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synced 2025-07-30 21:44:19 +08:00
Preliminary end to exp_footnote
This commit is contained in:
Grant Sanderson
@ -25,19 +25,30 @@ 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 topics.common_scenes import OpeningQuote
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from eoc.graph_scene import *
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class ExpFootnoteOpeningQuote(OpeningQuote):
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CONFIG = {
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"quote" : [
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"Who has not be amazed to learn that the function",
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"$y = e^x$,", "like a phoenix rising again from its own",
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"ashes, is its own derivative?",
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],
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"highlighted_quote_terms" : {
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"$y = e^x$" : MAROON_B
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},
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"author" : "Francois le Lionnais"
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}
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class LastVideo(TeacherStudentsScene):
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def construct(self):
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series = VideoSeries()
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series.to_edge(UP)
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last_video = series[2]
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next_video = series[3]
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last_video_color = last_video[0].get_fill_color()
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early_videos = VGroup(*series[:3])
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later_videos = VGroup(*series[3:])
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this_video = VideoIcon().scale(0.5)
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this_video.move_to(VGroup(last_video, next_video), DOWN)
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last_video.save_state()
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this_video = series[3]
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known_formulas = VGroup(*map(TexMobject, [
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"\\frac{d(x^n)}{dx} = nx^{n-1}",
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@ -69,32 +80,20 @@ class LastVideo(TeacherStudentsScene):
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)
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self.dither(2)
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self.play(known_formulas.replace, last_video)
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last_video.add(known_formulas)
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this_video_copy = this_video.copy()
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self.play(last_video_brace.next_to, this_video, DOWN)
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self.play(
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early_videos.stretch_to_fit_width,
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early_videos.get_width() - this_video_copy.get_width(),
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early_videos.next_to, this_video_copy, LEFT, SMALL_BUFF, DOWN,
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later_videos.stretch_to_fit_width,
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later_videos.get_width() - this_video_copy.get_width(),
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later_videos.next_to, this_video_copy, RIGHT, SMALL_BUFF, DOWN,
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last_video_brace.stretch_to_fit_width,
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this_video_copy.get_width(),
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last_video_brace.next_to, this_video_copy, DOWN, SMALL_BUFF,
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GrowFromCenter(this_video)
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)
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self.play(
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last_video.highlight, last_video_color,
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last_video.restore,
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this_video.highlight, YELLOW
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)
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self.play(
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FadeOut(self.get_students()[-1].bubble),
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self.play(
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exp_question.next_to, last_video_brace, DOWN,
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*[
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ApplyMethod(pi.change_mode, "pondering")
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for pi in self.get_students()
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]
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FadeOut(self.get_students()[-1].bubble),
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)
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self.change_student_modes(
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*["pondering"]*3,
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look_at_arg = exp_question
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)
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self.dither()
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class PopulationSizeGraphVsPopulationMassGraph(Scene):
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def construct(self):
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@ -476,6 +475,131 @@ class DoublingPopulation(PiCreatureScene):
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return top_words, bottom_words
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class GraphOfTwoToT(GraphScene):
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CONFIG = {
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"x_axis_label" : "$t$",
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"y_axis_label" : "$M$",
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"x_labeled_nums" : range(1, 7),
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"y_labeled_nums" : range(8, 40, 8),
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"x_max" : 6,
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"y_min" : 0,
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"y_max" : 32,
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"y_tick_frequency" : 2,
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"graph_origin" : 2.5*DOWN + 5*LEFT,
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}
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def construct(self):
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self.setup_axes()
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example_t = 3
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graph = self.get_graph(lambda t : 2**t, color = BLUE_C)
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self.graph = graph
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graph_label = self.get_graph_label(
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graph, "M(t) = 2^t",
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direction = LEFT,
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)
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label_group = self.get_label_group(example_t)
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v_line, brace, height_label, ss_group, slope_label = label_group
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self.animate_secant_slope_group_change(
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ss_group,
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target_dx = 1,
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run_time = 0
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)
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self.remove(ss_group)
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#Draw graph and revert to tangent
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self.play(ShowCreation(graph))
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self.play(Write(graph_label))
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self.dither()
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self.play(Write(ss_group))
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self.dither()
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for target_dx in 0.01, 1, 0.01:
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self.animate_secant_slope_group_change(
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ss_group,
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target_dx = target_dx
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)
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self.dither()
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#Mark up with values
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self.play(ShowCreation(v_line))
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self.play(
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GrowFromCenter(brace),
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Write(height_label, run_time = 1)
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)
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self.dither()
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self.play(
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FadeIn(
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slope_label,
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run_time = 4,
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submobject_mode = "lagged_start"
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),
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ReplacementTransform(
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height_label.copy(),
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slope_label.get_part_by_tex("2^")
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)
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)
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self.dither()
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#Vary value
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threes = VGroup(height_label[1], slope_label[2][1])
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ts = VGroup(*[
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TexMobject("t").highlight(YELLOW).scale(0.75).move_to(three)
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for three in threes
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])
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self.play(Transform(threes, ts))
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alt_example_t = example_t+1
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def update_label_group(group, alpha):
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t = interpolate(example_t, alt_example_t, alpha)
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new_group = self.get_label_group(t)
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Transform(group, new_group).update(1)
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for t, three in zip(ts, threes):
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t.move_to(three)
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Transform(threes, ts).update(1)
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return group
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self.play(UpdateFromAlphaFunc(
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label_group, update_label_group,
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run_time = 3,
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))
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self.play(UpdateFromAlphaFunc(
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label_group, update_label_group,
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run_time = 3,
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rate_func = lambda t : 1 - 1.5*smooth(t)
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))
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def get_label_group(self, t):
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graph = self.graph
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v_line = self.get_vertical_line_to_graph(
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t, graph,
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color = YELLOW,
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)
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brace = Brace(v_line, RIGHT)
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height_label = brace.get_text("$2^%d$"%t)
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ss_group = self.get_secant_slope_group(
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t, graph, dx = 0.01,
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df_label = "dM",
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dx_label = "dt",
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dx_line_color = GREEN,
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secant_line_color = RED,
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)
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slope_label = TexMobject(
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"\\text{Slope}", "=",
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"2^%d"%t,
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"(%.7f\\dots)"%np.log(2)
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)
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slope_label.next_to(
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ss_group.secant_line.point_from_proportion(0.65),
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DOWN+RIGHT,
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buff = 0
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)
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slope_label.highlight_by_tex("Slope", RED)
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return VGroup(
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v_line, brace, height_label,
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ss_group, slope_label
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)
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class AnalyzeExponentRatio(PiCreatureScene):
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CONFIG = {
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"base" : 2,
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@ -698,6 +822,12 @@ class AnalyzeExponentRatio(PiCreatureScene):
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self.change_mode("confused")
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self.dither()
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#Indicate distinction between dt group and t group again
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for mob in limit_term, extracted_two_to_t:
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self.play(FocusOn(mob))
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self.play(Indicate(mob))
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self.dither()
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#hold_final_value
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derivative = VGroup(
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lhs, extracted_two_to_t, parens, constant
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@ -765,8 +895,8 @@ class ExponentRatioWithThree(AnalyzeExponentRatio):
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class ExponentRatioWithSeven(AnalyzeExponentRatio):
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CONFIG = {
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"base" : 3,
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"base_str" : "3",
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"base" : 7,
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"base_str" : "7",
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}
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class ExponentRatioWithE(AnalyzeExponentRatio):
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@ -904,6 +1034,67 @@ class NaturalLog(Scene):
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expression.add(brace, brace_text)
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return expression
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class NextVideo(TeacherStudentsScene):
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def construct(self):
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series = VideoSeries()
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series.to_edge(UP)
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this_video = series[3]
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next_video = series[4]
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brace = Brace(this_video, DOWN)
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this_video.save_state()
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this_video.highlight(YELLOW)
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this_tex = TexMobject(
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"{d(", "a^t", ") \\over dt} = ", "a^t", "\\ln(a)"
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)
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this_tex[1][1].highlight(YELLOW)
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this_tex[3][1].highlight(YELLOW)
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this_tex.next_to(brace, DOWN)
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next_tex = VGroup(*map(TextMobject, [
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"Chain rule", "Product rule", "$\\vdots$"
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]))
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next_tex.arrange_submobjects(DOWN)
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next_tex.next_to(brace, DOWN)
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next_tex.shift(
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next_video.get_center()[0]*RIGHT\
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-next_tex.get_center()[0]*RIGHT
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)
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self.add(series, brace, *this_tex[:3])
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self.change_student_modes(
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"confused", "pondering", "erm",
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look_at_arg = this_tex
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)
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self.play(ReplacementTransform(
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this_tex[1].copy(), this_tex[3]
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))
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self.dither()
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self.play(
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Write(this_tex[4]),
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ReplacementTransform(
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this_tex[3][0].copy(),
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this_tex[4][3],
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path_arc = np.pi,
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remover = True
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)
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)
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self.dither(2)
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self.play(this_tex.replace, this_video)
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self.play(
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brace.next_to, next_video, DOWN,
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this_video.restore,
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Animation(this_tex),
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next_video.highlight, YELLOW,
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Write(next_tex),
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self.get_teacher().change_mode, "raise_right_hand"
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)
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self.change_student_modes(
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*["pondering"]*3,
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look_at_arg = next_tex
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)
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self.dither(3)
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@ -237,7 +237,6 @@ class GraphScene(Scene):
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dx = None,
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dx_line_color = None,
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df_line_color = None,
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slope_line_color = None,
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dx_label = None,
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df_label = None,
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include_secant_line = True,
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@ -44,9 +44,9 @@ class ParametricFunction(VMobject):
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t_values = np.linspace(
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self.t_min, self.t_max, self.num_anchor_points
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)
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points = self.function(t_values)
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points = np.array(map(self.function, t_values))
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okay_indices = np.apply_along_axis(np.all, 1, np.isfinite(points))
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point = point[okay_indices]
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points = points[okay_indices]
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self.set_anchor_points(points, mode = "smooth")
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@ -153,7 +153,7 @@ class VideoIcon(SVGMobject):
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class VideoSeries(VGroup):
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CONFIG = {
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"num_videos" : 10,
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"num_videos" : 11,
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"gradient_colors" : [BLUE_B, BLUE_D],
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}
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def __init__(self, **kwargs):
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@ -161,6 +161,7 @@ class VideoSeries(VGroup):
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videos = [VideoIcon() for x in range(self.num_videos)]
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VGroup.__init__(self, *videos, **kwargs)
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self.arrange_submobjects()
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self.scale_to_fit_width(2*SPACE_WIDTH-MED_LARGE_BUFF)
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self.gradient_highlight(*self.gradient_colors)
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