||||
y = TexMobject("y").highlight(RED)
|
stack = self.stacks[3]
|
||||||
add_x, add_y = [
|
equation = self.binomial_equations[3]
|
||||||
TextMobject("Prepend", "$%s$"%s).highlight_by_tex(s, color)
|
|
||||||
for s, color in ("x", BLUE), ("y", RED)
|
|
||||||
]
|
|
||||||
add_x.to_corner(UP+LEFT)
|
|
||||||
add_y.to_edge(LEFT).shift(MED_SMALL_BUFF*DOWN)
|
|
||||||
|
|
||||||
new_stacks, new_top_stacks = [
|
to_fade = VGroup(*self.stacks)
|
||||||
get_stacks(x, y, n, fixed_start = var)
|
to_fade.add(*self.binomial_equations)
|
||||||
for var in y, x
|
to_fade.add(self.n_choose_k, self.n_choose_k_words)
|
||||||
]
|
to_fade.remove(stack, equation)
|
||||||
new_top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
|
|
||||||
new_stacks.to_edge(DOWN)
|
|
||||||
for s in new_stacks, new_top_stacks:
|
|
||||||
s.start_terms = VGroup()
|
|
||||||
for stack in s:
|
|
||||||
for term in stack:
|
|
||||||
s.start_terms.add(term[0])
|
|
||||||
|
|
||||||
s_to_s_distance = \
|
|
||||||
new_stacks[1].get_center()[0] - \
|
|
||||||
new_stacks[0].get_center()[0]
|
|
||||||
|
|
||||||
self.play(
|
self.play(
|
||||||
FadeOut(to_fade),
|
FadeOut(to_fade),
|
||||||
stacks.to_edge, DOWN,
|
equation.scale, 1.5, equation.get_bottom(),
|
||||||
ReplacementTransform(stacks.copy(), top_stacks),
|
|
||||||
)
|
)
|
||||||
self.play(ShowCreation(line))
|
|
||||||
self.play(Write(add_x, run_time = 1))
|
|
||||||
self.play(Transform(top_stacks, new_top_stacks))
|
|
||||||
self.play(LaggedStart(
|
|
||||||
Indicate, new_top_stacks.start_terms,
|
|
||||||
rate_func = there_and_back,
|
|
||||||
run_time = 1,
|
|
||||||
remover = True
|
|
||||||
))
|
|
||||||
self.dither()
|
self.dither()
|
||||||
self.play(Write(add_y, run_time = 1))
|
for line in stack:
|
||||||
self.play(Transform(stacks, new_stacks))
|
ones = VGroup(*filter(
|
||||||
self.play(LaggedStart(
|
lambda mob : "1" in mob.get_tex_string(),
|
||||||
Indicate, new_stacks.start_terms,
|
line
|
||||||
rate_func = there_and_back,
|
|
||||||
run_time = 1,
|
|
||||||
remover = True
|
|
||||||
))
|
))
|
||||||
|
line.ones = ones
|
||||||
|
self.play(LaggedStart(
|
||||||
|
ApplyMethod, ones,
|
||||||
|
lambda mob : (mob.highlight, YELLOW),
|
||||||
|
rate_func = there_and_back,
|
||||||
|
lag_ratio = 0.7,
|
||||||
|
run_time = 1,
|
||||||
|
))
|
||||||
|
|
||||||
|
def count_chosen_stack(self):
|
||||||
|
stack = self.stacks[3]
|
||||||
|
for i, line in enumerate(stack):
|
||||||
|
number = TexMobject(str(i+1))
|
||||||
|
number.next_to(stack, LEFT)
|
||||||
|
brace = Brace(VGroup(*stack[:i+1]), LEFT)
|
||||||
|
number.next_to(brace, LEFT)
|
||||||
|
line.save_state()
|
||||||
|
line.highlight(YELLOW)
|
||||||
|
self.add(number, brace)
|
||||||
|
self.dither(0.25)
|
||||||
|
self.remove(number, brace)
|
||||||
|
line.restore()
|
||||||
|
self.add(number, brace)
|
||||||
self.dither()
|
self.dither()
|
||||||
|
|
||||||
|
self.set_variables_as_attrs(
|
||||||
|
stack_brace = brace,
|
||||||
|
stack_count = number
|
||||||
|
)
|
||||||
|
|
||||||
|
def count_ways_to_fill_slots(self):
|
||||||
|
lines = VGroup(*[Line(ORIGIN, 0.25*RIGHT) for x in range(5)])
|
||||||
|
lines.arrange_submobjects(RIGHT)
|
||||||
|
lines.next_to(self.stacks[3], LEFT, LARGE_BUFF, UP)
|
||||||
|
|
||||||
|
self.play(ShowCreation(lines))
|
||||||
|
count = 1
|
||||||
|
for indices in it.combinations(range(5), 3):
|
||||||
|
ones = VGroup(*[
|
||||||
|
self.get_obj1().next_to(lines[i], UP)
|
||||||
|
for i in indices
|
||||||
|
])
|
||||||
|
num = TexMobject(str(count))
|
||||||
|
num.next_to(lines, DOWN)
|
||||||
|
self.add(ones, num)
|
||||||
|
self.dither(0.35)
|
||||||
|
self.remove(ones, num)
|
||||||
|
count += 1
|
||||||
|
self.add(num, ones)
|
||||||
|
self.dither()
|
||||||
|
self.play(*map(FadeOut, [lines, num, ones]))
|
||||||
|
|
||||||
|
def walk_though_notation(self):
|
||||||
|
equation = self.binomial_equations[3]
|
||||||
|
rect = SurroundingRectangle(equation[0])
|
||||||
|
rect.highlight(WHITE)
|
||||||
|
words = TextMobject("``5 choose 3''")
|
||||||
|
words.next_to(rect, UP)
|
||||||
|
|
||||||
|
self.play(Write(words))
|
||||||
|
self.play(ShowCreation(rect))
|
||||||
|
self.play(FadeOut(rect))
|
||||||
|
self.dither(2)
|
||||||
|
|
||||||
|
def emphasize_pattern_over_number(self):
|
||||||
|
morty = Mortimer().flip()
|
||||||
|
morty.to_corner(DOWN+LEFT)
|
||||||
|
words = TextMobject("Remember the pattern \\\\ not the number")
|
||||||
|
words.next_to(morty, UP)
|
||||||
|
words.shift_onto_screen()
|
||||||
|
|
||||||
|
self.play(FadeIn(morty))
|
||||||
self.play(
|
self.play(
|
||||||
top_stacks.shift, s_to_s_distance*RIGHT/2,
|
morty.change, "speaking",
|
||||||
stacks.shift, s_to_s_distance*LEFT/2,
|
Write(words, run_time = 2)
|
||||||
)
|
)
|
||||||
self.play(*map(FadeOut, [add_x, add_y, line]))
|
self.play(
|
||||||
|
Blink(morty),
|
||||||
point = VectorizedPoint()
|
morty.change, "happy"
|
||||||
point.move_to(top_stacks[0].get_bottom())
|
|
||||||
point.shift(s_to_s_distance*LEFT)
|
|
||||||
top_stacks.add_to_back(point)
|
|
||||||
|
|
||||||
point = VectorizedPoint()
|
|
||||||
point.move_to(stacks[-1].get_bottom())
|
|
||||||
point.shift(s_to_s_distance*RIGHT)
|
|
||||||
point.shift(MED_SMALL_BUFF*DOWN)
|
|
||||||
stacks.add(point)
|
|
||||||
|
|
||||||
for k, stack, top_stack in zip(it.count(), stacks, top_stacks):
|
|
||||||
top_stack.generate_target()
|
|
||||||
top_stack.target.next_to(stack, UP, MED_SMALL_BUFF)
|
|
||||||
# term = TexMobject(
|
|
||||||
# str(choose(n+1, k)),
|
|
||||||
# "x^%d"%(n+1-k),
|
|
||||||
# "y^%d"%k
|
|
||||||
# )
|
|
||||||
term = TexMobject(
|
|
||||||
"{%d \\choose %d}"%(n+1, k),
|
|
||||||
"=",
|
|
||||||
str(choose(n+1, k))
|
|
||||||
)
|
)
|
||||||
term[0].scale(0.85, about_point = term[0].get_right())
|
self.revert_to_original_skipping_status()
|
||||||
term[0].highlight(YELLOW)
|
last_ones = VGroup()
|
||||||
term[2].highlight(YELLOW)
|
last_ones.save_state()
|
||||||
term.scale(0.85)
|
for x in range(2):
|
||||||
term.next_to(top_stack.target, UP)
|
for line in self.stacks[3]:
|
||||||
|
ones = line.ones
|
||||||
self.play(MoveToTarget(top_stack))
|
ones.save_state()
|
||||||
self.play(Write(term))
|
self.play(
|
||||||
|
ones.highlight, YELLOW,
|
||||||
|
last_ones.restore,
|
||||||
|
morty.look_at, ones,
|
||||||
|
run_time = 0.25
|
||||||
|
)
|
||||||
|
last_ones = ones
|
||||||
self.dither()
|
self.dither()
|
||||||
|
|
||||||
|
####
|
||||||
|
|
||||||
|
def get_obj1(self):
|
||||||
|
return TexMobject("1").highlight(self.one_color)
|
||||||
|
|
||||||
|
def get_obj2(self):
|
||||||
|
return TexMobject("0").highlight(self.zero_color)
|
||||||
|
|
||||||
|
# class Introduction(Scene):
|
||||||
|
# CONFIG = {
|
||||||
|
# "start_n" : 4,
|
||||||
|
# }
|
||||||
|
# def construct(self):
|
||||||
|
# self.write_n_choose_k()
|
||||||
|
# self.show_binomial_coefficients()
|
||||||
|
# self.perform_shift()
|
||||||
|
|
||||||
|
# def write_n_choose_k(self):
|
||||||
|
# symbol = TexMobject("n \\choose k")
|
||||||
|
# words = TextMobject("``n choose k''")
|
||||||
|
# group = VGroup(symbol, words)
|
||||||
|
# group.arrange_submobjects(RIGHT)
|
||||||
|
|
||||||
|
# self.play(
|
||||||
|
# FadeIn(symbol),
|
||||||
|
# Write(words)
|
||||||
|
# )
|
||||||
|
# self.dither()
|
||||||
|
|
||||||
|
# self.set_variables_as_attrs(n_choose_k_group = group)
|
||||||
|
|
||||||
|
# def show_binomial_coefficients(self):
|
||||||
|
# n = self.start_n
|
||||||
|
# n_choose_k, n_choose_k_words = self.n_choose_k_group
|
||||||
|
# binomials = VGroup(*[
|
||||||
|
# TexMobject("%d \\choose %d"%(n, k))
|
||||||
|
# for k in range(n+1)
|
||||||
|
# ])
|
||||||
|
# binomial_equations = VGroup()
|
||||||
|
# for k, binomial in enumerate(binomials):
|
||||||
|
# binomial.scale(0.75)
|
||||||
|
# number = TexMobject(str(choose(n, k)))
|
||||||
|
# equation = VGroup(binomial, TexMobject("="), number)
|
||||||
|
# equation.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
|
||||||
|
# equation.highlight(YELLOW)
|
||||||
|
# equation[1].highlight(WHITE)
|
||||||
|
# binomial_equations.add(equation)
|
||||||
|
# new_words = TextMobject("``Binomial coefficients''")
|
||||||
|
|
||||||
|
# stacks = get_stacks(
|
||||||
|
# TexMobject("x").highlight(BLUE),
|
||||||
|
# TexMobject("y").highlight(RED),
|
||||||
|
# n
|
||||||
|
# )
|
||||||
|
# stacks.to_edge(DOWN, buff = LARGE_BUFF)
|
||||||
|
# for stack, eq in zip(stacks, binomial_equations):
|
||||||
|
# eq.scale_to_fit_width(0.9*stack.get_width())
|
||||||
|
# eq.next_to(stack, UP)
|
||||||
|
|
||||||
|
# self.play(
|
||||||
|
# FadeIn(stacks, run_time = 2, submobject_mode = "lagged_start"),
|
||||||
|
# self.n_choose_k_group.to_edge, UP
|
||||||
|
# )
|
||||||
|
# new_words.move_to(n_choose_k_words, LEFT)
|
||||||
|
# self.play(Transform(n_choose_k_words, new_words))
|
||||||
|
# for eq in binomial_equations:
|
||||||
|
# point = VectorizedPoint(n_choose_k.get_center())
|
||||||
|
# self.play(ReplacementTransform(
|
||||||
|
# VGroup(n_choose_k, point, point).copy(),
|
||||||
|
# eq
|
||||||
|
# ))
|
||||||
|
# self.dither()
|
||||||
|
|
||||||
|
# self.set_variables_as_attrs(stacks, binomial_equations)
|
||||||
|
|
||||||
|
# def perform_shift(self):
|
||||||
|
# n = self.start_n
|
||||||
|
# to_fade = VGroup(
|
||||||
|
# self.n_choose_k_group,
|
||||||
|
# self.binomial_equations
|
||||||
|
# )
|
||||||
|
# stacks = self.stacks
|
||||||
|
# top_stacks = stacks.copy()
|
||||||
|
# top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||||
|
|
||||||
|
# line = Line(LEFT, RIGHT, color = WHITE)
|
||||||
|
# line.scale(SPACE_WIDTH)
|
||||||
|
# line.next_to(top_stacks, DOWN)
|
||||||
|
|
||||||
|
# x = TexMobject("x").highlight(BLUE)
|
||||||
|
# y = TexMobject("y").highlight(RED)
|
||||||
|
# add_x, add_y = [
|
||||||
|
# TextMobject("Prepend", "$%s$"%s).highlight_by_tex(s, color)
|
||||||
|
# for s, color in ("x", BLUE), ("y", RED)
|
