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InitialFiveChooseThreeExample of eop/combinations
This commit is contained in:
Grant Sanderson
parent
d585cc8edf
commit
1e8b10edb0
1 changed files with 325 additions and 119 deletions
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@ -110,7 +110,6 @@ class PascalsTraingle(VGroup):
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######################
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class ExperienceProblemSolver(PiCreatureScene):
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def construct(self):
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self.add_equation()
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@ -226,32 +225,38 @@ class ExperienceProblemSolver(PiCreatureScene):
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self.randy, self.jenny = randy, jenny
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return randy, jenny
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class Introduction(Scene):
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class InitialFiveChooseThreeExample(Scene):
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CONFIG = {
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"start_n" : 4,
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"n" : 5,
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"zero_color" : BLUE,
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"one_color" : PINK,
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}
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def construct(self):
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self.write_n_choose_k()
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self.show_binomial_coefficients()
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self.perform_shift()
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self.add_title()
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self.show_all_stacks()
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self.show_binomial_name()
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self.issolate_single_stack()
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self.count_chosen_stack()
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self.count_ways_to_fill_slots()
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self.walk_though_notation()
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self.emphasize_pattern_over_number()
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def write_n_choose_k(self):
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def add_title(self):
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symbol = TexMobject("n \\choose k")
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words = TextMobject("``n choose k''")
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group = VGroup(symbol, words)
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group.arrange_submobjects(RIGHT)
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group.to_edge(UP)
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self.play(
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FadeIn(symbol),
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Write(words)
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)
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self.dither()
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self.add(group)
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self.n_choose_k = symbol
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self.n_choose_k_words = words
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self.set_variables_as_attrs(n_choose_k_group = group)
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def show_all_stacks(self):
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n = self.n
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n_choose_k = self.n_choose_k
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n_choose_k_words = self.n_choose_k_words
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def show_binomial_coefficients(self):
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n = self.start_n
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n_choose_k, n_choose_k_words = self.n_choose_k_group
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binomials = VGroup(*[
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TexMobject("%d \\choose %d"%(n, k))
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for k in range(n+1)
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@ -265,137 +270,338 @@ class Introduction(Scene):
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equation.highlight(YELLOW)
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equation[1].highlight(WHITE)
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binomial_equations.add(equation)
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new_words = TextMobject("``Binomial coefficients''")
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stacks = get_stacks(
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TexMobject("x").highlight(BLUE),
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TexMobject("y").highlight(RED),
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n
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self.get_obj1(), self.get_obj2(), n,
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vertical_buff = SMALL_BUFF
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)
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stacks.to_edge(DOWN, buff = LARGE_BUFF)
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stacks.to_edge(DOWN, buff = MED_LARGE_BUFF)
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for stack, eq in zip(stacks, binomial_equations):
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eq.scale_to_fit_width(0.9*stack.get_width())
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eq.next_to(stack, UP)
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self.play(
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FadeIn(stacks, run_time = 2, submobject_mode = "lagged_start"),
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self.n_choose_k_group.to_edge, UP
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)
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new_words.move_to(n_choose_k_words, LEFT)
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self.play(Transform(n_choose_k_words, new_words))
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mover = VGroup()
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for eq in binomial_equations:
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point = VectorizedPoint(n_choose_k.get_center())
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self.play(ReplacementTransform(
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VGroup(n_choose_k, point, point).copy(),
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eq
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))
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self.dither()
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group = VGroup(n_choose_k, point, point).copy()
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group.target = eq
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mover.add(group)
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self.play(FadeIn(
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stacks,
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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self.play(LaggedStart(
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MoveToTarget, mover,
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run_time = 3,
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))
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self.remove(mover)
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self.add(binomial_equations)
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self.dither()
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self.set_variables_as_attrs(stacks, binomial_equations)
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def perform_shift(self):
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n = self.start_n
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to_fade = VGroup(
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self.n_choose_k_group,
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self.binomial_equations
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)
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stacks = self.stacks
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top_stacks = stacks.copy()
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top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
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def show_binomial_name(self):
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new_words = TextMobject("``Binomial coefficients''")
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new_words.move_to(self.n_choose_k_words, LEFT)
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line = Line(LEFT, RIGHT, color = WHITE)
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line.scale(SPACE_WIDTH)
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line.next_to(top_stacks, DOWN)
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self.play(Transform(self.n_choose_k_words, new_words))
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self.dither(2)
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x = TexMobject("x").highlight(BLUE)
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y = TexMobject("y").highlight(RED)
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add_x, add_y = [
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TextMobject("Prepend", "$%s$"%s).highlight_by_tex(s, color)
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for s, color in ("x", BLUE), ("y", RED)
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]
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add_x.to_corner(UP+LEFT)
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add_y.to_edge(LEFT).shift(MED_SMALL_BUFF*DOWN)
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def issolate_single_stack(self):
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stack = self.stacks[3]
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equation = self.binomial_equations[3]
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new_stacks, new_top_stacks = [
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get_stacks(x, y, n, fixed_start = var)
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for var in y, x
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]
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new_top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
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new_stacks.to_edge(DOWN)
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for s in new_stacks, new_top_stacks:
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s.start_terms = VGroup()
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for stack in s:
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for term in stack:
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s.start_terms.add(term[0])
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s_to_s_distance = \
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new_stacks[1].get_center()[0] - \
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new_stacks[0].get_center()[0]
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to_fade = VGroup(*self.stacks)
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to_fade.add(*self.binomial_equations)
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to_fade.add(self.n_choose_k, self.n_choose_k_words)
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to_fade.remove(stack, equation)
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self.play(
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FadeOut(to_fade),
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stacks.to_edge, DOWN,
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ReplacementTransform(stacks.copy(), top_stacks),
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equation.scale, 1.5, equation.get_bottom(),
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)
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self.play(ShowCreation(line))
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self.play(Write(add_x, run_time = 1))
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self.play(Transform(top_stacks, new_top_stacks))
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self.play(LaggedStart(
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Indicate, new_top_stacks.start_terms,
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rate_func = there_and_back,
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run_time = 1,
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remover = True
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))
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self.dither()
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self.play(Write(add_y, run_time = 1))
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self.play(Transform(stacks, new_stacks))
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self.play(LaggedStart(
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Indicate, new_stacks.start_terms,
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rate_func = there_and_back,
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run_time = 1,
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remover = True
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))
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for line in stack:
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ones = VGroup(*filter(
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lambda mob : "1" in mob.get_tex_string(),
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line
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))
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line.ones = ones
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self.play(LaggedStart(
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ApplyMethod, ones,
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lambda mob : (mob.highlight, YELLOW),
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rate_func = there_and_back,
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lag_ratio = 0.7,
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run_time = 1,
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))
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def count_chosen_stack(self):
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stack = self.stacks[3]
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for i, line in enumerate(stack):
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number = TexMobject(str(i+1))
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number.next_to(stack, LEFT)
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brace = Brace(VGroup(*stack[:i+1]), LEFT)
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number.next_to(brace, LEFT)
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line.save_state()
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line.highlight(YELLOW)
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self.add(number, brace)
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self.dither(0.25)
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self.remove(number, brace)
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line.restore()
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self.add(number, brace)
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self.dither()
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self.set_variables_as_attrs(
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stack_brace = brace,
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stack_count = number
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)
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def count_ways_to_fill_slots(self):
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lines = VGroup(*[Line(ORIGIN, 0.25*RIGHT) for x in range(5)])
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lines.arrange_submobjects(RIGHT)
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lines.next_to(self.stacks[3], LEFT, LARGE_BUFF, UP)
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self.play(ShowCreation(lines))
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count = 1
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for indices in it.combinations(range(5), 3):
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ones = VGroup(*[
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self.get_obj1().next_to(lines[i], UP)
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for i in indices
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])
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num = TexMobject(str(count))
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num.next_to(lines, DOWN)
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self.add(ones, num)
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self.dither(0.35)
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self.remove(ones, num)
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count += 1
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self.add(num, ones)
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self.dither()
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self.play(*map(FadeOut, [lines, num, ones]))
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def walk_though_notation(self):
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equation = self.binomial_equations[3]
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rect = SurroundingRectangle(equation[0])
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rect.highlight(WHITE)
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words = TextMobject("``5 choose 3''")
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words.next_to(rect, UP)
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self.play(Write(words))
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self.play(ShowCreation(rect))
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self.play(FadeOut(rect))
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self.dither(2)
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def emphasize_pattern_over_number(self):
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morty = Mortimer().flip()
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morty.to_corner(DOWN+LEFT)
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words = TextMobject("Remember the pattern \\\\ not the number")
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words.next_to(morty, UP)
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words.shift_onto_screen()
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self.play(FadeIn(morty))
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self.play(
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top_stacks.shift, s_to_s_distance*RIGHT/2,
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stacks.shift, s_to_s_distance*LEFT/2,
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morty.change, "speaking",
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Write(words, run_time = 2)
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)
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self.play(*map(FadeOut, [add_x, add_y, line]))
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self.play(
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Blink(morty),
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morty.change, "happy"
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)
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self.revert_to_original_skipping_status()
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last_ones = VGroup()
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last_ones.save_state()
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for x in range(2):
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for line in self.stacks[3]:
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ones = line.ones
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ones.save_state()
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self.play(
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ones.highlight, YELLOW,
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last_ones.restore,
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morty.look_at, ones,
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run_time = 0.25
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)
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last_ones = ones
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self.dither()
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point = VectorizedPoint()
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point.move_to(top_stacks[0].get_bottom())
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point.shift(s_to_s_distance*LEFT)
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top_stacks.add_to_back(point)
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####
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point = VectorizedPoint()
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point.move_to(stacks[-1].get_bottom())
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point.shift(s_to_s_distance*RIGHT)
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point.shift(MED_SMALL_BUFF*DOWN)
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stacks.add(point)
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def get_obj1(self):
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return TexMobject("1").highlight(self.one_color)
