def show_sin_thetas(self):
pc = Line(self.p_point, self.c_point)
mob = Mobject(self.theta, self.d_mob).copy()
mob.ingest_submobjects()
triplets = [
(pc, "D\\sin(\\theta)", 0.5),
(self.y_line, "D\\sin^2(\\theta)", 0.7),
]
for line, tex, scale in triplets:
trig_mob = TexMobject(tex)
trig_mob.scale_to_fit_width(
scale*line.get_length()
)
trig_mob.shift(-1.2*trig_mob.get_top())
trig_mob.rotate(line.get_angle())
trig_mob.shift(line.get_center())
if line is self.y_line:
trig_mob.shift(0.1*UP)
self.play(Transform(mob, trig_mob))
self.add(trig_mob)
self.dither()
self.remove(mob)
self.d_sin_squared_theta = trig_mob
def get_vector_label(self,
vector,
label,
direction="left",
rotate=False,
color=None,
label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject):
if len(label) == 1:
label = "\\vec{\\textbf{%s}}" % label
label = TexMobject(label)
if color is None:
color = vector.get_color()
label.highlight(color)
label.scale(label_scale_factor)
label.add_background_rectangle()
angle = vector.get_angle()
if not rotate:
label.rotate(-angle)
if direction is "left":
label.shift(-label.get_bottom() + 0.1 * UP)
else:
label.shift(-label.get_top() + 0.1 * DOWN)
label.rotate(angle)
label.shift((vector.get_end() - vector.get_start()) / 2)
return label
def get_vector_label(self, vector, label,
direction = "left",
rotate = False,
color = None,
label_scale_factor = VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject):
if len(label) == 1:
label = "\\vec{\\textbf{%s}}"%label
label = TexMobject(label)
if color is None:
color = vector.get_color()
label.highlight(color)
label.scale(label_scale_factor)
label.add_background_rectangle()
angle = vector.get_angle()
if not rotate:
label.rotate(-angle)
if direction is "left":
label.shift(-label.get_bottom() + 0.1*UP)
else:
label.shift(-label.get_top() + 0.1*DOWN)
label.rotate(angle)
label.shift((vector.get_end() - vector.get_start())/2)
return label
def show_sin_thetas(self):
pc = Line(self.p_point, self.c_point)
mob = Mobject(self.theta, self.d_mob).copy()
mob.ingest_submobjects()
triplets = [
(pc, "D\\sin(\\theta)", 0.5),
(self.y_line, "D\\sin^2(\\theta)", 0.7),
]
for line, tex, scale in triplets:
trig_mob = TexMobject(tex)
trig_mob.scale_to_fit_width(
scale*line.get_length()
)
trig_mob.shift(-1.2*trig_mob.get_top())
trig_mob.rotate(line.get_angle())
trig_mob.shift(line.get_center())
if line is self.y_line:
trig_mob.shift(0.1*UP)
self.play(Transform(mob, trig_mob))
self.add(trig_mob)
self.wait()
self.remove(mob)
self.d_sin_squared_theta = trig_mob
def ask_about_probability_p3_lands_in_this_arc(self):
arc = self.arc
arrow = Vector(LEFT, color = BLUE)
arrow.next_to(arc.get_center(), RIGHT, MED_LARGE_BUFF)
question = TextMobject("Probability of landing \\\\ in this arc?")
question.scale(0.8)
question.next_to(arrow, RIGHT)
question.shift_onto_screen()
question.shift(SMALL_BUFF*UP)
answer = TexMobject(
"{\\text{Length of arc}", "\\over",
"\\text{Circumference}}"
)
answer.highlight_by_tex("arc", BLUE)
answer.scale(0.8)
answer.next_to(arrow, RIGHT)
equals = TexMobject("=")
equals.rotate(np.pi/2)
equals.next_to(answer, UP, buff = 0.35)
self.play(FadeIn(question), GrowArrow(arrow))
self.have_p3_jump_around_randomly(15)
self.play(
question.next_to, answer, UP, LARGE_BUFF,
Write(equals),
FadeIn(answer)
)
self.have_p3_jump_around_randomly(4)
angles = self.get_point_mob_angles()
self.change_point_mobs(
[0, 0, 1.35*np.pi - angles[2]],
run_time = 0,
)
self.dither()
question.add(equals)
self.arc_prob_question = question
self.arc_prob = answer
self.arc_size_arrow = arrow
def draw_triangle(self):
hyp_length = TexMobject("u", "^2", "+", "v", "^2")
hyp_length.highlight_by_tex("u", U_COLOR)
hyp_length.highlight_by_tex("v", V_COLOR)
hyp_length.add_background_rectangle()
line = self.square_line
hyp_length.next_to(line.get_center(), UP, SMALL_BUFF)
hyp_length.rotate(line.get_angle(), about_point=line.get_center())
triangle = Polygon(
ORIGIN,
RIGHT,
RIGHT + UP,
stroke_width=0,
fill_color=MAROON_B,
fill_opacity=0.5,
)
triangle.replace(line, stretch=True)
self.play(Write(hyp_length))
self.dither()
self.play(FadeIn(triangle))
self.dither()
def construct(self):
#self.force_skipping()
bubble = SVGMobject(file_name = "thought_bubble",
initial_scale_factor = 0.31)
bubble.set_color(WHITE)
bubble.stretch(1.25, 0)
bubble.to_corner(DOWN+RIGHT)
self.play(ShowCreation(VGroup(*bubble[:2])))
self.play(ShowCreation(bubble[2]))
self.dither()
subbubbles = self.make_fractal(bubble[-1], [0.8*LEFT, 0.8*RIGHT])
self.play(ShowCreation(subbubbles, submobject_mode = "all_at_once", run_time = 2))
self.dither()
main_rect = Rectangle(width = 2*SPACE_WIDTH-1, height = 2*SPACE_HEIGHT-1)
rect_template = main_rect.copy()
rect_template.stretch_about_point(0.5, 1, rect_template.get_edge_center(UP))
subrects = self.make_fractal(rect_template, [0.9*LEFT, 0.9*RIGHT], ratio = (0.45, 0.8, 0.6))
self.play(ReplacementTransform(bubble[-1], main_rect),
ReplacementTransform(subbubbles, subrects),
bubble[0].behind_edge, DOWN,
bubble[1].behind_edge, DOWN,
run_time = 2)
#self.dither()
implications = TexMobject("\Rightarrow\Leftarrow")
implications.arrange_submobjects(DOWN, buff = 0.5)
implications.rotate(-np.pi/2)
contradiction = VGroup(
TexMobject("X\\in X"),
implications,
TexMobject("X\\not\\in X"),
)
contradiction.arrange_submobjects(DOWN)
contradiction.to_corner(LEFT+DOWN, buff = 1)
contradiction.shift(RIGHT)
contradiction.add(implications[1])
implications.remove(implications[1])
self.revert_to_original_skipping_status()
#self.dither()
self.play(FadeIn(contradiction, submobject_mode = "lagged_start"))
#self.dither()
questionmarks = TextMobject("???")
questionmarks.next_to(contradiction, buff = 0.5)
#self.play(Write(questionmarks))
#self.dither()
#contradiction.add(questionmarks)
cross = Cross().set_color(RED)
cross.scale((
contradiction.get_width() / cross.get_width(),
contradiction.get_height() / cross.get_height(),
1,
))
cross.move_to(contradiction)
title = TextMobject("Set Theory").scale(1.3).to_edge(UP)
division = DashedLine(title.get_edge_center(DOWN) + 0.2*DOWN, SPACE_HEIGHT*DOWN)
self.play(
contradiction.highlight, DARK_GREY,
ShowCreation(cross),
)
axioms = TextMobject("Axioms")
axioms.next_to(division)
self.play(Write(axioms))
self.dither()
left_rect, right_rect = [], []
for rect in subrects:
if rect.get_center()[0] < 0: left_rect.append(rect)
else: right_rect.append(rect)
left_rect = VGroup(*left_rect)
right_rect = VGroup(*right_rect)
self.play(FadeOut(VGroup(right_rect, main_rect, contradiction, cross)))
self.play(
ShowCreation(division),
UnapplyMethod(title.behind_edge, UP),
left_rect.to_edge, DOWN, 0.8,
)
self.dither()
theory_of_infinity = TextMobject("Theory of Infinity").highlight(BLUE)
foundations_of_mathematics = TextMobject("Foundations of\\\\ Mathematics",
alignment = "\\raggedright")
theory_of_infinity.next_to(division, LEFT, aligned_edge = UP)
foundations_of_mathematics.next_to(division, RIGHT, aligned_edge = UP)
VGroup(theory_of_infinity, foundations_of_mathematics).shift(0.2*DOWN)
self.play(FadeIn(theory_of_infinity), run_time = 2, submobject_mode = "lagged_start")
self.dither()
self.play(FadeIn(foundations_of_mathematics), run_time = 2, submobject_mode = "lagged_start")
self.dither()
