mirror of
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Up through PointOutSimplicityOfFormula of eop/independence
This commit is contained in:
Grant Sanderson
parent
029c4f3c1f
commit
ceb7f467ad
4 changed files with 802 additions and 9 deletions
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@ -28,6 +28,8 @@ from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from scene.scene import ProgressDisplay
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#revert_to_original_skipping_status
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def get_binomial_distribution(n, p):
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@ -2027,14 +2029,801 @@ class CorrelationsWith35Percent(ThousandPossibleQuizzes):
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)
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self.dither()
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class NameBinomial(Scene):
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CONFIG = {
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"flip_indices" : [1, 2, 4, 5, 7, 9],
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}
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def construct(self):
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self.name_distribution()
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self.add_quiz_questions()
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self.change_to_gender()
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self.change_bar_chart_for_gender_example()
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self.point_out_example_input()
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self.write_probability_of_girl()
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self.think_through_probabilities()
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def name_distribution(self):
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ns = [3, 10]
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p = 0.65
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charts = VGroup()
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for n in ns:
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dist = get_binomial_distribution(n, p)
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values = map(dist, range(n+1))
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chart = BarChart(values, bar_names = range(n+1))
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chart.to_edge(LEFT)
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charts.add(chart)
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probability = TexMobject(
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"P(", "\\checkmark", ")", "=", str(p)
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)
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probability.highlight_by_tex("checkmark", GREEN)
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probability.move_to(charts, UP)
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title = TextMobject("``Binomial distribution''")
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title.next_to(charts, UP)
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title.to_edge(UP)
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formula = TexMobject(
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"P(X=", "k", ")=",
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"{n \\choose k}",
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"p", "^k",
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"(1-", "p", ")", "^{n-", "k}",
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arg_separator = ""
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)
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formula.highlight_by_tex("p", YELLOW)
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formula.highlight_by_tex("k", GREEN)
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choose_part = formula.get_part_by_tex("choose")
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choose_part.highlight(WHITE)
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choose_part[-2].highlight(GREEN)
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formula.to_corner(UP+RIGHT)
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self.add(charts[0], probability)
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self.dither()
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self.play(Write(title))
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self.dither()
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self.play(ReplacementTransform(*charts))
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self.play(Write(formula))
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self.dither()
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self.play(
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formula.scale, 0.7,
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formula.next_to, charts, DOWN,
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)
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self.chart = charts[1]
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self.probability = probability
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self.title = title
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self.formula = formula
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def add_quiz_questions(self):
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n = 10
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checkmarks = VGroup(*[
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TexMobject("\\checkmark").highlight(GREEN)
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for x in range(n)
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])
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checkmarks.arrange_submobjects(DOWN, buff = 0.3)
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crosses = VGroup()
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arrows = VGroup()
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for checkmark in checkmarks:
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cross = TexMobject("\\times")
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cross.highlight(RED)
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cross.next_to(checkmark, RIGHT, LARGE_BUFF)
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crosses.add(cross)
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arrow = Arrow(
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checkmark, cross,
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tip_length = 0.15,
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color = WHITE
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)
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arrows.add(arrow)
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full_group = VGroup(checkmarks, crosses, arrows)
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full_group.center().to_corner(UP + RIGHT, buff = MED_LARGE_BUFF)
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flip_indices = self.flip_indices
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flipped_arrows, faded_crosses, full_checks = [
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VGroup(*[group[i] for i in flip_indices])
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for group in arrows, crosses, checkmarks
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]
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faded_checkmarks = VGroup(*filter(
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lambda m : m not in full_checks,
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checkmarks
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))
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self.play(*[
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LaggedStart(
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Write, mob,
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run_time = 3,
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lag_ratio = 0.3
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)
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for mob in full_group
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])
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self.dither()
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self.play(
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LaggedStart(
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Rotate, flipped_arrows,
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angle = np.pi,
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in_place = True,
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run_time = 2,
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lag_ratio = 0.5
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),
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faded_crosses.set_fill, None, 0.5,
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faded_checkmarks.set_fill, None, 0.5,
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)
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self.dither()
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self.checkmarks = checkmarks
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self.crosses = crosses
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self.arrows = arrows
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def change_to_gender(self):
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flip_indices = self.flip_indices
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male = self.get_male()
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female = self.get_female()
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girls, boys = [
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VGroup(*[
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template.copy().move_to(mob)
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for mob in group
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])
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for template, group in [
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(female, self.checkmarks), (male, self.crosses)
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]
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]
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for i in range(len(boys)):
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mob = boys[i] if i in flip_indices else girls[i]
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mob.set_fill(opacity = 0.5)
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brace = Brace(girls, LEFT)
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words = brace.get_text("$n$ children")
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self.play(
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GrowFromCenter(brace),
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FadeIn(words)
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)
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for m1, m2 in (self.checkmarks, girls), (self.crosses, boys):
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self.play(ReplacementTransform(
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m1, m2,
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submobject_mode = "lagged_start"
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))
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self.dither()
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self.boys = boys
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self.girls = girls
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self.children_brace = brace
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self.n_children_words = words
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def change_bar_chart_for_gender_example(self):
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checkmark = self.probability.get_part_by_tex("checkmark")
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p_mob = self.probability[-1]
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female = self.get_female()
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female.move_to(checkmark)
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new_p_mob = TexMobject("0.49")
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new_p_mob.move_to(p_mob, LEFT)
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dist = get_binomial_distribution(10, 0.49)
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values = map(dist, range(11))
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self.play(
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Transform(checkmark, female),
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Transform(p_mob, new_p_mob),
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)
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self.play(self.chart.change_bar_values, values)
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self.dither()
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def point_out_example_input(self):
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boy_girl_groups = VGroup(*[
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VGroup(boy, girl)
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for boy, girl in zip(self.boys, self.girls)
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])
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girl_rects = VGroup(*[
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SurroundingRectangle(
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boy_girl_groups[i],
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color = MAROON_B,
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buff = SMALL_BUFF,
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)
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for i in sorted(self.flip_indices)
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])
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chart = self.chart
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n_girls = len(girl_rects)
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chart_rect = SurroundingRectangle(
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VGroup(chart.bars[n_girls], chart.bar_labels[n_girls]),
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buff = SMALL_BUFF
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)
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self.play(ShowCreation(chart_rect))
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self.play(LaggedStart(
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ShowCreation, girl_rects,
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run_time = 2,
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lag_ratio = 0.5,
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))
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self.dither()
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self.chart_rect = chart_rect
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self.girl_rects = girl_rects
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def write_probability_of_girl(self):
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probability = self.probability
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probability_copies = VGroup(*[
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probability.copy().scale(0.7).next_to(
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girl, LEFT, MED_LARGE_BUFF
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)
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for girl in self.girls
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])
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self.play(FocusOn(probability))
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self.play(Indicate(probability[-1]))
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self.dither()
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self.play(
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ReplacementTransform(
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VGroup(probability.copy()), probability_copies
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),
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FadeOut(self.children_brace),
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FadeOut(self.n_children_words),
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)
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self.dither()
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self.probability_copies = probability_copies
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def think_through_probabilities(self):
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randy = Randolph().scale(0.5)
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randy.next_to(self.probability_copies, LEFT, LARGE_BUFF)
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self.play(FadeIn(randy))
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self.play(randy.change, "pondering")
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self.play(Blink(randy))
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self.dither()
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##
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def get_male(self):
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return TexMobject("\\male").scale(1.3).highlight(BLUE)
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def get_female(self):
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return TexMobject("\\female").scale(1.3).highlight(MAROON_B)
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class CycleThroughPatterns(NameBinomial):
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CONFIG = {
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"n_patterns_shown" : 100,
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"pattern_scale_value" : 2.7,
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"n" : 10,
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"k" : 6,
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}
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def construct(self):
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n = self.n
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k = self.k
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question = TextMobject(
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"How many patterns have \\\\ %d "%k,
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"$\\female$",
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" and %d "%(n-k),
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"$\\male$",
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"?",
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arg_separator = ""
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)
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question.highlight_by_tex("male", BLUE)
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question.highlight_by_tex("female", MAROON_B)
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question.scale_to_fit_width(2*SPACE_WIDTH - 1)
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question.to_edge(UP, buff = LARGE_BUFF)
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self.add(question)
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all_combinations = list(it.combinations(range(n), k))
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shown_combinations = all_combinations[:self.n_patterns_shown]
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patterns = VGroup(*[
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self.get_pattern(indicies)
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for indicies in shown_combinations
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])
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patterns.to_edge(DOWN, buff = LARGE_BUFF)
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pattern = patterns[0]
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self.add(pattern)
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for new_pattern in ProgressDisplay(patterns[1:]):
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self.play(*[
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Transform(
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getattr(pattern, attr),
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getattr(new_pattern, attr),
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path_arc = np.pi
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)
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for attr in "boys", "girls"
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])
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####
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def get_pattern(self, indices):
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pattern = VGroup()
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pattern.boys = VGroup()
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pattern.girls = VGroup()
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for i in range(self.n):
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if i in indices:
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mob = self.get_female()
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pattern.girls.add(mob)
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else:
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mob = self.get_male()
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pattern.boys.add(mob)
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mob.shift(i*MED_LARGE_BUFF*RIGHT)
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pattern.add(mob)
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pattern.scale(self.pattern_scale_value)
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pattern.to_edge(LEFT)
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return pattern
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class Compute6of10GirlsProbability(CycleThroughPatterns):
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def construct(self):
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self.show_combinations()
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self.write_n_choose_k()
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def show_combinations(self):
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pattern_rect = ScreenRectangle(height = 4)
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pattern_rect.center()
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pattern_rect.to_edge(UP, buff = MED_SMALL_BUFF)
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self.add(pattern_rect)
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self.dither(5)
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self.pattern_rect = pattern_rect
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def write_n_choose_k(self):
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brace = Brace(self.pattern_rect, DOWN)
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ten_choose_six = brace.get_tex("{10 \\choose 6}")
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see_chapter_one = TextMobject("(See chapter 1)")
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see_chapter_one.next_to(ten_choose_six, DOWN)
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see_chapter_one.highlight(GREEN)
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computation = TexMobject(
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"=\\frac{%s}{%s}"%(
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"\\cdot ".join(map(str, range(10, 4, -1))),
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"\\cdot ".join(map(str, range(1, 7))),
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)
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)
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computation.move_to(ten_choose_six, UP)
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rhs = TexMobject("=", "210")
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rhs.next_to(computation, RIGHT)
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self.play(
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FadeIn(see_chapter_one),
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GrowFromCenter(brace)
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)
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self.play(Write(ten_choose_six))
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self.dither(2)
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self.play(
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ten_choose_six.next_to, computation.copy(), LEFT,
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Write(VGroup(computation, rhs))
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)
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self.dither()
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self.ten_choose_six = ten_choose_six
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self.rhs = rhs
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class ProbabilityOfAGivenBoyGirlPattern(CycleThroughPatterns):
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def construct(self):
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self.write_total_count()
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self.write_example_probability()
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self.write_total_probability()
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def write_total_count(self):
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count = TextMobject(
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"${10 \\choose 6}$", " $= 210$",
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"total patterns."
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)
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count.to_edge(UP)
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self.add(count)
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self.count = count
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def write_example_probability(self):
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prob = TexMobject("P\\big(", "O "*15, "\\big)", "=")
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indices = [1, 2, 4, 6, 8, 9]
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pattern = self.get_pattern(indices)
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pattern.replace(prob[1], dim_to_match = 0)
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prob.submobjects[1] = pattern
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prob.next_to(self.count, DOWN, LARGE_BUFF)
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gp = TexMobject("(0.49)").highlight(MAROON_B)
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bp = TexMobject("(0.51)").highlight(BLUE)
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factored = VGroup()
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gps = VGroup()
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bps = VGroup()
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for i in range(10):
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if i in indices:
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mob = gp.copy()
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gps.add(mob)
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else:
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mob = bp.copy()
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bps.add(mob)
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factored.add(mob)
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factored.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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factored.next_to(prob, DOWN, MED_LARGE_BUFF)
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gps.save_state()
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bps.save_state()
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final_probability = TexMobject(
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"(0.49)^6", "(0.51)^4"
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)
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final_probability.highlight_by_tex("0.49", MAROON_B)
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final_probability.highlight_by_tex("0.51", BLUE)
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final_probability.next_to(factored, DOWN, LARGE_BUFF)
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self.play(FadeIn(prob))
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self.dither()
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self.play(ReplacementTransform(
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pattern.copy(), factored,
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run_time = 1.5,
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))
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self.dither(2)
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for group, tex in (gps, "0.49"), (bps, "0.51"):
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part = final_probability.get_part_by_tex(tex)
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self.play(group.shift, MED_LARGE_BUFF*DOWN)
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self.play(
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ReplacementTransform(
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group.copy(), VGroup(VGroup(*part[:-1]))
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),
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Write(part[-1])
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)
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self.dither()
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self.play(group.restore)
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self.dither()
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self.final_probability = final_probability
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def write_total_probability(self):
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ten_choose_six = self.count[0].copy()
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ten_choose_six.generate_target()
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ten_choose_six.target.move_to(self.final_probability)
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p_tex = TexMobject("P(", "\\text{6 Girls}", ")", "=")
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p_tex.highlight_by_tex("Girls", MAROON_B)
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p_tex.next_to(ten_choose_six.target, LEFT)
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self.play(
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Write(p_tex, run_time = 2),
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self.final_probability.next_to,
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ten_choose_six.target, RIGHT
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)
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self.play(MoveToTarget(ten_choose_six))
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self.dither()
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class CycleThroughPatternsForThree(CycleThroughPatterns):
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CONFIG = {
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"k" : 3,
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"n_patterns_shown" : 20,
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}
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class GeneralBinomialDistributionValues(Scene):
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CONFIG = {
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"n" : 10,
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"alt_n" : 8,
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"p" : 0.49,
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}
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def construct(self):
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self.add_chart()
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self.show_a_few_values()
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self.compare_to_pascal_row()
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self.mention_center_concentration()
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self.generalize()
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self.play_with_p_value()
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def add_chart(self):
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dist = get_binomial_distribution(self.n, self.p)
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values = map(dist, range(self.n+1))
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chart = BarChart(
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values,
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bar_names = range(self.n+1)
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)
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chart.to_edge(LEFT)
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full_probability = self.get_probability_expression(
|
||||
"10", "k", "(0.49)", "(0.51)"
|
||||
)
|
||||
full_probability.next_to(chart, UP, aligned_edge = LEFT)
|
||||
|
||||
self.add(chart, full_probability)
|
||||
|
||||
self.chart = chart
|
||||
self.full_probability = full_probability
|
||||
|
||||
def show_a_few_values(self):
|
||||
chart = self.chart
|
||||
probabilities = VGroup()
|
||||
for i, bar in enumerate(chart.bars):
|
||||
prob = self.get_probability_expression(
|
||||
"10", str(i), "(0.49)", "(0.51)",
|
||||
full = False
|
||||
)
|
||||
arrow = Arrow(
|
||||
UP, DOWN,
|
||||
color = WHITE,
|
||||
tip_length = 0.15
|
||||
)
|
||||
arrow.next_to(bar, UP, SMALL_BUFF)
|
||||
prob.next_to(arrow, UP, SMALL_BUFF)
|
||||
##
|
||||
prob.shift(LEFT)
|
||||
prob.shift_onto_screen()
|
||||
prob.shift(RIGHT)
|
||||
##
|
||||
prob.add(arrow)
|
||||
probabilities.add(prob)
|
||||
shown_prob = probabilities[6].copy()
|
||||
|
||||
self.play(FadeIn(shown_prob))
|
||||
self.dither()
|
||||
last_k = 6
|
||||
for k in 3, 8, 5, 9, 6:
|
||||
self.play(Transform(
|
||||
shown_prob, probabilities[k],
|
||||
path_arc = -np.pi/6 if k > last_k else np.pi/6
|
||||
))
|
||||
self.dither(2)
|
||||
last_k = k
|
||||
|
||||
self.shown_prob = shown_prob
|
||||
|
||||
def compare_to_pascal_row(self):
|
||||
triangle = PascalsTriangle(nrows = 11)
|
||||
triangle.scale_to_fit_width(6)
|
||||
triangle.to_corner(UP+RIGHT)
|
||||
last_row = VGroup(*[
|
||||
triangle.coords_to_mobs[10][k]
|
||||
for k in range(11)
|
||||
])
|
||||
ten_choose_ks = VGroup()
|
||||
for k, mob in enumerate(last_row):
|
||||
ten_choose_k = TexMobject("10 \\choose %s"%k)
|
||||
ten_choose_k.scale(0.5)
|
||||
ten_choose_k.stretch(0.8, 0)
|
||||
ten_choose_k.next_to(mob, DOWN)
|
||||
ten_choose_ks.add(ten_choose_k)
|
||||
ten_choose_ks.gradient_highlight(BLUE, YELLOW)
|
||||
|
||||
self.play(
|
||||
LaggedStart(FadeIn, triangle),
|
||||
FadeOut(self.shown_prob)
|
||||
)
|
||||
self.play(
|
||||
last_row.gradient_highlight, BLUE, YELLOW,
|
||||
Write(ten_choose_ks, run_time = 2)
|
||||
)
|
||||
self.dither()
|
||||
self.play(ApplyWave(self.chart.bars, direction = UP))
|
||||
self.play(FocusOn(last_row))
|
||||
self.play(LaggedStart(
|
||||
ApplyMethod, last_row,
|
||||
lambda m : (m.scale_in_place, 1.2),
|
||||
rate_func = there_and_back,
|
||||
))
|
||||
self.dither()
|
||||
|
||||
self.pascals_triangle = triangle
|
||||
self.ten_choose_ks = ten_choose_ks
|
||||
|
||||
def mention_center_concentration(self):
|
||||
bars = self.chart.bars
|
||||
bars.generate_target()
|
||||
bars.save_state()
|
||||
bars.target.arrange_submobjects(UP, buff = 0)
|
||||
bars.target.stretch_to_fit_height(self.chart.height)
|
||||
bars.target.move_to(
|
||||
self.chart.x_axis.point_from_proportion(0.05),
|
||||
DOWN
|
||||
)
|
||||
brace = Brace(VGroup(*bars.target[4:7]), RIGHT)
|
||||
words = brace.get_text("Most probability \\\\ in middle values")
|
||||
|
||||
self.play(MoveToTarget(bars))
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
FadeIn(words)
|
||||
)
|
||||
self.dither(2)
|
||||
self.play(
|
||||
bars.restore,
|
||||
*map(FadeOut, [
|
||||
brace, words,
|
||||
self.pascals_triangle,
|
||||
self.ten_choose_ks
|
||||
])
|
||||
)
|
||||
|
||||
def generalize(self):
|
||||
alt_n = self.alt_n
|
||||
dist = get_binomial_distribution(alt_n, self.p)
|
||||
values = map(dist, range(alt_n + 1))
|
||||
alt_chart = BarChart(
|
||||
values, bar_names = range(alt_n + 1)
|
||||
)
|
||||
alt_chart.move_to(self.chart)
|
||||
|
||||
alt_probs = [
|
||||
self.get_probability_expression("n", "k", "(0.49)", "(0.51)"),
|
||||
self.get_probability_expression("n", "k", "p", "(1-p)"),
|
||||
]
|
||||
for prob in alt_probs:
|
||||
prob.move_to(self.full_probability)
|
||||
|
||||
self.play(FocusOn(
|
||||
self.full_probability.get_part_by_tex("choose")
|
||||
))
|
||||
self.play(
|
||||
ReplacementTransform(self.chart, alt_chart),
|
||||
Transform(self.full_probability, alt_probs[0])
|
||||
)
|
||||
self.chart = alt_chart
|
||||
self.dither(2)
|
||||
self.play(Transform(self.full_probability, alt_probs[1]))
|
||||
self.dither()
|
||||
|
||||
def play_with_p_value(self):
|
||||
p = self.p
|
||||
interval = UnitInterval(color = WHITE)
|
||||
interval.scale_to_fit_width(5)
|
||||
interval.next_to(self.full_probability, DOWN, LARGE_BUFF)
|
||||
interval.add_numbers(0, 0.5, 1)
|
||||
triangle = RegularPolygon(
|
||||
n=3, start_angle = -np.pi/2,
|
||||
fill_color = MAROON_B,
|
||||
fill_opacity = 1,
|
||||
stroke_width = 0,
|
||||
)
|
||||
triangle.scale_to_fit_height(0.25)
|
||||
triangle.move_to(interval.number_to_point(p), DOWN)
|
||||
p_mob = TexMobject("p")
|
||||
p_mob.highlight(MAROON_B)
|
||||
p_mob.next_to(triangle, UP, SMALL_BUFF)
|
||||
triangle.add(p_mob)
|
||||
|
||||
new_p_values = [0.8, 0.4, 0.2, 0.9, 0.97, 0.6]
|
||||
|
||||
self.play(
|
||||
ShowCreation(interval),
|
||||
Write(triangle, run_time = 1)
|
||||
)
|
||||
self.dither()
|
||||
for new_p in new_p_values:
|
||||
p = new_p
|
||||
dist = get_binomial_distribution(self.alt_n, p)
|
||||
values = map(dist, range(self.alt_n + 1))
|
||||
self.play(
|
||||
self.chart.change_bar_values, values,
|
||||
triangle.move_to, interval.number_to_point(p), DOWN
|
||||
)
|
||||
self.dither()
|
||||
|
||||
#######
|
||||
|
||||
def get_probability_expression(
|
||||
self, n = "n", k = "k", p = "p", q = "(1-p)",
|
||||
full = True
|
||||
):
|
||||
args = []
|
||||
if full:
|
||||
args += ["P(", "\\# \\text{Girls}", "=", k, ")", "="]
|
||||
args += [
|
||||
"{%s \\choose %s}"%(n, k),
|
||||
p, "^%s"%k,
|
||||
q, "^{%s"%n, "-", "%s}"%k,
|
||||
]
|
||||
result = TexMobject(*args, arg_separator = "")
|
||||
color_map = {
|
||||
"Girls" : MAROON_B,
|
||||
n : WHITE,
|
||||
k : YELLOW,
|
||||
p : MAROON_B,
|
||||
q : BLUE,
|
||||
}
|
||||
result.highlight_by_tex_to_color_map(color_map)
|
||||
choose_part = result.get_part_by_tex("choose")
|
||||
choose_part.highlight(WHITE)
|
||||
VGroup(*choose_part[1:1+len(n)]).highlight(color_map[n])
|
||||
VGroup(*choose_part[-1-len(k):-1]).highlight(color_map[k])
|
||||
return result
|
||||
|
||||
class PointOutSimplicityOfFormula(TeacherStudentsScene, GeneralBinomialDistributionValues):
|
||||
def construct(self):
|
||||
prob = self.get_probability_expression(full = False)
|
||||
corner = self.teacher.get_corner(UP+LEFT)
|
||||
prob.next_to(corner, UP, MED_LARGE_BUFF)
|
||||
prob.save_state()
|
||||
prob.move_to(corner)
|
||||
prob.set_fill(opacity = 0)
|
||||
|
||||
self.play(
|
||||
prob.restore,
|
||||
self.teacher.change_mode, "raise_right_hand"
|
||||
)
|
||||
self.change_student_modes(
|
||||
*["pondering"]*3,
|
||||
look_at_arg = prob
|
||||
)
|
||||
self.dither()
|
||||
self.student_says(
|
||||
"Simpler than I feared",
|
||||
target_mode = "hooray",
|
||||
student_index = 0,
|
||||
added_anims = [prob.to_corner, UP+RIGHT]
|
||||
)
|
||||
self.dither()
|
||||
self.teacher_says("Due to \\\\ independence")
|
||||
self.dither(2)
|
||||
|
||||
class CorrectForDependence(NameBinomial):
|
||||
CONFIG = {
|
||||
"flip_indices" : [3, 6, 8],
|
||||
}
|
||||
def setup(self):
|
||||
self.force_skipping()
|
||||
self.name_distribution()
|
||||
self.add_quiz_questions()
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
|
||||
self.mention_dependence()
|
||||
self.show_tendency_to_align()
|
||||
self.adjust_chart()
|
||||
|
||||
def mention_dependence(self):
|
||||
brace = Brace(self.checkmarks, LEFT)
|
||||
words = brace.get_text("What if there's \\\\ correlation?")
