mirror of
https://github.com/3b1b/manim.git
synced 2026-04-26 03:00:23 -04:00
Preliminary end to eop/combinations animations
This commit is contained in:
Grant Sanderson
@@ -2997,7 +2997,7 @@ class NineChooseFourExample(HowToComputeNChooseK):
|
||||
self.play(FadeIn(line, run_time = 0.1))
|
||||
self.dither(2)
|
||||
self.play(FadeOut(
|
||||
stacks, submobject_mode = "lagged_start", run_time = 2
|
||||
stack, submobject_mode = "lagged_start", run_time = 2
|
||||
))
|
||||
|
||||
def choose_k_people(self):
|
||||
@@ -3047,6 +3047,7 @@ class NineChooseFourExample(HowToComputeNChooseK):
|
||||
|
||||
def finish_computation(self):
|
||||
equals = TexMobject("=")
|
||||
equals.shift(2*LEFT)
|
||||
fraction = self.fraction
|
||||
six = fraction[0][0][3]
|
||||
eight = fraction[0][0][1]
|
||||
@@ -3087,6 +3088,340 @@ class NineChooseFourExample(HowToComputeNChooseK):
|
||||
self.play(Write(rhs))
|
||||
self.dither()
|
||||
|
||||
class WeirdKindOfCancelation(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
fraction = TexMobject(
|
||||
"{5 \\cdot 4 \\cdot 3",
|
||||
"\\text{ ordered}", "\\text{ triplets}",
|
||||
"\\over",
|
||||
"1 \\cdot 2 \\cdot 3", "\\text{ orderings \\;\\qquad}}"
|
||||
)
|
||||
top_numbers, ordered, triplets, frac_line, bottom_numbers, orderings = fraction
|
||||
for mob in top_numbers, bottom_numbers:
|
||||
mob.gradient_highlight(GREEN, YELLOW)
|
||||
fraction.next_to(self.teacher, UP+LEFT)
|
||||
|
||||
names = VGroup(*map(TextMobject, [
|
||||
"Ali", "Ben", "Cam", "Denis", "Evan"
|
||||
]))
|
||||
names.arrange_submobjects(RIGHT)
|
||||
names.to_edge(UP, buff = LARGE_BUFF)
|
||||
names.save_state()
|
||||
lb, rb = braces = TexMobject("\\{\\}")
|
||||
braces.scale(2)
|
||||
lb.next_to(names, LEFT, SMALL_BUFF)
|
||||
rb.next_to(names, RIGHT, SMALL_BUFF)
|
||||
|
||||
chosen_names = VGroup(*random.sample(names, 3))
|
||||
chosen_names.generate_target()
|
||||
chosen_names.target.arrange_submobjects(RIGHT)
|
||||
chosen_names.target.next_to(top_numbers, UP, MED_LARGE_BUFF)
|
||||
for name, name_target in zip(chosen_names, chosen_names.target):
|
||||
name.target = name_target
|
||||
|
||||
self.teacher_says("It's like unit cancellation.")
|
||||
self.change_student_modes(*["confused"]*3)
|
||||
self.play(
|
||||
RemovePiCreatureBubble(
|
||||
self.teacher, target_mode = "raise_right_hand"
|
||||
),
|
||||
LaggedStart(FadeIn, fraction, run_time = 1),
|
||||
FadeIn(braces),
|
||||
LaggedStart(FadeIn, names)
|
||||
)
|
||||
self.change_student_modes(
|
||||
*["pondering"]*3,
|
||||
look_at_arg = fraction
|
||||
)
|
||||
|
||||
#Go through numerators
|
||||
for num, name in zip(top_numbers[::2], chosen_names):
|
||||
rect = SurroundingRectangle(num)
|
||||
name.target.highlight(num.get_color())
|
||||
self.play(
|
||||
ShowCreationThenDestruction(rect),
|
||||
MoveToTarget(name),
|
||||
)
|
||||
self.dither(2)
|
||||
|
||||
#Go through denominators
|
||||
permutations = list(it.permutations(range(3)))[1:]
|
||||
|
||||
self.shuffle(chosen_names, permutations[:2])
|
||||
self.play(LaggedStart(
|
||||
ShowCreationThenDestruction,
|
||||
VGroup(*map(SurroundingRectangle, bottom_numbers[::2]))
|
||||
))
|
||||
self.shuffle(chosen_names, permutations[2:])
|
||||
self.dither()
|
||||
|
||||
#Show cancelation
|
||||
top_cross = Cross(ordered)
|
||||
bottom_cross = Cross(orderings)
|
||||
|
||||
self.play(
|
||||
ShowCreation(top_cross),
|
||||
self.teacher.change, "maybe",
|
||||
)
|
||||
self.play(ShowCreation(bottom_cross))
|
||||
self.change_student_modes(*["happy"]*3)
|
||||
self.dither(3)
|
||||
|
||||
###
|
||||
|
||||
def shuffle(self, mobject, permutations):
|
||||
for permutation in permutations:
|
||||
self.play(*[
|
||||
ApplyMethod(
|
||||
m.move_to, mobject[i].get_center(),
|
||||
path_arc = np.pi,
|
||||
)
|
||||
for i, m in zip(permutation, mobject)
|
||||
])
|
||||
|
||||
class SumsToPowerOf2(Scene):
|
||||
CONFIG = {
|
||||
"n" : 5,
|
||||
"alt_n" : 7,
|
||||
}
|
||||
def construct(self):
|
||||
self.setup_stacks()
|
||||
self.count_32()
|
||||
self.show_sum_as_n_choose_k()
|
||||
self.show_alternate_sum()
|
||||
|
||||
def setup_stacks(self):
|
||||
stacks = get_stacks(
|
||||
TexMobject("1").highlight(PINK),
|
||||
TexMobject("0").highlight(BLUE),
|
||||
n = self.n,
|
||||
vertical_buff = SMALL_BUFF,
|
||||
)
|
||||
stacks.to_corner(DOWN+LEFT)
|
||||
numbers = VGroup(*[
|
||||
TexMobject(str(choose(self.n, k)))
|
||||
for k in range(self.n + 1)
|
||||
])
|
||||
for number, stack in zip(numbers, stacks):
|
||||
number.next_to(stack, UP)
|
||||
|
||||
self.play(
|
||||
LaggedStart(FadeIn, stacks),
|
||||
LaggedStart(FadeIn, numbers),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.set_variables_as_attrs(stacks, numbers)
|
||||
|
||||
def count_32(self):
|
||||
lines = VGroup(*it.chain(*self.stacks))
|
||||
rhs = TexMobject("= 2^{%d}"%self.n)
|
||||
rhs.to_edge(UP, buff = LARGE_BUFF)
|
||||
rhs.to_edge(RIGHT, buff = 2)
|
||||
|
||||
numbers = self.numbers.copy()
|
||||
numbers.target = VGroup(*[
|
||||
TexMobject("{%d \\choose %d}"%(self.n, k))
|
||||
for k in range(self.n + 1)
|
||||
])
|
||||
plusses = VGroup(*[TexMobject("+") for n in numbers])
|
||||
plusses.remove(plusses[-1])
|
||||
plusses.add(TexMobject("="))
|
||||
sum_group = VGroup(*it.chain(*zip(
|
||||
numbers.target, plusses
|
||||
)))
|
||||
sum_group.arrange_submobjects(RIGHT, SMALL_BUFF)
|
||||
sum_group.next_to(numbers, UP, LARGE_BUFF)
|
||||
sum_group.shift(MED_LARGE_BUFF*RIGHT)
|
||||
|
||||
for i, line in zip(it.count(1), lines):
|
||||
line_copy = line.copy().highlight(YELLOW)
|
||||
number = Integer(i)
|
||||
number.scale(1.5)
|
||||
number.to_edge(UP)
|
||||
VGroup(number, line_copy).highlight(YELLOW)
|
||||
self.add(line_copy, number)
|
||||
self.dither(0.15)
|
||||
self.remove(line_copy, number)
|
||||
sum_result = number
|
||||
self.add(sum_result)
|
||||
self.dither()
|
||||
|
||||
sum_result.target = TexMobject(str(2**self.n))
|
||||
sum_result.target.highlight(sum_result.get_color())
|
||||
sum_result.target.next_to(sum_group, RIGHT)
|
||||
rhs.next_to(sum_result.target, RIGHT, aligned_edge = DOWN)
|
||||
self.play(
|
||||
MoveToTarget(sum_result),
|
||||
MoveToTarget(numbers),
|
||||
Write(plusses),
|
||||
Write(rhs),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.set_variables_as_attrs(
|
||||
plusses, sum_result, rhs,
|
||||
n_choose_k_terms = numbers
|
||||
)
|
||||
|
||||
def show_sum_as_n_choose_k(self):
|
||||
numbers = self.numbers
|
||||
plusses = self.plusses
|
||||
n_choose_k_terms = self.n_choose_k_terms
|
||||
rhs = VGroup(self.sum_result, self.rhs)
|
||||
n = self.n
|
||||
|
||||
|
||||
fractions = self.get_fractions(n)
|
||||
plusses.generate_target()
|
||||
sum_group = VGroup(*it.chain(*zip(
|
||||
fractions, plusses.target
|
||||
)))
|
||||
sum_group.arrange_submobjects(RIGHT, buff = 2*SMALL_BUFF)
|
||||
sum_group.next_to(rhs, LEFT)
|
||||
sum_group.shift(0.5*SMALL_BUFF*DOWN)
|
||||
|
||||
self.play(
|
||||
Transform(n_choose_k_terms, fractions),
|
||||
MoveToTarget(plusses),
|
||||
submobject_mode = "lagged_start",
|
||||
run_time = 2
|
||||
)
|
||||
self.dither()
|
||||
|
||||
def show_alternate_sum(self):
|
||||
fractions = self.get_fractions(self.alt_n)
|
||||
fractions.remove(*fractions[4:-1])
|
||||
fractions.submobjects.insert(4, TexMobject("\\cdots"))
|
||||
plusses = VGroup(*[
|
||||
TexMobject("+") for f in fractions[:-1]
|
||||
] + [TexMobject("=")])
|
||||
sum_group = VGroup(*it.chain(*zip(
|
||||
fractions, plusses
|
||||
)))
|
||||
sum_group.arrange_submobjects(RIGHT)
|
||||
sum_group.next_to(
|
||||
self.n_choose_k_terms, DOWN,
|
||||
aligned_edge = LEFT, buff = LARGE_BUFF
|
||||
)
|
||||
sum_group.shift(SMALL_BUFF*DOWN)
|
||||
rhs = TexMobject(
|
||||
str(2**self.alt_n),
|
||||
"=", "2^{%d}"%(self.alt_n)
|
||||
)
|
||||
rhs[0].highlight(YELLOW)
|
||||
rhs.next_to(sum_group, RIGHT)
|
||||
|
||||
self.play(
|
||||
LaggedStart(FadeOut, self.stacks),
|
||||
LaggedStart(FadeOut, self.numbers),
|
||||
LaggedStart(FadeIn, sum_group),
|
||||
)
|
||||
self.play(LaggedStart(FadeIn, rhs))
|
||||
self.dither(2)
|
||||
|
||||
####
|
||||
|
||||
def get_fractions(self, n):
|
||||
fractions = VGroup(TexMobject("1"))
|
||||
dot_str = " \\!\\cdot\\! "
|
||||
for k in range(1, n+1):
|
||||
ts = str(n)
|
||||
bs = "1"
|
||||
for i in range(1, k):
|
||||
ts += dot_str + str(n-i)
|
||||
bs += dot_str + str(i+1)
|
||||
fraction = TexMobject("{%s \\over %s}"%(ts, bs))
|
||||
fractions.add(fraction)
|
||||
return fractions
|
||||
|
||||
class AskWhyTheyAreCalledBinomial(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
example_binomials = VGroup(*[
|
||||
TexMobject("(x+y)^%d"%d)
|
||||
for d in range(2, 7)
|
||||
])
|
||||
example_binomials.arrange_submobjects(UP)
|
||||
example_binomials.next_to(
|
||||
self.teacher.get_corner(UP+LEFT), UP
|
||||
)
|
||||
|
||||
pascals = PascalsTraingle(n_rows = 6)
|
||||
pascals.scale_to_fit_height(3)
|
||||
pascals.to_corner(UP+LEFT, buff = MED_SMALL_BUFF)
|
||||
pascals.gradient_highlight(BLUE, YELLOW)
|
||||
|
||||
binomial_word = TextMobject(
|
||||
"Bi", "nomials",
|
||||
arg_separator = "",
|
||||
)
|
||||
binomial_word.highlight_by_tex("Bi", YELLOW)
|
||||
binomial_word.highlight_by_tex("nomials", WHITE)
|
||||
binomial_word.next_to(example_binomials, LEFT, buff = 1.5)
|
||||
arrows = VGroup(*[
|
||||
Arrow(binomial_word.get_right(), binom.get_left())
|
||||
for binom in example_binomials
|
||||
])
|
||||
arrows.highlight(BLUE)
|
||||
|
||||
two_variables = TextMobject("Two", "variables")
|
||||
two_variables.next_to(binomial_word, DOWN)
|
||||
two_variables.shift(SMALL_BUFF*LEFT)
|
||||
for tv, bw in zip(two_variables, binomial_word):
|
||||
tv.highlight(bw.get_color())
|
||||
|
||||
self.student_says(
|
||||
"Why are they called \\\\ ``binomial coefficients''?"
|
||||
)
|
||||
self.play(LaggedStart(FadeIn, pascals))
|
||||
self.dither()
|
||||
self.play(
|
||||
FadeIn(example_binomials[0]),
|
||||
RemovePiCreatureBubble(self.students[1]),
|
||||
self.teacher.change, "raise_right_hand",
|
||||
)
|
||||
moving_binom = example_binomials[0].copy()
|
||||
for binom in example_binomials[1:]:
|
||||
self.play(Transform(moving_binom, binom))
|
||||
self.add(binom)
|
||||
self.dither()
|
||||
|
||||
#Name themn
|
||||
self.play(
|
||||
Write(binomial_word),
|
||||
LaggedStart(GrowArrow, arrows)
|
||||
)
|
||||
self.change_student_modes(*["pondering"]*3)
|
||||
self.play(Write(two_variables))
|
||||
self.dither(2)
|
||||
|
||||
class NextVideo(Scene):
|
||||
def construct(self):
|
||||
title = TextMobject("Next video: Binomial distribution")
|
||||
title.to_edge(UP)
|
||||
screen = ScreenRectangle(height = 6)
|
||||
screen.next_to(title, DOWN)
|
||||
|
||||
self.play(
|
||||
Write(title),
|
||||
ShowCreation(screen)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user