def construct(self):
v_color = MAROON_C
w_color = BLUE
definition = TextMobject("""
The ``span'' of $\\vec{\\textbf{v}}$ and
$\\vec{\\textbf{w}}$ is the \\\\ set of all their
linear combinations.
""")
definition.scale_to_fit_width(2*SPACE_WIDTH-1)
definition.to_edge(UP)
def_mobs = np.array(definition.split())
VMobject(*def_mobs[4:4+4]).highlight(PINK)
VMobject(*def_mobs[11:11+2]).highlight(v_color)
VMobject(*def_mobs[16:16+2]).highlight(w_color)
VMobject(*def_mobs[-19:-1]).highlight(YELLOW)
equation = TexMobject([
"a", "\\vec{\\textbf{v}}", "+", "b", "\\vec{\\textbf{w}}"
])
equation.arrange_submobjects(buff = 0.1, aligned_edge = DOWN)
equation.split()[1].highlight(v_color)
equation.split()[4].highlight(w_color)
a, b = np.array(equation.split())[[0, 3]]
equation.scale(2)
equation.next_to(definition, DOWN, buff = 1)
vary_words = TextMobject(
"Let $a$ and $b$ vary \\\\ over all real numbers"
)
vary_words.scale(1.5)
vary_words.next_to(equation, DOWN, buff = 2)
arrows = [
Arrow(vary_words, letter)
for letter in a, b
]
self.play(Write(definition))
self.play(Write(equation))
self.dither()
self.play(
FadeIn(vary_words),
ShowCreation(VMobject(*arrows))
)
self.dither()
def construct(self):
v_color = MAROON_C
w_color = BLUE
words = TextMobject([
"``Linear combination'' of",
"$\\vec{\\textbf{v}}$",
"and",
"$\\vec{\\textbf{w}}$"
])
words.split()[1].highlight(v_color)
words.split()[3].highlight(w_color)
words.scale_to_fit_width(2*SPACE_WIDTH - 1)
words.to_edge(UP)
equation = TexMobject([
"a", "\\vec{\\textbf{v}}", "+", "b", "\\vec{\\textbf{w}}"
])
equation.arrange_submobjects(buff = 0.1, aligned_edge = DOWN)
equation.split()[1].highlight(v_color)
equation.split()[4].highlight(w_color)
a, b = np.array(equation.split())[[0, 3]]
equation.scale(2)
equation.next_to(words, DOWN, buff = 1)
scalars_word = TextMobject("Scalars")
scalars_word.scale(1.5)
scalars_word.next_to(equation, DOWN, buff = 2)
arrows = [
Arrow(scalars_word, letter)
for letter in a, b
]
self.add(equation)
self.play(Write(words))
self.play(
ShowCreation(VMobject(*arrows)),
Write(scalars_word)
)
self.dither(2)
def construct(self):
v_color = MAROON_C
w_color = BLUE
definition = TextMobject("""
The ``span'' of $\\vec{\\textbf{v}}$ and
$\\vec{\\textbf{w}}$ is the \\\\ set of all their
linear combinations.
""")
definition.scale_to_fit_width(2 * SPACE_WIDTH - 1)
definition.to_edge(UP)
def_mobs = np.array(definition.split())
VMobject(*def_mobs[4:4 + 4]).highlight(PINK)
VMobject(*def_mobs[11:11 + 2]).highlight(v_color)
VMobject(*def_mobs[16:16 + 2]).highlight(w_color)
VMobject(*def_mobs[-19:-1]).highlight(YELLOW)
equation = TexMobject(
["a", "\\vec{\\textbf{v}}", "+", "b", "\\vec{\\textbf{w}}"])
equation.arrange_submobjects(buff=0.1, aligned_edge=DOWN)
equation.split()[1].highlight(v_color)
equation.split()[4].highlight(w_color)
a, b = np.array(equation.split())[[0, 3]]
equation.scale(2)
equation.next_to(definition, DOWN, buff=1)
vary_words = TextMobject(
"Let $a$ and $b$ vary \\\\ over all real numbers")
vary_words.scale(1.5)
vary_words.next_to(equation, DOWN, buff=2)
arrows = [Arrow(vary_words, letter) for letter in a, b]
self.play(Write(definition))
self.play(Write(equation))
self.dither()
self.play(FadeIn(vary_words), ShowCreation(VMobject(*arrows)))
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()