|
||||
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
Write(words)
|
||||
)
|
||||
self.dither(2)
|
||||
|
||||
def show_tendency_to_align(self):
|
||||
checkmarks = self.checkmarks
|
||||
arrows = self.arrows
|
||||
crosses = self.crosses
|
||||
groups = [
|
||||
VGroup(*trip)
|
||||
for trip in zip(checkmarks, arrows, crosses)
|
||||
]
|
||||
top_rect = SurroundingRectangle(groups[0])
|
||||
top_rect.highlight(GREEN)
|
||||
indices_to_follow = [1, 4, 5, 7]
|
||||
|
||||
self.revert_to_original_skipping_status()
|
||||
self.play(ShowCreation(top_rect))
|
||||
self.play(*self.get_arrow_flip_anims([0]))
|
||||
self.dither()
|
||||
self.play(*self.get_arrow_flip_anims(indices_to_follow))
|
||||
self.dither()
|
||||
|
||||
def adjust_chart(self):
|
||||
pass
|
||||
|
||||
######
|
||||
|
||||
def get_arrow_flip_anims(self, indices):
|
||||
checkmarks, arrows, crosses = movers = [
|
||||
VGroup(*[
|
||||
group[i]
|
||||
for i in range(len(group))
|
||||
if i in indices
|
||||
])
|
||||
for group in self.checkmarks, self.arrows, self.crosses
|
||||
]
|
||||
for arrow in arrows:
|
||||
arrow.target = arrow.deepcopy()
|
||||
arrow.target.rotate_in_place(np.pi)
|
||||
for group in checkmarks, crosses:
|
||||
for mob, arrow in zip(group, arrows):
|
||||
mob.generate_target()
|
||||
c = mob.get_center()
|
||||
start, end = arrow.target.get_start_and_end()
|
||||
to_end = np.linalg.norm(c - end)
|
||||
to_start = np.linalg.norm(c - start)
|
||||
if to_end < to_start:
|
||||
mob.target.set_fill(opacity = 1)
|
||||
else:
|
||||
mob.target.set_fill(opacity = 0.5)
|
||||
for checkmark in checkmarks:
|
||||
checkmark.target.scale_in_place(1.2)
|
||||
|
||||
kwargs = {"path_arc" : np.pi}
|
||||
if len(indices) > 1:
|
||||
kwargs.update({"run_time" : 2})
|
||||
return [
|
||||
LaggedStart(
|
||||
MoveToTarget, mover,
|
||||
**kwargs
|
||||
)
|
||||
for mover in movers
|
||||
]
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -10,6 +10,7 @@
|
|||
\usepackage{relsize}
|
||||
\usepackage{mathrsfs}
|
||||
\usepackage{calligra}
|
||||
\usepackage{wasysym}
|
||||
|
||||
\begin{document}
|
||||
\centering
|
||||
|
|
|
|||
|
|
@ -11,6 +11,7 @@
|
|||
\usepackage{textcomp}
|
||||
\usepackage{mathrsfs}
|
||||
\usepackage{calligra}
|
||||
\usepackage{wasysym}
|
||||
|
||||
\begin{document}
|
||||
|
||||
|
|
|
|||
|
|
@ -86,9 +86,11 @@ class NumberLine(VMobject):
|
|||
#TODO, handle decimals
|
||||
if len(numbers) == 0:
|
||||
numbers = self.default_numbers_to_display()
|
||||
if "force_integers" in kwargs and kwargs["force_integers"]:
|
||||
numbers = map(int, numbers)
|
||||
result = VGroup()
|
||||
for number in numbers:
|
||||
mob = TexMobject(str(int(number)))
|
||||
mob = TexMobject(str(number))
|
||||
mob.scale_to_fit_height(3*self.tick_size)
|
||||
mob.shift(
|
||||
self.number_to_point(number),
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue