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finished sum manipulation scene
This commit is contained in:
Ben Hambrecht
parent
e2f6a1f2a0
commit
e6dca3b44d
1 changed files with 158 additions and 40 deletions
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@ -2771,12 +2771,17 @@ class FinalSumManipulationScene(PiCreatureScene):
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LAKE_STROKE_COLOR = BLUE
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TEX_SCALE = 0.8
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LIGHT_COLOR2 = RED
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LIGHT_COLOR3 = BLUE
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unit_length = 1.5
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vertical_spacing = 1.8 * DOWN
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vertical_spacing = 2.5 * DOWN
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switch_on_time = 0.2
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sum_vertical_spacing = 1.5
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randy = self.get_primary_pi_creature()
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randy.scale(0.7).to_edge(DOWN + RIGHT)
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randy.scale(0.7).flip().to_edge(DOWN + LEFT)
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ls_template = LightSource(
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radius = 2,
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@ -2785,9 +2790,9 @@ class FinalSumManipulationScene(PiCreatureScene):
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)
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odd_range = np.arange(1,13,2)
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even_range = np.arange(2,28,2)
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full_range = np.arange(1,14,1)
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odd_range = np.arange(1,9,2)
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even_range = np.arange(2,16,2)
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full_range = np.arange(1,8,1)
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self.number_line1 = NumberLine(
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x_min = 0,
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@ -2803,107 +2808,220 @@ class FinalSumManipulationScene(PiCreatureScene):
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include_tip = True
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)
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self.number_line1.next_to(3 * UP + 3 * LEFT, RIGHT, buff = 0)
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self.number_line1.next_to(2.5 * UP + 3 * LEFT, RIGHT, buff = 0)
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odd_lights = VMobject()
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for i in odd_range:
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pos = self.number_line1.number_to_point(i)
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ls = ls_template.copy()
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ls.move_source_to(pos)
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odd_lights.add(ls)
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labels1 = self.number_line1.get_labels()
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self.play(
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ShowCreation(self.number_line1),
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ShowCreation(labels1)
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)
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for ls in odd_lights.submobjects:
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self.play(SwitchOn(ls.ambient_light), run_time = switch_on_time)
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odd_terms = VMobject()
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for i in odd_range:
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if i == 1:
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term = TexMobject("\phantom{+\,}{1\over " + str(i) + "^2}", fill_color = LIGHT_COLOR)
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else:
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term = TexMobject("+\, {1\over " + str(i) + "^2}", fill_color = LIGHT_COLOR)
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result1 = TexMobject("{\pi^2\over 8} =")
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result1.next_to(self.number_line1, LEFT, buff = 2)
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term.next_to(self.number_line1.number_to_point(i), DOWN, buff = 1.5)
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odd_terms.add(term)
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for (ls, term) in zip(odd_lights.submobjects, odd_terms.submobjects):
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self.play(
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FadeIn(ls.lighthouse, run_time = switch_on_time),
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SwitchOn(ls.ambient_light, run_time = switch_on_time),
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Write(term, run_time = switch_on_time)
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)
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result1 = TexMobject("{\pi^2\over 8} =", fill_color = LIGHT_COLOR)
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result1.next_to(self.number_line1, LEFT, buff = 0.5)
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self.play(Write(result1))
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self.number_line2 = self.number_line1.copy()
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self.number_line2.numbers_to_show = full_range
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self.number_line2.shift(2 * vertical_spacing)
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labels2 = self.number_line2.get_labels()
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full_lights = VMobject()
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for i in full_range:
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pos = self.number_line2.number_to_point(i)
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ls = ls_template.copy()
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ls.color = LIGHT_COLOR3
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ls.move_source_to(pos)
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full_lights.add(ls)
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self.play(
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ShowCreation(self.number_line2),
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ShowCreation(labels2)
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)
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for ls in full_lights.submobjects:
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self.play(SwitchOn(ls.ambient_light, run_time = 0.1 * switch_on_time))
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self.play(
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FadeIn(ls.lighthouse, run_time = 0.1),#5 * switch_on_time),
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SwitchOn(ls.ambient_light, run_time = 0.1)#5 * switch_on_time),
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)
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self.number_line3 = self.number_line1.copy()
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self.number_line3.numbers_to_show = even_range
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self.number_line3.shift(vertical_spacing)
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labels3 = self.number_line3.get_labels()
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missing_text = TextMobject("missing:")
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missing_text.next_to(self.number_line3, LEFT, buff = 2)
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even_terms = VMobject()
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for i in even_range:
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term = TexMobject("+\, {1\over " + str(i) + "^2}", fill_color = LIGHT_COLOR2)
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term.next_to(self.number_line1.number_to_point(i), DOWN, buff = sum_vertical_spacing)
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even_terms.add(term)
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even_lights = VMobject()
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for i in even_range:
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pos = self.number_line3.number_to_point(i)
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pos = self.number_line1.number_to_point(i)
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ls = ls_template.copy()
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ls.color = LIGHT_COLOR2
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ls.move_source_to(pos)
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even_lights.add(ls)
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self.play(Write(missing_text))
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for (ls, term) in zip(even_lights.submobjects, even_terms.submobjects):
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self.play(
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SwitchOn(ls.ambient_light, run_time = switch_on_time),
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Write(term)
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)
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self.play(
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ShowCreation(self.number_line3),
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ShowCreation(labels3),
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)
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for ls in even_lights.submobjects:
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self.play(SwitchOn(ls.ambient_light), run_time = switch_on_time)
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# now morph the even lights into the full lights
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even_lights_line = VMobject()
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even_lights_line.add(even_lights, self.number_line2)
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even_lights_line_copy = even_lights_line.copy()
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full_lights_copy = full_lights.copy()
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even_lights_copy = even_lights.copy()
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full_lights_line = VMobject()
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number_line2p = self.number_line2
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number_line2p.tick_frequency = 0.5
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full_lights_line.add(full_lights.copy(), number_line2p)
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self.play(
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Transform(even_lights_line,full_lights_line)
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Transform(even_lights,full_lights)
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)
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# draw arrows
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P1 = self.number_line2.number_to_point(1)
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P2 = even_terms.submobjects[0].get_center()
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Q1 = interpolate(P1, P2, 0.2)
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Q2 = interpolate(P1, P2, 0.8)
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quarter_arrow = Arrow(Q1, Q2,
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color = LIGHT_COLOR2)
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quarter_label = TexMobject("\\times {1\over 4}", fill_color = LIGHT_COLOR2)
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quarter_label.scale(0.7)
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quarter_label.next_to(quarter_arrow.get_center(), RIGHT)
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self.play(
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ShowCreation(quarter_arrow),
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Write(quarter_label),
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Transform(even_lights,even_lights_copy)
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)
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P3 = odd_terms.submobjects[0].get_center()
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R1 = interpolate(P1, P3, 0.2)
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R2 = interpolate(P1, P3, 0.8)
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three_quarters_arrow = Arrow(R1, R2,
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color = LIGHT_COLOR)
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three_quarters_label = TexMobject("\\times {3\over 4}", fill_color = LIGHT_COLOR)
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three_quarters_label.scale(0.7)
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three_quarters_label.next_to(three_quarters_arrow.get_center(), LEFT)
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self.play(
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ShowCreation(three_quarters_arrow),
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Write(three_quarters_label)
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)
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four_thirds_arrow = Arrow(R2, R1, color = LIGHT_COLOR)
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four_thirds_label = TexMobject("\\times {4\over 3}", fill_color = LIGHT_COLOR)
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four_thirds_label.scale(0.7)
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four_thirds_label.next_to(four_thirds_arrow.get_center(), LEFT)
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self.play(
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ReplacementTransform(three_quarters_arrow, four_thirds_arrow),
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ReplacementTransform(three_quarters_label, four_thirds_label)
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)
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self.play(
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Transform(even_lights_line,even_lights_line_copy)
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FadeOut(quarter_label),
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FadeOut(quarter_arrow),
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FadeOut(even_lights),
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FadeOut(even_terms)
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)
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full_terms = VMobject()
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for i in full_range:
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if i == 1:
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term = TexMobject("\phantom{+\,}{1\over " + str(i) + "^2}", fill_color = LIGHT_COLOR3)
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else:
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term = TexMobject("+\, {1\over " + str(i) + "^2}", fill_color = LIGHT_COLOR3)
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term.move_to(self.number_line2.number_to_point(i))
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full_terms.add(term)
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self.play(
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FadeOut(self.number_line1),
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FadeOut(odd_lights),
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FadeOut(self.number_line2),
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FadeOut(full_lights),
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FadeIn(full_terms)
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)
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v = (sum_vertical_spacing + 0.5) * UP
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self.play(
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odd_terms.shift, v,
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four_thirds_arrow.shift, v,
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four_thirds_label.shift, v,
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odd_terms.shift, v,
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full_terms.shift, v
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)
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arrow_copy = four_thirds_arrow.copy()
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label_copy = four_thirds_label.copy()
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arrow_copy.shift(2.5 * LEFT)
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label_copy.shift(2.5 * LEFT)
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self.play(
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FadeIn(arrow_copy),
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FadeIn(label_copy)
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)
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final_result = TexMobject("{\pi^2 \over 6}=", fill_color = LIGHT_COLOR3)
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final_result.next_to(arrow_copy, DOWN)
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self.play(
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Write(final_result),
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randy.change_mode,"hooray"
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)
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equation = VMobject()
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equation.add(final_result)
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equation.add(full_terms)
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buffer = 2
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result_box = Rectangle(width = 15,
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height = buffer*equation.get_height(), color = LIGHT_COLOR3)
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result_box.move_to(equation)
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equation.add(result_box)
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self.play(
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FadeOut(result1),
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FadeOut(odd_terms),
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FadeOut(arrow_copy),
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FadeOut(label_copy),
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FadeOut(four_thirds_arrow),
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FadeOut(four_thirds_label),
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ShowCreation(result_box)
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)
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self.play(equation.shift, -equation.get_center()[1] * UP + UP)
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