||||||
|
# ]
|
||||||
|
# add_x.to_corner(UP+LEFT)
|
||||||
|
# add_y.to_edge(LEFT).shift(MED_SMALL_BUFF*DOWN)
|
||||||
|
|
||||||
|
# new_stacks, new_top_stacks = [
|
||||||
|
# get_stacks(x, y, n, fixed_start = var)
|
||||||
|
# for var in y, x
|
||||||
|
# ]
|
||||||
|
# new_top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||||
|
# new_stacks.to_edge(DOWN)
|
||||||
|
# for s in new_stacks, new_top_stacks:
|
||||||
|
# s.start_terms = VGroup()
|
||||||
|
# for stack in s:
|
||||||
|
# for term in stack:
|
||||||
|
# s.start_terms.add(term[0])
|
||||||
|
|
||||||
|
# s_to_s_distance = \
|
||||||
|
# new_stacks[1].get_center()[0] - \
|
||||||
|
# new_stacks[0].get_center()[0]
|
||||||
|
|
||||||
|
# self.play(
|
||||||
|
# FadeOut(to_fade),
|
||||||
|
# stacks.to_edge, DOWN,
|
||||||
|
# ReplacementTransform(stacks.copy(), top_stacks),
|
||||||
|
# )
|
||||||
|
# self.play(ShowCreation(line))
|
||||||
|
# self.play(Write(add_x, run_time = 1))
|
||||||
|
# self.play(Transform(top_stacks, new_top_stacks))
|
||||||
|
# self.play(LaggedStart(
|
||||||
|
# Indicate, new_top_stacks.start_terms,
|
||||||
|
# rate_func = there_and_back,
|
||||||
|
# run_time = 1,
|
||||||
|
# remover = True
|
||||||
|
# ))
|
||||||
|
# self.dither()
|
||||||
|
# self.play(Write(add_y, run_time = 1))
|
||||||
|
# self.play(Transform(stacks, new_stacks))
|
||||||
|
# self.play(LaggedStart(
|
||||||
|
# Indicate, new_stacks.start_terms,
|
||||||
|
# rate_func = there_and_back,
|
||||||
|
# run_time = 1,
|
||||||
|
# remover = True
|
||||||
|
# ))
|
||||||
|
# self.dither()
|
||||||
|
|
||||||
|
# self.play(
|
||||||
|
# top_stacks.shift, s_to_s_distance*RIGHT/2,
|
||||||
|
# stacks.shift, s_to_s_distance*LEFT/2,
|
||||||
|
# )
|
||||||
|
# self.play(*map(FadeOut, [add_x, add_y, line]))
|
||||||
|
|
||||||
|
# point = VectorizedPoint()
|
||||||
|
# point.move_to(top_stacks[0].get_bottom())
|
||||||
|
# point.shift(s_to_s_distance*LEFT)
|
||||||
|
# top_stacks.add_to_back(point)
|
||||||
|
|
||||||
|
# point = VectorizedPoint()
|
||||||
|
# point.move_to(stacks[-1].get_bottom())
|
||||||
|
# point.shift(s_to_s_distance*RIGHT)
|
||||||
|
# point.shift(MED_SMALL_BUFF*DOWN)
|
||||||
|
# stacks.add(point)
|
||||||
|
|
||||||
|
# for k, stack, top_stack in zip(it.count(), stacks, top_stacks):
|
||||||
|
# top_stack.generate_target()
|
||||||
|
# top_stack.target.next_to(stack, UP, MED_SMALL_BUFF)
|
||||||
|
# # term = TexMobject(
|
||||||
|
# # str(choose(n+1, k)),
|
||||||
|
# # "x^%d"%(n+1-k),
|
||||||
|
# # "y^%d"%k
|
||||||
|
# # )
|
||||||
|
# term = TexMobject(
|
||||||
|
# "{%d \\choose %d}"%(n+1, k),
|
||||||
|
# "=",
|
||||||
|
# str(choose(n+1, k))
|
||||||
|
# )
|
||||||
|
# term[0].scale(0.85, about_point = term[0].get_right())
|
||||||
|
# term[0].highlight(YELLOW)
|
||||||
|
# term[2].highlight(YELLOW)
|
||||||
|
# term.scale(0.85)
|
||||||
|
# term.next_to(top_stack.target, UP)
|
||||||
|
|
||||||
|
# self.play(MoveToTarget(top_stack))
|
||||||
|
# self.play(Write(term))
|
||||||
|
# self.dither()
|
||||||
|
|
||||||
class DifferentWaysToThinkAboutNChooseK(Scene):
|
class DifferentWaysToThinkAboutNChooseK(Scene):
|
||||||
CONFIG = {
|
CONFIG = {
|
||||||
"n" : 5,
|
"n" : 5,
|
||||||
|
|
|
||||||
Loading…
Add table
Reference in a new issue