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for k, stack, top_stack in zip(it.count(), stacks, top_stacks):
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top_stack.generate_target()
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top_stack.target.next_to(stack, UP, MED_SMALL_BUFF)
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# term = TexMobject(
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# str(choose(n+1, k)),
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# "x^%d"%(n+1-k),
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# "y^%d"%k
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# )
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term = TexMobject(
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"{%d \\choose %d}"%(n+1, k),
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"=",
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str(choose(n+1, k))
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)
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term[0].scale(0.85, about_point = term[0].get_right())
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term[0].highlight(YELLOW)
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term[2].highlight(YELLOW)
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term.scale(0.85)
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term.next_to(top_stack.target, UP)
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def get_obj2(self):
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return TexMobject("0").highlight(self.zero_color)
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self.play(MoveToTarget(top_stack))
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self.play(Write(term))
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self.dither()
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# class Introduction(Scene):
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# CONFIG = {
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# "start_n" : 4,
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# }
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# def construct(self):
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# self.write_n_choose_k()
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# self.show_binomial_coefficients()
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# self.perform_shift()
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# def write_n_choose_k(self):
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# symbol = TexMobject("n \\choose k")
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# words = TextMobject("``n choose k''")
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# group = VGroup(symbol, words)
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# group.arrange_submobjects(RIGHT)
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# self.play(
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# FadeIn(symbol),
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# Write(words)
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# )
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# self.dither()
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# self.set_variables_as_attrs(n_choose_k_group = group)
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# def show_binomial_coefficients(self):
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# n = self.start_n
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# n_choose_k, n_choose_k_words = self.n_choose_k_group
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# binomials = VGroup(*[
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# TexMobject("%d \\choose %d"%(n, k))
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# for k in range(n+1)
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# ])
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# binomial_equations = VGroup()
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# for k, binomial in enumerate(binomials):
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# binomial.scale(0.75)
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# number = TexMobject(str(choose(n, k)))
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# equation = VGroup(binomial, TexMobject("="), number)
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# equation.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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# equation.highlight(YELLOW)
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# equation[1].highlight(WHITE)
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# binomial_equations.add(equation)
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# new_words = TextMobject("``Binomial coefficients''")
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# stacks = get_stacks(
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# TexMobject("x").highlight(BLUE),
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# TexMobject("y").highlight(RED),
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# n
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# )
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# stacks.to_edge(DOWN, buff = LARGE_BUFF)
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# for stack, eq in zip(stacks, binomial_equations):
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# eq.scale_to_fit_width(0.9*stack.get_width())
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# eq.next_to(stack, UP)
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# self.play(
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# FadeIn(stacks, run_time = 2, submobject_mode = "lagged_start"),
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# self.n_choose_k_group.to_edge, UP
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# )
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# new_words.move_to(n_choose_k_words, LEFT)
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# self.play(Transform(n_choose_k_words, new_words))
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# for eq in binomial_equations:
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# point = VectorizedPoint(n_choose_k.get_center())
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# self.play(ReplacementTransform(
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# VGroup(n_choose_k, point, point).copy(),
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# eq
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# ))
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# self.dither()
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# self.set_variables_as_attrs(stacks, binomial_equations)
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# def perform_shift(self):
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# n = self.start_n
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# to_fade = VGroup(
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# self.n_choose_k_group,
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# self.binomial_equations
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# )
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# stacks = self.stacks
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# top_stacks = stacks.copy()
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# top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
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# line = Line(LEFT, RIGHT, color = WHITE)
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# line.scale(SPACE_WIDTH)
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# line.next_to(top_stacks, DOWN)
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# x = TexMobject("x").highlight(BLUE)
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# y = TexMobject("y").highlight(RED)
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# add_x, add_y = [
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# TextMobject("Prepend", "$%s$"%s).highlight_by_tex(s, color)
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# for s, color in ("x", BLUE), ("y", RED)
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# ]
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# add_x.to_corner(UP+LEFT)
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# add_y.to_edge(LEFT).shift(MED_SMALL_BUFF*DOWN)
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# new_stacks, new_top_stacks = [
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# get_stacks(x, y, n, fixed_start = var)
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# for var in y, x
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# ]
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# new_top_stacks.to_edge(UP, buff = MED_SMALL_BUFF)
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# new_stacks.to_edge(DOWN)
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# for s in new_stacks, new_top_stacks:
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# s.start_terms = VGroup()
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# for stack in s:
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# for term in stack:
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# s.start_terms.add(term[0])
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# s_to_s_distance = \
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# new_stacks[1].get_center()[0] - \
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# new_stacks[0].get_center()[0]
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# self.play(
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# FadeOut(to_fade),
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# stacks.to_edge, DOWN,
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# ReplacementTransform(stacks.copy(), top_stacks),
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# )
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# self.play(ShowCreation(line))
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# self.play(Write(add_x, run_time = 1))
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# self.play(Transform(top_stacks, new_top_stacks))
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# self.play(LaggedStart(
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# Indicate, new_top_stacks.start_terms,
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# rate_func = there_and_back,
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# run_time = 1,
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# remover = True
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# ))
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# self.dither()
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# self.play(Write(add_y, run_time = 1))
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||||
# 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):
|
||||
CONFIG = {
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue