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Incremental additions to WindingNumber_G
This commit is contained in:
Grant Sanderson
parent
8ad9135697
commit
f208149e9c
1 changed files with 152 additions and 101 deletions
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@ -109,13 +109,21 @@ class IntroSceneWrapper(PiCreatureScene):
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rainbow_solver2.gradient_highlight(*reversed(colors))
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xy_equation = TexMobject(
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"y", "e", "^x", "=\\sin(|", "x", "y", "|)"
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)
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xy_equation.highlight_by_tex_to_color_map({
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"x" : BLUE,
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"y" : YELLOW
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})
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xy_equation = TexMobject("""
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\\left[\\begin{array}{c}
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ye^x \\\\
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\\sin(|xy|)
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\\end{array}\\right] =
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\\left[\\begin{array}{c}
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y^2 \\\\
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3y
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\\end{array}\\right]
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""")
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# xy_equation.highlight_by_tex_to_color_map({
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# "x" : BLUE,
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# "y" : YELLOW
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# })
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xy_equation.scale(0.8)
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xy_equation.next_to(solver, DOWN, MED_LARGE_BUFF)
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z_equation = TexMobject("z", "^5", "+", "z", "+", "1", "=", "0")
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@ -426,6 +434,7 @@ class Introduce1DFunctionCase(Scene):
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rect.target.stretch_to_fit_height(self.search_range_rect_height)
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self.play(
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MoveToTarget(rect),
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Animation(all_leftovers),
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FadeOut(to_fade),
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*added_anims
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)
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@ -518,6 +527,8 @@ class TransitionFromEquationSolverToZeroFinder(Introduce1DFunctionCase):
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tex_mob.move_to(equation.get_right())
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equation.add(tex_mob)
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find_sqrt_2 = self.find_sqrt_2
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rect = SurroundingRectangle(VGroup(equation, find_sqrt_2))
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rect.highlight(WHITE)
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f_graph = self.squared_graph
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g_graph = self.two_graph
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@ -538,6 +549,11 @@ class TransitionFromEquationSolverToZeroFinder(Introduce1DFunctionCase):
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LEFT
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)
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fg_labels = VGroup(f_label, g_label)
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fg_labels.generate_target()
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fg_labels.target.arrange_submobjects(DOWN, aligned_edge = LEFT)
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fg_labels.target.to_corner(UP+RIGHT)
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new_equation = TexMobject("x^2", "-", "2", "=", "0")
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new_equation[0].match_style(equation[0])
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new_equation[2].match_style(equation[2])
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@ -545,19 +561,20 @@ class TransitionFromEquationSolverToZeroFinder(Introduce1DFunctionCase):
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for tex in equation, new_equation:
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tex.sort_submobjects_alphabetically()
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self.play(ShowCreation(rect))
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self.play(FadeOut(rect))
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self.play(
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ReplacementTransform(equation, new_equation, path_arc = np.pi),
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ReplacementTransform(equation, new_equation, path_arc = TAU/4),
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find_sqrt_2.next_to, new_equation, DOWN,
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)
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self.play(MoveToTarget(fg_labels))
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self.play(
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ReplacementTransform(f_graph, new_graph),
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ReplacementTransform(g_graph, zero_graph),
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)
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self.play(
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ReplacementTransform(f_label[0], new_label[0]),
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ReplacementTransform(g_label[0], new_label[2]),
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FadeOut(f_label[1:]),
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FadeOut(g_label[1:]),
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ReplacementTransform(f_label[0].copy(), new_label[0]),
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ReplacementTransform(g_label[0].copy(), new_label[2]),
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Write(new_label[1]),
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)
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self.wait()
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@ -565,95 +582,90 @@ class TransitionFromEquationSolverToZeroFinder(Introduce1DFunctionCase):
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self.set_variables_as_attrs(new_graph, zero_graph)
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def show_binary_search_with_signs(self):
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self.play(FadeOut(self.axes.x_axis.numbers[2]))
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self.binary_search(
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self.new_graph, self.zero_graph,
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1, 2,
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n_iterations = 8,
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n_iterations = 9,
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n_iterations_with_sign_mention = 2,
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zoom = True,
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)
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class RewriteEquationWithTeacher(AltTeacherStudentsScene):
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def construct(self):
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equations = VGroup(
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TexMobject(
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"f(\\text{2d input})", "", "=",
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"g(\\text{2d input})", ""
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),
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TexMobject(
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"f(\\text{2d input})", "-",
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"g(\\text{2d input})", "=", "0"
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),
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)
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specific_equations = VGroup(
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root_two_equations = VGroup(
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TexMobject("x^2", "", "=", "2", ""),
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TexMobject("x^2", "-", "2", "=", "0"),
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)
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for equation in it.chain(equations, specific_equations):
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for equation in root_two_equations:
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equation.sort_submobjects_alphabetically()
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for part in equation.get_parts_by_tex("text"):
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part[2:-1].highlight(YELLOW)
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part[2:-1].scale(0.9)
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equation.move_to(self.hold_up_spot, DOWN)
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self.teacher_holds_up(specific_equations[0])
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self.play(Transform(*specific_equations, path_arc = TAU/4))
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brace = Brace(root_two_equations[1], UP)
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f_equals_0 = brace.get_tex("f(x) = 0")
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self.teacher_holds_up(root_two_equations[0])
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self.wait()
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self.play(Transform(
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*root_two_equations,
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run_time = 1.5,
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path_arc = TAU/2
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))
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self.play(self.get_student_changes(*["pondering"]*3))
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self.play(FadeOut(specific_equations[0]), FadeIn(equations[0]))
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self.wait()
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self.play(Transform(*equations, path_arc = TAU/4))
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self.change_student_modes(*["happy"]*3)
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# 2d plane
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plane = NumberPlane(x_radius = 2.5, y_radius = 2.5)
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plane.scale(0.8)
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plane.to_corner(UP+LEFT)
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plane.add_coordinates()
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dot = Dot(color = YELLOW)
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label = TextMobject("Sign?")
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label.add_background_rectangle()
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label.scale(0.5)
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label.next_to(dot, UP, SMALL_BUFF)
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dot.add(label)
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dot.move_to(plane.coords_to_point(1, 1))
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dot.save_state()
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dot.fade(1)
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dot.center()
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question = TextMobject(
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"Wait...what would \\\\ positive and negative \\\\ be in 2d?",
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)
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# question.highlight_by_tex_to_color_map({
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# "+" : "green",
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# "textminus" : "red"
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# })
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self.student_says(
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question,
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target_mode = "sassy",
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student_index = 2,
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added_anims = [
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equations[0].to_corner, UP+RIGHT,
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self.teacher.change, "plain",
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],
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bubble_kwargs = {"direction" : LEFT},
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run_time = 1,
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)
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self.play(
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Write(plane, run_time = 1),
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self.students[0].change, "confused",
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self.students[1].change, "confused",
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GrowFromCenter(brace),
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self.teacher.change, "happy"
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)
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self.play(dot.restore)
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for coords in (-1, 1), (1, -1), (0, -2), (-2, 1):
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self.wait(0.5)
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self.play(dot.move_to, plane.coords_to_point(*coords))
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self.play(Write(f_equals_0))
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self.change_student_modes(*["happy"]*3)
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self.wait()
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#
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to_remove = VGroup(root_two_equations[0], brace, f_equals_0)
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two_d_equation = TexMobject("""
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\\left[\\begin{array}{c}
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ye^x \\\\
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\\sin(xy)
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\\end{array}\\right] =
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\\left[\\begin{array}{c}
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y^2 + x^3 \\\\
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3y - x
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\\end{array}\\right]
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""")
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complex_equation = TexMobject("z", "^5 + ", "z", " + 1 = 0")
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z_def = TextMobject(
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"(", "$z$", " is complex, ", "$a + bi$", ")",
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arg_separator = ""
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)
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complex_group = VGroup(complex_equation, z_def)
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complex_group.arrange_submobjects(DOWN)
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for tex in complex_group:
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tex.highlight_by_tex("z", GREEN)
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complex_group.move_to(self.hold_up_spot, DOWN)
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self.play(
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ApplyMethod(
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to_remove.next_to, SPACE_WIDTH*RIGHT, RIGHT,
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remover = True,
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rate_func = running_start,
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path_arc = -TAU/4,
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),
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self.teacher.change, "hesitant",
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self.get_student_changes(*["erm"]*3)
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)
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self.teacher_holds_up(two_d_equation)
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self.change_all_student_modes("horrified")
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self.wait()
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self.play(
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FadeOut(two_d_equation),
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FadeInFromDown(complex_group),
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)
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self.change_all_student_modes("confused")
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self.wait(3)
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class InputOutputScene(Scene):
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CONFIG = {
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"plane_width" : 6,
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@ -673,11 +685,13 @@ class InputOutputScene(Scene):
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def func(self, coord_pair):
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out_coords = np.array(self.non_renormalized_func(coord_pair))
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out_norm = np.linalg.norm(out_coords)
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if out_norm > 0.01:
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if out_norm > 1:
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angle = angle_of_vector(out_coords)
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factor = 0.5-0.1*np.cos(4*angle)
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target_norm = factor*np.log(out_norm)
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out_coords *= target_norm / out_norm
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else:
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out_coords = (0, 0)
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return tuple(out_coords)
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def point_function(self, point):
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@ -1229,16 +1243,20 @@ class DotsHoppingToColor(InputOutputScene):
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# Show black zero
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zeros = tuple(it.starmap(input_plane.coords_to_point, [
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(-2, -1), (1, 2), (2, -2),
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(-2., -1), (1, 1), (2, -2),
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]))
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for x in range(2):
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for zero in zeros:
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path = ParametricFunction(
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bezier([
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inspector.get_center(),
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input_plane.coords_to_point(0, 0),
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zero
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]),
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t_min = 0, t_max = 1
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)
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self.play(
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ApplyMethod(
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inspector.move_to, zero,
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path_arc = -TAU/8,
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run_time = 2,
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),
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MoveAlongPath(inspector, path, run_time = 2),
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inspector_image_update_anim,
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)
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self.wait()
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@ -1300,6 +1318,54 @@ class SoWeFoundTheZeros(AltTeacherStudentsScene):
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)
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self.wait(3)
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class AskAboutHowToGeneralizeSigns(AltTeacherStudentsScene):
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def construct(self):
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# 2d plane
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plane = NumberPlane(x_radius = 2.5, y_radius = 2.5)
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plane.scale(0.8)
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plane.to_corner(UP+LEFT)
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plane.add_coordinates()
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dot = Dot(color = YELLOW)
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label = TextMobject("Sign?")
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label.add_background_rectangle()
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label.scale(0.5)
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label.next_to(dot, UP, SMALL_BUFF)
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dot.add(label)
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dot.move_to(plane.coords_to_point(1, 1))
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dot.save_state()
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dot.fade(1)
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dot.center()
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question = TextMobject(
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"Wait...what would \\\\ positive and negative \\\\ be in 2d?",
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)
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# question.highlight_by_tex_to_color_map({
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# "+" : "green",
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# "textminus" : "red"
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# })
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self.student_says(
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question,
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target_mode = "sassy",
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student_index = 2,
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added_anims = [
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self.teacher.change, "plain",
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],
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bubble_kwargs = {"direction" : LEFT},
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run_time = 1,
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)
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self.play(
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Write(plane, run_time = 1),
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self.students[0].change, "confused",
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self.students[1].change, "confused",
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)
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self.play(dot.restore)
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for coords in (-1, 1), (1, -1), (0, -2), (-2, 1):
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self.wait(0.5)
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self.play(dot.move_to, plane.coords_to_point(*coords))
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self.wait()
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class HypothesisAboutFullyColoredBoundary(ColorMappedObjectsScene):
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CONFIG = {
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"func" : plane_func_from_complex_func(lambda z : z**3),
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@ -1396,23 +1462,8 @@ class ForeverNarrowingLoop(InputOutputScene):
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run_time = 3,
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rate_func = bezier([0, 0, 1, 1])
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)
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# self.play(
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# ReplacementTransform(
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# circle.copy(),
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# circle_image.copy().match_background_image_file(
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# input_coloring
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# ).set_stroke(width = 0)
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# ),
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# ReplacementTransform(
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# circle.copy().match_background_image_file(
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# output_coloring
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# ).set_stroke(width = 0),
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# circle_image
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# ),
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# run_time = 2
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# )
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self.play(
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circle.scale, 0.015,
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circle.scale, 0,
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circle.move_to, input_plane.coords_to_point(1, 1),
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circle_image_update_anim,
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run_time = 20,
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