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Finished first AreaUnderParabola scene
This commit is contained in:
Grant Sanderson
parent
0e09120092
commit
dc435e5aa3
1 changed files with 268 additions and 4 deletions
272
eoc/chapter1.py
272
eoc/chapter1.py
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@ -1799,6 +1799,9 @@ class ExampleIntegralProblems(PiCreatureScene, GraphScene):
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run_time = self.t_max
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)
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self.dither()
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for mob in v_dt:
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self.play(Indicate(mob))
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self.dither(2)
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self.v_dt_brace_group = v_dt_brace_group
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self.line = line
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@ -1875,7 +1878,7 @@ class ExampleIntegralProblems(PiCreatureScene, GraphScene):
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dx = self.dt/(2**n),
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stroke_width = 1./(2**n)
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)
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for n in range(1, 5)
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for n in range(1, 4)
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]
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self.play(
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@ -1896,16 +1899,277 @@ class ExampleIntegralProblems(PiCreatureScene, GraphScene):
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self.dither()
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def show_confusion(self):
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randy = Randolph()
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randy = Randolph(color = BLUE_C)
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randy.to_corner(DOWN+LEFT)
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randy.to_edge(LEFT, buff = MED_SMALL_BUFF)
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self.play(FadeIn(randy))
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self.play(randy.change_mode, "confused")
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self.change_mode("plain")
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self.play(
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randy.change_mode, "confused",
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randy.look_at, self.rects
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)
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self.play(
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self.pi_creature.change_mode, "confused",
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self.pi_creature.look_at, randy.eyes
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)
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self.play(Blink(randy))
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self.dither()
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class MathematicianPonderingAreaUnderDifferentCurves(PiCreatureScene):
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def construct(self):
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self.play(
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self.pi_creature.change_mode, "raise_left_hand",
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self.pi_creature.look, UP+LEFT
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)
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self.dither(4)
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self.play(
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self.pi_creature.change_mode, "raise_right_hand",
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self.pi_creature.look, UP+RIGHT
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)
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self.dither(4)
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self.play(
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self.pi_creature.change_mode, "pondering",
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self.pi_creature.look, UP+LEFT
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)
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self.dither(2)
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def create_pi_creature(self):
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self.pi_creature = Randolph(color = BLUE_C)
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self.pi_creature.to_edge(DOWN)
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return self.pi_creature
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class AreaUnderParabola(GraphScene):
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CONFIG = {
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"x_max" : 4,
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"x_labeled_nums" : range(-1, 5),
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"y_min" : 0,
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"y_max" : 15,
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"y_tick_frequency" : 2.5,
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"y_labeled_nums" : range(5, 20, 5),
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"n_rect_iteration" : 6,
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}
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def construct(self):
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self.force_skipping()
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self.setup_axes()
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self.show_graph()
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self.show_area()
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self.ask_about_area()
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self.show_confusion()
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self.show_variable_endpoint()
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self.name_integral()
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def show_graph(self):
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graph = self.get_graph(lambda x : x**2)
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graph_label = self.get_graph_label(
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graph, "x^2",
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direction = LEFT,
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x_val = 3.8,
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)
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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.graph = graph
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self.graph_label = graph_label
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def show_area(self):
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dx_list = [0.25/(2**n) for n in range(self.n_rect_iteration)]
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rect_lists = [
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self.get_riemann_rectangles(
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self.graph,
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x_min = 0,
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x_max = 3,
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dx = dx,
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stroke_width = 4*dx,
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)
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for dx in dx_list
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]
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rects = rect_lists[0]
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foreground_mobjects = [self.axes, self.graph]
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self.play(
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DrawBorderThenFill(
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rects,
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run_time = 2,
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rate_func = smooth,
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submobject_mode = "lagged_start",
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),
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*map(Animation, foreground_mobjects)
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)
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self.dither()
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for new_rects in rect_lists[1:]:
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self.play(
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Transform(
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rects, new_rects,
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submobject_mode = "lagged_start",
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),
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*map(Animation, foreground_mobjects)
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)
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self.dither()
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self.rects = rects
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self.dx = dx_list[-1]
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self.foreground_mobjects = foreground_mobjects
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def ask_about_area(self):
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rects = self.rects
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question = TextMobject("Area?")
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question.next_to(rects, RIGHT, aligned_edge = UP)
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mid_rect = rects[2*len(rects)/3]
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arrow = Arrow(question.get_bottom(), mid_rect)
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v_lines = VGroup(*[
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DashedLine(
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2*SPACE_HEIGHT*UP, ORIGIN,
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color = RED
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).move_to(self.coords_to_point(x, 0), DOWN)
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for x in 0, 3
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])
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self.play(
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Write(question),
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ShowCreation(arrow)
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)
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self.dither()
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self.play(ShowCreation(v_lines, run_time = 2))
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self.dither()
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self.foreground_mobjects += [question, arrow]
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self.question = question
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self.question_arrow = arrow
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self.v_lines = v_lines
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def show_confusion(self):
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morty = Mortimer()
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morty.to_corner(DOWN+RIGHT)
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self.play(FadeIn(morty))
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self.play(
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morty.change_mode, "confused",
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morty.look_at, self.question,
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)
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self.play(morty.look_at, self.rects.get_bottom())
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self.play(Blink(morty))
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self.play(morty.look_at, self.question)
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self.dither()
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self.play(Blink(morty))
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self.play(FadeOut(morty))
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def show_variable_endpoint(self):
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triangle = RegularPolygon(
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n = 3,
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start_angle = np.pi/2,
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stroke_width = 0,
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fill_color = WHITE,
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fill_opacity = 1,
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)
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triangle.scale_to_fit_height(0.25)
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triangle.move_to(self.v_lines[1].get_bottom(), UP)
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x_label = TexMobject("x")
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x_label.next_to(triangle, DOWN)
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self.right_point_slider = VGroup(triangle, x_label)
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A_func = TexMobject("A(x)")
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A_func.move_to(self.question, DOWN)
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self.play(FadeOut(self.x_axis.numbers))
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self.x_axis.remove(*self.x_axis.numbers)
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self.foreground_mobjects.remove(self.axes)
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self.play(DrawBorderThenFill(self.right_point_slider))
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self.move_right_point_to(2)
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self.dither()
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self.move_right_point_to(3)
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self.dither()
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self.play(ReplacementTransform(self.question, A_func))
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self.dither()
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self.A_func = A_func
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def name_integral(self):
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words = TextMobject("``Integral'' of ", "$x^2$")
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words.highlight_by_tex("x^2", self.graph_label.get_color())
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words.next_to(self.A_func, UP, LARGE_BUFF)
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words.to_edge(RIGHT)
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arrow = Arrow(words.get_bottom(), self.A_func)
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arrow.highlight(WHITE)
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self.foreground_mobjects += [words, arrow]
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self.revert_to_original_skipping_status()
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self.play(
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Write(words),
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ShowCreation(arrow)
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)
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self.dither()
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for x in 4, 2, 3:
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self.move_right_point_to(x, run_time = 2)
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####
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def move_right_point_to(self, target_x, **kwargs):
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v_line = self.v_lines[1]
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slider = self.right_point_slider
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rects = self.rects
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curr_x = self.x_axis.point_to_number(v_line.get_bottom())
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group = VGroup(rects, v_line, slider)
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def update_group(group, alpha):
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rects, v_line, slider = group
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new_x = interpolate(curr_x, target_x, alpha)
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new_rects = self.get_riemann_rectangles(
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self.graph,
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x_min = 0,
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x_max = new_x,
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dx = self.dx*new_x/3.0,
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stroke_width = rects[0].get_stroke_width(),
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)
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point = self.coords_to_point(new_x, 0)
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v_line.move_to(point, DOWN)
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slider.move_to(point, UP)
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Transform(rects, new_rects).update(1)
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return VGroup(rects, v_line, slider)
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self.play(
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UpdateFromAlphaFunc(
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group, update_group,
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**kwargs
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),
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*map(Animation, self.foreground_mobjects)
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)
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class WhoCaresAboutArea(TeacherStudentsScene):
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def construct(self):
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point = 2*RIGHT+3*UP
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self.student_says(
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"Who cares!?!", target_mode = "angry",
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)
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self.play(self.teacher.change_mode, "guilty")
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self.dither()
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self.play(
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RemovePiCreatureBubble(self.students[1]),
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self.teacher.change_mode, "raise_right_hand",
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self.teacher.look_at, point
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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 = point,
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added_anims = [self.teacher.look_at, point]
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)
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self.dither(3)
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