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More clacks animations
This commit is contained in:
Grant Sanderson
parent
c4a0e65089
commit
5f86fd811f
1 changed files with 247 additions and 0 deletions
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@ -2279,3 +2279,250 @@ class AnalyzeCircleGeometry1e2(AnalyzeCircleGeometry):
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class CentralQuestionFor1e3(CentralQuestionFor1e2):
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CONFIG = {"exp": 3}
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class AskAboutArctanOfSmallValues(TeacherStudentsScene):
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def construct(self):
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self.add_title()
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equation1 = TexMobject(
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"\\arctan", "(", "x", ")", "\\approx", "x"
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)
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equation1.set_color_by_tex("arctan", YELLOW)
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equation2 = TexMobject(
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"x", "\\approx", "\\tan", "(", "x", ")",
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)
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equation2.set_color_by_tex("tan", BLUE)
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for mob in equation1, equation2:
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mob.move_to(self.hold_up_spot, DOWN)
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self.play(
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FadeInFromDown(equation1),
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self.teacher.change, "raise_right_hand",
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self.get_student_changes(
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"erm", "sassy", "confused"
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)
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)
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self.wait()
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self.play(equation1.shift, UP)
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self.play(
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TransformFromCopy(
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VGroup(*[equation1[i] for i in (2, 4, 5)]),
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VGroup(*[equation2[i] for i in (0, 1, 4)]),
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)
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)
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self.play(
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TransformFromCopy(
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VGroup(*[equation1[i] for i in (0, 1, 3)]),
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VGroup(*[equation2[i] for i in (2, 3, 5)]),
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),
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self.get_student_changes(
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"confused", "erm", "sassy"
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),
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)
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self.wait()
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self.student_says("Why?", target_mode="maybe")
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self.wait(3)
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def add_title(self):
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title = TextMobject("For small $x$")
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subtitle = TextMobject("(e.g. $x = 0.001$)")
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title.scale(1.5)
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title.to_edge(UP, buff=MED_SMALL_BUFF)
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subtitle.next_to(title, DOWN)
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self.add(title, subtitle)
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class UnitCircleIntuition(Scene):
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def construct(self):
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self.draw_unit_circle()
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self.show_angle()
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self.show_fraction()
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self.show_fraction_approximation()
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def draw_unit_circle(self):
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unit_size = 2.5
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axes = Axes(
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number_line_config={"unit_size": unit_size},
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x_min=-2.5, x_max=2.5,
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y_min=-1.5, y_max=1.5,
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)
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axes.set_stroke(width=1)
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self.add(axes)
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radius_line = Line(ORIGIN, axes.coords_to_point(1, 0))
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radius_line.set_color(BLUE)
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r_label = TexMobject("1")
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r_label.add_updater(
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lambda m: m.next_to(radius_line.get_center(), DOWN, SMALL_BUFF)
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)
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circle = Circle(radius=unit_size, color=WHITE)
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self.add(radius_line, r_label)
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self.play(
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Rotating(radius_line, about_point=ORIGIN),
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ShowCreation(circle),
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run_time=2,
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rate_func=smooth,
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)
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self.radius_line = radius_line
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self.r_label = r_label
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self.circle = circle
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self.axes = axes
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def show_angle(self):
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circle = self.circle
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tan_eq = TexMobject(
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"\\tan", "(", "\\theta", ")", "=",
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tex_to_color_map={"\\theta": RED},
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)
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tan_eq.next_to(ORIGIN, RIGHT, LARGE_BUFF)
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tan_eq.to_edge(UP, buff=LARGE_BUFF)
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theta_tracker = ValueTracker(0)
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get_theta = theta_tracker.get_value
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def get_r_line():
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return Line(
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circle.get_center(),
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circle.get_point_from_angle(get_theta())
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)
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r_line = updating_mobject_from_func(get_r_line)
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def get_arc(radius=None, **kwargs):
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if radius is None:
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alpha = inverse_interpolate(0, 20 * DEGREES, get_theta())
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radius = interpolate(2, 1, alpha)
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return Arc(
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radius=radius,
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start_angle=0,
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angle=get_theta(),
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arc_center=circle.get_center(),
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**kwargs
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)
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arc = updating_mobject_from_func(get_arc)
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self.circle_arc = updating_mobject_from_func(
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lambda: get_arc(radius=circle.radius, color=RED)
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)
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def get_theta_label():
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label = TexMobject("\\theta")
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label.set_height(min(arc.get_height(), 0.3))
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label.set_color(RED)
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center = circle.get_center()
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vect = arc.point_from_proportion(0.5) - center
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vect = (get_norm(vect) + 2 * SMALL_BUFF) * normalize(vect)
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label.move_to(center + vect)
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return label
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theta_label = updating_mobject_from_func(get_theta_label)
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def get_height_line():
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p2 = circle.get_point_from_angle(get_theta())
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p1 = np.array(p2)
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p1[1] = circle.get_center()[1]
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return Line(
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p1, p2,
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stroke_color=YELLOW,
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stroke_width=3,
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)
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self.height_line = updating_mobject_from_func(get_height_line)
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def get_width_line():
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p2 = circle.get_center()
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p1 = circle.get_point_from_angle(get_theta())
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p1[1] = p2[1]
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return Line(
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p1, p2,
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stroke_color=PINK,
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stroke_width=3,
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)
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self.width_line = updating_mobject_from_func(get_width_line)
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def get_h_label():
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label = TexMobject("h")
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height_line = self.height_line
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label.match_color(height_line)
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label.set_height(min(height_line.get_height(), 0.3))
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label.set_stroke(BLACK, 3, background=True)
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label.next_to(height_line, RIGHT, SMALL_BUFF)
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return label
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self.h_label = updating_mobject_from_func(get_h_label)
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def get_w_label():
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label = TexMobject("w")
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width_line = self.width_line
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label.match_color(width_line)
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label.next_to(width_line, DOWN, SMALL_BUFF)
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return label
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self.w_label = updating_mobject_from_func(get_w_label)
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self.add(r_line, theta_label, arc, self.radius_line)
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self.play(
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FadeInFromDown(tan_eq),
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theta_tracker.set_value, 20 * DEGREES,
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)
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self.wait()
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self.tan_eq = tan_eq
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self.theta_tracker = theta_tracker
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def show_fraction(self):
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height_line = self.height_line
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width_line = self.width_line
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h_label = self.h_label
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w_label = self.w_label
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tan_eq = self.tan_eq
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rhs = TexMobject(
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"{\\text{height}", "\\over", "\\text{width}}"
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)
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rhs.next_to(tan_eq, RIGHT)
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rhs.get_part_by_tex("height").match_color(height_line)
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rhs.get_part_by_tex("width").match_color(width_line)
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for mob in [height_line, width_line, h_label, w_label]:
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mob.update()
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self.play(
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ShowCreation(height_line.copy().clear_updaters(), remover=True),
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FadeInFrom(h_label.copy().clear_updaters(), RIGHT, remover=True),
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Write(rhs[:2])
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)
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self.add(height_line, h_label)
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self.play(
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ShowCreation(width_line.copy().clear_updaters(), remover=True),
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FadeInFrom(w_label.copy().clear_updaters(), UP, remover=True),
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self.r_label.fade, 1,
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Write(rhs[2])
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)
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self.add(width_line, w_label)
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self.wait()
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self.rhs = rhs
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def show_fraction_approximation(self):
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theta_tracker = self.theta_tracker
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approx_rhs = TexMobject(
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"\\approx", "{\\theta", "\\over", "1}",
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)
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height, over1, width = self.rhs
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approx, theta, over2, one = approx_rhs
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approx_rhs.set_color_by_tex("\\theta", RED)
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approx_rhs.next_to(self.rhs, RIGHT, MED_SMALL_BUFF)
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self.play(theta_tracker.set_value, 5 * DEGREES)
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self.play(Write(VGroup(approx, over2)))
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self.wait()
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self.play(Indicate(width))
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self.play(TransformFromCopy(width, one))
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self.wait()
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self.play(Indicate(height))
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self.play(TransformFromCopy(height, theta))
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self.wait()
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class TangentTaylorSeries(Scene):
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def construct(self):
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pass
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