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Finished large ExplainTrigFunctionDistances scene
This commit is contained in:
Grant Sanderson
parent
e153b169aa
commit
b1eb9a135b
1 changed files with 460 additions and 10 deletions
470
tattoo.py
470
tattoo.py
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@ -41,7 +41,7 @@ class TrigRepresentationsScene(Scene):
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def setup(self):
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self.init_axes()
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self.init_circle()
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self.init_theta_mobs()
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self.init_theta_group()
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def init_axes(self):
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self.axes = Axes(
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@ -57,9 +57,9 @@ class TrigRepresentationsScene(Scene):
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)
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self.add(self.circle)
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def init_theta_mobs(self):
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self.theta_mobs = self.get_theta_mobs()
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self.add(self.theta_mobs)
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def init_theta_group(self):
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self.theta_group = self.get_theta_group()
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self.add(self.theta_group)
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def add_trig_lines(self, *funcs, **kwargs):
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lines = VGroup(*[
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@ -68,7 +68,7 @@ class TrigRepresentationsScene(Scene):
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])
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self.add(*lines)
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def get_theta_mobs(self):
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def get_theta_group(self):
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arc = Arc(
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self.theta_value,
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radius = self.arc_radius,
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@ -147,7 +147,7 @@ class IntroduceCSC(TrigRepresentationsScene):
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csc_of_theta.next_to, brace, LEFT,
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path_arc = np.pi/2,
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)
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self.play(Write(self.theta_mobs, run_time = 1))
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self.play(Write(self.theta_group, run_time = 1))
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self.play(ShowCreation(cot_line))
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self.play(
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ShowCreation(csc_line),
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@ -155,10 +155,460 @@ class IntroduceCSC(TrigRepresentationsScene):
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)
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self.dither(3)
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class TeachObscureTrigFunctions(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"$\\sec(\\theta)$, ",
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"$\\csc(\\theta)$, ",
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"$\\cot(\\theta)$",
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)
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content = self.teacher.bubble.content.copy()
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self.change_student_modes(*["confused"]*3)
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self.student_says(
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"But why?",
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target_mode = "pleading",
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added_anims = [content.to_corner, UP+RIGHT]
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)
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self.dither()
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self.play(self.get_teacher().change_mode, "pondering")
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self.dither(3)
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class CanYouExplainTheTattoo(TeacherStudentsScene):
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def construct(self):
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self.student_says("""
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Wait, can you explain
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the actual tattoo here?
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""")
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self.random_blink()
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self.play(self.get_teacher().change_mode, "hooray")
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self.dither()
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class ExplainTrigFunctionDistances(TrigRepresentationsScene, PiCreatureScene):
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CONFIG = {
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"use_morty" : False,
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"alt_theta_val" : 2*np.pi/5,
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}
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def setup(self):
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PiCreatureScene.setup(self)
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TrigRepresentationsScene.setup(self)
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def construct(self):
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self.introduce_angle()
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self.show_sine_and_cosine()
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self.show_tangent_and_cotangent()
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self.show_secant_and_cosecant()
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self.explain_cosecant()
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self.summarize_full_group()
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def introduce_angle(self):
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self.remove(self.circle)
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self.remove(self.theta_group)
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line, arc, theta, dot = self.theta_group
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line.rotate(-self.theta_value)
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brace = Brace(line, UP, buff = SMALL_BUFF)
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one = brace.get_text("1", buff = SMALL_BUFF)
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VGroup(line, brace, one).rotate(self.theta_value)
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one.rotate_in_place(-self.theta_value)
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self.circle.rotate(self.theta_value)
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words = TextMobject("Corresponding point")
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words.next_to(dot, UP+RIGHT, buff = 1.5*LARGE_BUFF)
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words.shift_onto_screen()
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arrow = Arrow(words.get_bottom(), dot, buff = SMALL_BUFF)
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self.play(
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ShowCreation(line),
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ShowCreation(arc),
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)
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self.play(Write(theta))
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self.play(self.pi_creature.change_mode, "pondering")
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self.play(
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ShowCreation(self.circle),
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Rotating(line, rate_func = smooth, in_place = False),
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run_time = 2
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)
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self.play(
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Write(words),
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ShowCreation(arrow),
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ShowCreation(dot)
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)
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self.dither()
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self.play(
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GrowFromCenter(brace),
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Write(one)
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)
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self.dither(2)
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self.play(*map(FadeOut, [
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words, arrow, brace, one
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]))
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self.radial_line_label = VGroup(brace, one)
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def show_sine_and_cosine(self):
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sin_line, sin_brace, sin_text = sin_group = self.get_line_brace_text("sin")
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cos_line, cos_brace, cos_text = cos_group = self.get_line_brace_text("cos")
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self.play(ShowCreation(sin_line))
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self.play(
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GrowFromCenter(sin_brace),
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Write(sin_text),
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)
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self.play(self.pi_creature.change_mode, "happy")
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self.play(ShowCreation(cos_line))
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self.play(
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GrowFromCenter(cos_brace),
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Write(cos_text),
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)
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self.dither()
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self.change_mode("well")
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original_theta_value = self.theta_value
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self.theta_value = self.alt_theta_val
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sin_group.target = self.get_line_brace_text("sin")
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cos_group.target = self.get_line_brace_text("cos")
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self.theta_group.target = self.get_theta_group()
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self.play(
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*map(MoveToTarget,
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[sin_group, cos_group, self.theta_group]
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),
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path_arc = self.theta_value - original_theta_value,
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rate_func = there_and_back,
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run_time = 5
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)
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self.theta_value = original_theta_value
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self.change_mode("happy")
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self.dither()
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self.sin_group, self.cos_group = sin_group, cos_group
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def show_tangent_and_cotangent(self):
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tan_group = self.get_line_brace_text("tan")
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cot_group = self.get_line_brace_text("cot")
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tan_text = tan_group[-1]
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cot_text = cot_group[-1]
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line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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line.rotate(self.theta_value)
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line.move_to(self.theta_group[-1])
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line.set_stroke(width = 2)
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sin_tex = "{\\sin(\\theta)}"
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cos_tex = "{\\cos(\\theta)}"
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tan_frac = TexMobject("= \\frac" + sin_tex + cos_tex)
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cot_frac = TexMobject("= \\frac" + cos_tex + sin_tex)
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tan_frac.to_corner(UP+LEFT)
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tan_frac.shift(2*RIGHT)
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cot_frac.next_to(tan_frac, DOWN)
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self.change_mode("pondering")
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for frac, text in (tan_frac, tan_text), (cot_frac, cot_text):
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VGroup(frac[5], frac[-2]).highlight(YELLOW)
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frac.scale_in_place(0.7)
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text.save_state()
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text.next_to(frac, LEFT)
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self.play(Write(VGroup(text, frac)))
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self.dither()
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self.change_mode("confused")
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self.dither()
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self.play(*map(FadeOut, [
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tan_frac, cot_frac, self.sin_group, self.cos_group
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]))
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self.dither()
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self.play(
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self.theta_group[-1].highlight, YELLOW,
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ShowCreation(line),
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self.pi_creature.change_mode, 'pondering'
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)
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small_lines = VGroup()
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for group in tan_group, cot_group:
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small_line, brace, text = group
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self.play(
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ShowCreation(small_line),
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GrowFromCenter(brace),
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text.restore,
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)
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self.dither()
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small_lines.add(small_line)
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self.play(FadeOut(line), Animation(small_lines))
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original_theta_value = self.theta_value
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self.theta_value = self.alt_theta_val
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tan_group.target = self.get_line_brace_text("tan")
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cot_group.target = self.get_line_brace_text("cot")
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self.theta_group.target = self.get_theta_group()
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self.play(
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*map(MoveToTarget,
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[tan_group, cot_group, self.theta_group]
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),
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path_arc = self.theta_value - original_theta_value,
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rate_func = there_and_back,
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run_time = 5
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)
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self.theta_value = original_theta_value
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self.change_mode("happy")
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self.dither(2)
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self.tangent_line = self.get_tangent_line()
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self.add(self.tangent_line)
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self.play(*it.chain(*[
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map(FadeOut, [tan_group, cot_group]),
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[Animation(self.theta_group[-1])]
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]))
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def show_secant_and_cosecant(self):
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sec_group = self.get_line_brace_text("sec")
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csc_group = self.get_line_brace_text("csc")
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sec_line, sec_brace, sec_text = sec_group
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csc_line, csc_brace, csc_text = csc_group
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sec_frac = TexMobject("= \\frac{1}{\\cos(\\theta)}")
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sec_frac.to_corner(UP+LEFT).shift(2*RIGHT)
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csc_frac = TexMobject("= \\frac{1}{\\sin(\\theta)}")
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csc_frac.next_to(sec_frac, DOWN)
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sec_dot, csc_dot = [
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Dot(line.get_end(), color = line.get_color())
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for line in sec_line, csc_line
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]
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sec_group.add(sec_dot)
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csc_group.add(csc_dot)
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for text, frac in (sec_text, sec_frac), (csc_text, csc_frac):
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frac[-2].highlight(YELLOW)
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frac.scale_in_place(0.7)
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text.save_state()
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text.next_to(frac, LEFT)
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frac.add_to_back(text.copy())
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self.play(
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Write(frac),
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self.pi_creature.change_mode, "erm"
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)
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self.dither()
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self.dither()
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for group in sec_group, csc_group:
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line, brace, text, dot = group
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dot.save_state()
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dot.move_to(text)
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dot.set_fill(opacity = 0)
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self.play(dot.restore)
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self.dither()
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self.play(
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ShowCreation(line),
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GrowFromCenter(brace),
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text.restore,
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self.pi_creature.change_mode, "pondering"
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)
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self.dither()
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original_theta_value = self.theta_value
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self.theta_value = self.alt_theta_val
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sec_group.target = self.get_line_brace_text("sec")
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csc_group.target = self.get_line_brace_text("csc")
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for group in sec_group, csc_group:
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line = group.target[0]
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group.target.add(
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Dot(line.get_end(), color = line.get_color())
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)
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self.theta_group.target = self.get_theta_group()
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self.tangent_line.target = self.get_tangent_line()
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self.play(
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*map(MoveToTarget,
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[sec_group, csc_group, self.tangent_line, self.theta_group]
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),
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path_arc = self.theta_value - original_theta_value,
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rate_func = there_and_back,
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run_time = 5
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)
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self.theta_value = original_theta_value
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self.change_mode("confused")
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self.dither(2)
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self.play(*map(FadeOut, [
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sec_group, sec_frac
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]))
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self.csc_group = csc_group
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self.csc_frac =csc_frac
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def explain_cosecant(self):
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sin_group = self.get_line_brace_text("sin")
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sin_line, sin_brace, sin_text = sin_group
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csc_line, csc_brace, csc_text, csc_dot = self.csc_group
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csc_subgroup = VGroup(csc_brace, csc_text)
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arc_theta = VGroup(*self.theta_group[1:3]).copy()
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arc_theta.rotate(-np.pi/2)
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arc_theta.shift(csc_line.get_end())
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arc_theta[1].rotate_in_place(np.pi/2)
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radial_line = self.theta_group[0]
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tri1 = Polygon(
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ORIGIN, radial_line.get_end(), sin_line.get_end(),
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color = GREEN
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)
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tri2 = Polygon(
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csc_line.get_end(), ORIGIN, radial_line.get_end(),
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color = GREEN
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)
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opp_over_hyp = TexMobject(
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"\\frac{\\text{Opposite}}{\\text{Hypotenuse}} ="
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)
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frac1 = TexMobject("\\frac{\\sin(\\theta)}{1}")
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frac1.next_to(opp_over_hyp)
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frac1[-4].highlight(YELLOW)
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frac2 = TexMobject("= \\frac{1}{\\csc(\\theta)}")
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frac2.next_to(frac1)
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frac2[-2].highlight(YELLOW)
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frac_group = VGroup(opp_over_hyp, frac1, frac2)
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frac_group.scale_to_fit_width(SPACE_WIDTH-1)
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frac_group.next_to(ORIGIN, RIGHT).to_edge(UP)
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one_brace, one = self.radial_line_label
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one.move_to(one_brace.get_center_of_mass())
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self.play(ShowCreation(tri1))
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self.play(
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ApplyMethod(tri1.rotate_in_place, np.pi/12, rate_func = wiggle),
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self.pi_creature.change_mode, "thinking"
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)
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self.dither()
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tri1.save_state()
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self.play(Transform(tri1, tri2, path_arc = np.pi/2))
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self.play(Write(arc_theta))
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self.dither(2)
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self.play(Write(opp_over_hyp))
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self.dither()
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csc_subgroup.save_state()
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self.play(
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tri1.restore,
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csc_subgroup.fade, 0.7
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)
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self.play(
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ShowCreation(sin_line),
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GrowFromCenter(sin_brace),
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Write(sin_text)
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)
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self.dither()
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self.play(Write(one))
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self.dither()
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self.play(Write(frac1))
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self.dither()
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self.play(
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Transform(tri1, tri2),
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FadeOut(sin_group)
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)
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self.play(
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radial_line.rotate_in_place, np.pi/12,
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rate_func = wiggle
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)
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self.dither()
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self.play(csc_subgroup.restore)
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self.dither()
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self.play(Write(frac2))
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self.change_mode("happy")
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self.play(FadeOut(opp_over_hyp))
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self.reciprocate(frac1, frac2)
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self.play(*map(FadeOut, [
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one, self.csc_group, tri1,
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frac1, frac2, self.csc_frac,
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arc_theta
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]))
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def reciprocate(self, frac1, frac2):
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# Not general, meant only for these definitions:
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# frac1 = TexMobject("\\frac{\\sin(\\theta)}{1}")
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# frac2 = TexMobject("= \\frac{1}{\\csc(\\theta)}")
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num1 = VGroup(*frac1[:6])
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dem1 = frac1[-1]
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num2 = frac2[1]
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dem2 = VGroup(*frac2[-6:])
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group = VGroup(frac1, frac2)
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self.play(
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group.scale, 1/0.7,
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group.to_corner, UP+RIGHT,
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)
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self.play(
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num1.move_to, dem1,
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dem1.move_to, num1,
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num2.move_to, dem2,
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dem2.move_to, num2,
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path_arc = np.pi
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)
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self.dither()
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self.play(
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dem2.move_to, frac2[-2],
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VGroup(*frac2[-2:]).highlight, BLACK
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)
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def summarize_full_group(self):
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scale_factor = 1.5
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theta_subgroup = VGroup(self.theta_group[0], self.theta_group[-1])
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self.play(
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self.circle.scale, scale_factor,
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self.axes.scale, scale_factor,
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theta_subgroup.scale, scale_factor,
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)
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self.unit_length *= scale_factor
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to_fade = VGroup()
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for func_name in ["sin", "tan", "sec", "cos", "cot", "csc"]:
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line, brace, text = self.get_line_brace_text(func_name)
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angle = line.get_angle()
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if np.cos(angle) < 0:
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angle += np.pi
|
||||
if func_name is "sin":
|
||||
target = line.get_center()+0.2*LEFT+0.1*DOWN
|
||||
else:
|
||||
target = VGroup(brace, line).get_center_of_mass()
|
||||
if func_name in ["sin", "cos"]:
|
||||
text.scale(0.75)
|
||||
text.rotate(angle)
|
||||
text.move_to(target)
|
||||
line.set_stroke(width = 6)
|
||||
self.play(
|
||||
ShowCreation(line),
|
||||
Write(text, run_time = 1)
|
||||
)
|
||||
if func_name is "sec":
|
||||
self.dither()
|
||||
if func_name in ["sec", "csc", "cot"]:
|
||||
to_fade.add(line, text)
|
||||
self.dither()
|
||||
self.change_mode("surprised")
|
||||
self.dither(2)
|
||||
self.remove(self.tangent_line)
|
||||
self.play(
|
||||
FadeOut(to_fade),
|
||||
self.pi_creature.change_mode, "sassy"
|
||||
)
|
||||
self.dither(2)
|
||||
|
||||
def get_line_brace_text(self, func_name = "sin"):
|
||||
line = self.get_trig_line(func_name)
|
||||
angle = line.get_angle()
|
||||
vect = rotate_vector(UP, angle)
|
||||
vect = np.round(vect, 1)
|
||||
if (vect[1] < 0) ^ (func_name is "sec"):
|
||||
vect = -vect
|
||||
angle += np.pi
|
||||
brace = Brace(line, vect)
|
||||
brace.highlight(line.get_color())
|
||||
text = TexMobject("\\%s(\\theta)"%func_name)
|
||||
text.scale(0.75)
|
||||
text[-2].highlight(self.theta_color)
|
||||
text.add_background_rectangle()
|
||||
text.next_to(brace.get_center(), vect, buff = 1.2*MED_BUFF)
|
||||
return VGroup(line, brace, text)
|
||||
|
||||
def get_tangent_line(self):
|
||||
return Line(
|
||||
self.unit_length*(1./np.sin(self.theta_value))*UP,
|
||||
self.unit_length*(1./np.cos(self.theta_value))*RIGHT,
|
||||
color = GREY
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue