def construct(self):
words = map(TextMobject, [
"Just brushing up",
"Has yet to take the course",
"Supplementing course concurrently",
])
students = VMobject(*[
Randolph(color = c)
for c in BLUE_D, BLUE_C, BLUE_E
])
modes = ["pondering", "speaking_looking_left", "sassy"]
students.arrange_submobjects(RIGHT)
students.scale(0.8)
students.center().to_edge(DOWN)
last_word, last_arrow = None, None
for word, student, mode in zip(words, students.split(), modes):
word.shift(2*UP)
arrow = Arrow(word, student)
if last_word:
word_anim = Transform(last_word, word)
arrow_anim = Transform(last_arrow, arrow)
else:
word_anim = Write(word, run_time = 1)
arrow_anim = ShowCreation(arrow, submobject_mode = "one_at_a_time")
last_word = word
last_arrow = arrow
self.play(
word_anim, arrow_anim,
ApplyMethod(student.change_mode, mode)
)
self.play(Blink(student))
self.dither()
self.dither()
def construct(self):
physy = Physicist()
mathy = Mathematician(mode = "pondering")
compy = ComputerScientist()
creatures = [physy, compy, mathy]
physy.title = TextMobject("Physics student").to_corner(DOWN+LEFT)
compy.title = TextMobject("CS student").to_corner(DOWN+RIGHT)
mathy.title = TextMobject("Mathematician").to_edge(DOWN)
names = VMobject(physy.title, mathy.title, compy.title)
names.arrange_submobjects(RIGHT, buff = 1)
names.to_corner(DOWN+LEFT)
for pi in creatures:
pi.next_to(pi.title, UP)
vector, symbol, coordinates = self.intro_vector()
for pi in creatures:
self.play(
Write(pi.title),
FadeIn(pi),
run_time = 1
)
self.dither(2)
self.remove(symbol, coordinates)
self.physics_conception(creatures, vector)
self.cs_conception(creatures)
self.handle_mathy(creatures)
def add_scaling(self, arrows, syms, arrays):
s_arrows = VMobject(
TexMobject("2"), Vector([1, 1]).highlight(YELLOW),
TexMobject("="), Vector([2, 2]).highlight(WHITE)
)
s_arrows.arrange_submobjects(RIGHT)
s_arrows.scale(0.75)
s_arrows.next_to(arrows, DOWN)
s_arrays = VMobject(
TexMobject("2"),
matrix_to_mobject([3, -5]).highlight(YELLOW),
TextMobject("="),
matrix_to_mobject(["2(3)", "2(-5)"])
)
s_arrays.arrange_submobjects(RIGHT)
s_arrays.scale(0.5)
s_arrays.next_to(arrays, DOWN)
s_syms = TexMobject(["2", "\\vec{\\textbf{v}}"])
s_syms.split()[-1].highlight(YELLOW)
s_syms.next_to(syms, DOWN)
self.play(
Write(s_arrows), Write(s_arrays), Write(s_syms),
run_time = 2
)
self.dither()
def construct(self):
matrix = Matrix([
[2, 0],
[-1, 1],
[-2, 1],
])
matrix.highlight_columns(X_COLOR, Y_COLOR)
brace = Brace(matrix)
words = VMobject(
TextMobject("Span", "of columns"),
TexMobject("\\Updownarrow"),
TextMobject("``Column space''")
)
words.arrange_submobjects(DOWN, buff = 0.1)
words.next_to(brace, DOWN)
words[0][0].highlight(PINK)
words[2].highlight(TEAL)
words[0].add_background_rectangle()
words[2].add_background_rectangle()
VMobject(matrix, brace, words).center()
self.add(matrix)
self.play(
GrowFromCenter(brace),
Write(words, run_time = 2)
)
self.dither()
def construct(self):
v_sum = VMobject(
Vector([1, 1], color = YELLOW),
Vector([3, 1], color = BLUE).shift(RIGHT+UP),
Vector([4, 2], color = GREEN),
)
scalar_multiplication = VMobject(
TexMobject("2 \\cdot "),
Vector([1, 1]),
TexMobject("="),
Vector([2, 2], color = WHITE)
)
scalar_multiplication.arrange_submobjects(RIGHT)
both = VMobject(v_sum, scalar_multiplication)
both.arrange_submobjects(RIGHT, buff = 1)
both.shift(2*DOWN)
self.add(both)
UpcomingSeriesOfVidoes.construct(self)
last_video = self.mobjects[-1]
self.play(ApplyMethod(last_video.highlight, YELLOW))
self.dither()
everything = VMobject(*self.mobjects)
everything.remove(last_video)
big_last_video = last_video.copy()
big_last_video.center()
big_last_video.scale_to_fit_height(2.5*SPACE_HEIGHT)
big_last_video.set_fill(opacity = 0)
self.play(
ApplyMethod(everything.shift, 2*SPACE_WIDTH*LEFT),
Transform(last_video, big_last_video),
run_time = 2
)
def describe_scalars(self, v, plane):
axes = plane.get_axes()
long_v = Vector(2*v.get_end())
long_minus_v = Vector(-2*v.get_end())
original_v = v.copy()
scaling_word = TextMobject("``Scaling''").to_corner(UP+LEFT)
scaling_word.shift(2*RIGHT)
scalars = VMobject(*map(TexMobject, [
"2,", "\\dfrac{1}{3},", "-1.8,", "\\dots"
]))
scalars.arrange_submobjects(RIGHT, buff = 0.4)
scalars.next_to(scaling_word, DOWN, aligned_edge = LEFT)
scalars_word = TextMobject("``Scalars''")
scalars_word.next_to(scalars, DOWN, aligned_edge = LEFT)
self.remove(plane)
self.add(axes)
self.play(
Write(scaling_word),
Transform(v, long_v),
run_time = 1.5
)
self.play(Transform(v, long_minus_v, run_time = 3))
self.play(Write(scalars))
self.dither()
self.play(Write(scalars_word))
self.play(Transform(v, original_v), run_time = 3)
self.dither(2)
def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff = 2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(
v_array, TexMobject("+"), w_array, TexMobject("="), sum_array
)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2*UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff = 1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(
Write(syms), Write(arrays),
ShowCreation(arrows, submobject_mode = "one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time = 2
)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.dither()
self.play(
ShowCreation(circle),
ApplyMethod(mathy.change_mode, "plain")
)
self.dither()
def construct(self):
mob = VMobject(
TextMobject("Computer graphics"),
TextMobject("Robotics")
)
mob.arrange_submobjects(DOWN, buff = 1)
self.play(Write(mob, run_time = 1))
self.dither()
def construct(self):
arrays = VMobject(*map(matrix_to_mobject, [
[-2, 3], [1, 2], [2, -1], [4, 0]
]))
arrays.arrange_submobjects(buff = 0.4)
arrays.scale(2)
self.play(Write(arrays))
self.dither(2)
def construct(self):
arrow = Vector(2 * UP + RIGHT)
vs = TextMobject("vs.")
array = Matrix([1, 2])
array.highlight(TEAL)
everyone = VMobject(arrow, vs, array)
everyone.arrange_submobjects(RIGHT, buff=0.5)
everyone.scale_to_fit_height(4)
self.add(everyone)
def construct(self):
physy = Physicist()
compy = ComputerScientist()
physy.title = TextMobject("Physics student").to_corner(DOWN+LEFT)
compy.title = TextMobject("CS student").to_corner(DOWN+RIGHT)
for pi in physy, compy:
pi.next_to(pi.title, UP)
self.add(pi, pi.title)
compy_speech = compy.get_bubble("speech")
physy_speech = physy.get_bubble("speech")
arrow = Vector([2, 1])
array = matrix_to_mobject([2, 1])
goes_to = TexMobject("\\Rightarrow")
physy_statement = VMobject(arrow, goes_to, array)
physy_statement.arrange_submobjects(RIGHT)
compy_statement = physy_statement.copy()
compy_statement.arrange_submobjects(LEFT)
physy_speech.position_mobject_inside(physy_statement)
compy_speech.position_mobject_inside(compy_statement)
new_arrow = Vector([2, 1])
x_line = Line(ORIGIN, 2*RIGHT, color = X_COLOR)
y_line = Line(2*RIGHT, 2*RIGHT+UP, color = Y_COLOR)
x_mob = TexMobject("2").next_to(x_line, DOWN)
y_mob = TexMobject("1").next_to(y_line, RIGHT)
new_arrow.add(x_line, y_line, x_mob, y_mob)
back_and_forth = VMobject(
new_arrow,
TexMobject("\\Leftrightarrow"),
matrix_to_mobject([2, 1])
)
back_and_forth.arrange_submobjects(LEFT).center()
self.dither()
self.play(
ApplyMethod(physy.change_mode, "speaking"),
ShowCreation(physy_speech),
Write(physy_statement),
run_time = 1
)
self.play(Blink(compy))
self.play(
ApplyMethod(physy.change_mode, "sassy"),
ApplyMethod(compy.change_mode, "speaking"),
FadeOut(physy_speech),
ShowCreation(compy_speech),
Transform(physy_statement, compy_statement, path_arc = np.pi)
)
self.dither(2)
self.play(
ApplyMethod(physy.change_mode, "pondering"),
ApplyMethod(compy.change_mode, "pondering"),
Transform(compy_speech, VectorizedPoint(compy_speech.get_tip())),
Transform(physy_statement, back_and_forth)
)
self.dither()
def construct(self):
arrow = Vector(2*UP+RIGHT)
vs = TextMobject("vs.")
array = Matrix([1, 2])
array.highlight(TEAL)
everyone = VMobject(arrow, vs, array)
everyone.arrange_submobjects(RIGHT, buff = 0.5)
everyone.scale_to_fit_height(4)
self.add(everyone)
def construct(self):
physy = Physicist()
compy = ComputerScientist()
physy.title = TextMobject("Physics student").to_corner(DOWN+LEFT)
compy.title = TextMobject("CS student").to_corner(DOWN+RIGHT)
for pi in physy, compy:
pi.next_to(pi.title, UP)
self.add(pi, pi.title)
compy_speech = compy.get_bubble(SpeechBubble)
physy_speech = physy.get_bubble(SpeechBubble)
arrow = Vector([2, 1])
array = matrix_to_mobject([2, 1])
goes_to = TexMobject("\\Rightarrow")
physy_statement = VMobject(arrow, goes_to, array)
physy_statement.arrange_submobjects(RIGHT)
compy_statement = physy_statement.copy()
compy_statement.arrange_submobjects(LEFT)
physy_speech.position_mobject_inside(physy_statement)
compy_speech.position_mobject_inside(compy_statement)
new_arrow = Vector([2, 1])
x_line = Line(ORIGIN, 2*RIGHT, color = X_COLOR)
y_line = Line(2*RIGHT, 2*RIGHT+UP, color = Y_COLOR)
x_mob = TexMobject("2").next_to(x_line, DOWN)
y_mob = TexMobject("1").next_to(y_line, RIGHT)
new_arrow.add(x_line, y_line, x_mob, y_mob)
back_and_forth = VMobject(
new_arrow,
TexMobject("\\Leftrightarrow"),
matrix_to_mobject([2, 1])
)
back_and_forth.arrange_submobjects(LEFT).center()
self.wait()
self.play(
ApplyMethod(physy.change_mode, "speaking"),
ShowCreation(physy_speech),
Write(physy_statement),
run_time = 1
)
self.play(Blink(compy))
self.play(
ApplyMethod(physy.change_mode, "sassy"),
ApplyMethod(compy.change_mode, "speaking"),
FadeOut(physy_speech),
ShowCreation(compy_speech),
Transform(physy_statement, compy_statement, path_arc = np.pi)
)
self.wait(2)
self.play(
ApplyMethod(physy.change_mode, "pondering"),
ApplyMethod(compy.change_mode, "pondering"),
Transform(compy_speech, VectorizedPoint(compy_speech.get_tip())),
Transform(physy_statement, back_and_forth)
)
self.wait()
def add_symbols(self):
v = matrix_to_mobject(self.v_coords).highlight(self.v_color)
w = matrix_to_mobject(self.w_coords).highlight(self.w_color)
v.add_background_rectangle()
w.add_background_rectangle()
dot = TexMobject("\\cdot")
eq = VMobject(v, dot, w)
eq.arrange_submobjects(RIGHT, buff=SMALL_BUFF)
eq.to_corner(UP + LEFT)
self.play(Write(eq), run_time=1)
def add_symbols(self):
v = matrix_to_mobject(self.v_coords).highlight(self.v_color)
w = matrix_to_mobject(self.w_coords).highlight(self.w_color)
v.add_background_rectangle()
w.add_background_rectangle()
dot = TexMobject("\\cdot")
eq = VMobject(v, dot, w)
eq.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
eq.to_corner(UP+LEFT)
self.play(Write(eq), run_time = 1)
def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff=2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(v_array, TexMobject("+"), w_array, TexMobject("="),
sum_array)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2 * UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff=1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(Write(syms),
Write(arrays),
ShowCreation(arrows, submobject_mode="one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time=2)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.dither()
self.play(ShowCreation(circle), ApplyMethod(mathy.change_mode,
"plain"))
self.dither()
def construct(self):
v = TexMobject(self.v_str)
v.highlight(YELLOW)
eq = TexMobject("=")
coords = Matrix(["x", "y", "z"])
eq2 = eq.copy()
if self.post_transform:
L, l_paren, r_paren = map(TexMobject, "L()")
parens = VMobject(l_paren, r_paren)
parens.scale(2)
parens.stretch_to_fit_height(
coords.get_height()
)
VMobject(L, l_paren, coords, r_paren).arrange_submobjects(buff = 0.1)
coords.submobjects = [L, l_paren] + coords.submobjects + [r_paren]
lin_comb = VMobject(*map(TexMobject, [
"x", self.i_str, "+",
"y", self.j_str, "+",
"z", self.k_str,
]))
lin_comb.arrange_submobjects(
RIGHT, buff = 0.1,
aligned_edge = ORIGIN if self.post_transform else DOWN
)
lin_comb_parts = np.array(lin_comb.split())
new_x, new_y, new_z = lin_comb_parts[[0, 3, 6]]
i, j, k = lin_comb_parts[[1, 4, 7]]
plusses = lin_comb_parts[[2, 5]]
i.highlight(X_COLOR)
j.highlight(Y_COLOR)
k.highlight(Z_COLOR)
everything = VMobject(v, eq, coords, eq2, lin_comb)
everything.arrange_submobjects(buff = 0.2)
everything.scale_to_fit_width(2*SPACE_WIDTH - 1)
everything.to_edge(DOWN)
if not self.post_transform:
lin_comb.shift(0.35*UP)
self.play(*map(Write, [v, eq, coords]))
self.dither()
self.play(
Transform(
coords.get_entries().copy(),
VMobject(new_x, new_y, new_z),
path_arc = -np.pi,
submobject_mode = "lagged_start"
),
Write(VMobject(*[eq2, i, j, k] + list(plusses))),
run_time = 3
)
self.dither()
def construct(self):
title = TextMobject("Essence of Linear Algebra")
title.highlight(BLUE)
title.to_corner(UP+LEFT)
h_line = Line(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
h_line.next_to(title, DOWN)
h_line.to_edge(LEFT, buff = 0)
chapters = VMobject(*map(TextMobject, [
"Chapter 1: Vectors, what even are they?",
"Chapter 2: Linear combinations, span and bases",
"Chapter 3: Matrices as linear transformations",
"Chapter 4: Matrix multiplication as composition",
"Chapter 5: The determinant",
"Chapter 6: Inverse matrices, column space and null space",
"Chapter 7: Dot products and cross products",
"Chapter 8: Change of basis",
"Chapter 9: Eigenvectors and eigenvalues",
"Chapter 10: Abstract vector spaces",
]))
chapters.arrange_submobjects(DOWN)
chapters.scale(0.7)
chapters.next_to(h_line, DOWN)
self.play(
Write(title),
ShowCreation(h_line)
)
for chapter in chapters.split():
chapter.to_edge(LEFT, buff = 1)
self.play(FadeIn(chapter))
self.dither(2)
entry3 = chapters.split()[2]
added_words = TextMobject("(Personally, I'm most excited \\\\ to do this one)")
added_words.scale(0.5)
added_words.highlight(YELLOW)
added_words.next_to(h_line, DOWN)
added_words.to_edge(RIGHT)
arrow = Arrow(added_words.get_bottom(), entry3)
self.play(
ApplyMethod(entry3.highlight, YELLOW),
ShowCreation(arrow, submobject_mode = "one_at_a_time"),
Write(added_words),
run_time = 1
)
self.dither()
removeable = VMobject(added_words, arrow, h_line, title)
self.play(FadeOut(removeable))
self.remove(removeable)
self.series_of_videos(chapters)
def construct(self):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2 * SPACE_WIDTH / 12.)
icon.set_stroke(color=WHITE, width=0)
icon.set_fill(WHITE, opacity=1)
icons = VMobject(*[icon.copy() for x in range(10)])
icons.submobject_gradient_highlight(BLUE_A, BLUE_D)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
self.play(FadeIn(icons, submobject_mode="lagged_start"), run_time=3)
self.wait()
def construct(self):
title = TextMobject("Questions to ponder")
title.highlight(YELLOW).to_edge(UP)
self.add(title)
questions = VMobject(*map(TextMobject, [
"1. Can you visualize these transformations?",
"2. Can you represent them with matrices?",
"3. How many rows and columns?",
"4. When can you multiply these matrices?",
]))
questions.arrange_submobjects(DOWN, buff = 1, aligned_edge = LEFT)
questions.to_edge(LEFT)
for question in questions.split():
self.play(Write(question, run_time = 1))
self.dither()
def construct(self):
title = TextMobject("Questions to ponder")
title.highlight(YELLOW).to_edge(UP)
self.add(title)
questions = VMobject(*map(TextMobject, [
"1. Can you visualize these transformations?",
"2. Can you represent them with matrices?",
"3. How many rows and columns?",
"4. When can you multiply these matrices?",
]))
questions.arrange_submobjects(DOWN, buff=1, aligned_edge=LEFT)
questions.to_edge(LEFT)
for question in questions.split():
self.play(Write(question, run_time=1))
self.wait()
def construct(self):
matrix = Matrix(np.arange(9).reshape((3, 3)))
vect = Matrix(list("xyz"))
vect.scale_to_fit_height(matrix.get_height())
col1, col2, col3 = columns = [
Matrix(col) for col in matrix.copy().get_mob_matrix().transpose()
]
coords = x, y, z = [m.copy() for m in vect.get_entries().split()]
eq, plus1, plus2 = map(TexMobject, list("=++"))
everything = VMobject(matrix, vect, eq, x, col1, plus1, y, col2, plus2,
z, col3)
everything.arrange_submobjects(buff=0.1)
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
result = VMobject(x, col1, plus1, y, col2, plus2, z, col3)
trips = [
(matrix, DOWN, "Transformation"),
(vect, UP, "Input vector"),
(result, DOWN, "Output vector"),
]
braces = []
for mob, direction, text in trips:
brace = Brace(mob, direction)
words = TextMobject(text)
words.next_to(brace, direction)
brace.add(words)
braces.append(brace)
matrix_brace, vect_brace, result_brace = braces
self.play(*map(Write, [matrix, vect]), run_time=2)
self.play(Write(matrix_brace, run_time=1))
self.play(Write(vect_brace, run_time=1))
sexts = zip(matrix.get_mob_matrix().transpose(), columns,
vect.get_entries().split(), coords, [eq, plus1, plus2],
[X_COLOR, Y_COLOR, Z_COLOR])
for o_col, col, start_coord, coord, sym, color in sexts:
o_col = VMobject(*o_col)
self.play(start_coord.highlight, YELLOW, o_col.highlight, color)
coord.highlight(YELLOW)
col.highlight(color)
self.play(
Write(col.get_brackets()),
Transform(o_col.copy(), col.get_entries(), path_arc=-np.pi),
Transform(start_coord.copy(), coord, path_arc=-np.pi),
Write(sym))
self.wait()
self.play(Write(result_brace, run_time=1))
self.wait()
def construct(self):
title = TextMobject("Essence of Linear Algebra")
title.highlight(BLUE)
title.to_corner(UP + LEFT)
h_line = Line(SPACE_WIDTH * LEFT, SPACE_WIDTH * RIGHT)
h_line.next_to(title, DOWN)
h_line.to_edge(LEFT, buff=0)
chapters = VMobject(*map(TextMobject, [
"Chapter 1: Vectors, what even are they?",
"Chapter 2: Linear combinations, span and bases",
"Chapter 3: Matrices as linear transformations",
"Chapter 4: Matrix multiplication as composition",
"Chapter 5: The determinant",
"Chapter 6: Inverse matrices, column space and null space",
"Chapter 7: Dot products and cross products",
"Chapter 8: Change of basis",
"Chapter 9: Eigenvectors and eigenvalues",
"Chapter 10: Abstract vector spaces",
]))
chapters.arrange_submobjects(DOWN)
chapters.scale(0.7)
chapters.next_to(h_line, DOWN)
self.play(Write(title), ShowCreation(h_line))
for chapter in chapters.split():
chapter.to_edge(LEFT, buff=1)
self.play(FadeIn(chapter))
self.wait(2)
entry3 = chapters.split()[2]
added_words = TextMobject(
"(Personally, I'm most excited \\\\ to do this one)")
added_words.scale(0.5)
added_words.highlight(YELLOW)
added_words.next_to(h_line, DOWN)
added_words.to_edge(RIGHT)
arrow = Arrow(added_words.get_bottom(), entry3)
self.play(ApplyMethod(entry3.highlight, YELLOW),
ShowCreation(arrow, submobject_mode="one_at_a_time"),
Write(added_words),
run_time=1)
self.wait()
removeable = VMobject(added_words, arrow, h_line, title)
self.play(FadeOut(removeable))
self.remove(removeable)
self.series_of_videos(chapters)
def construct(self):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2*SPACE_WIDTH/12.)
icon.set_stroke(color = WHITE, width = 0)
icon.set_fill(WHITE, opacity = 1)
icons = VMobject(*[icon.copy() for x in range(10)])
icons.submobject_gradient_highlight(BLUE_A, BLUE_D)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
self.play(
FadeIn(icons, submobject_mode = "lagged_start"),
run_time = 3
)
self.dither()
def construct(self):
self.setup()
matrix = Matrix(np.array(self.transposed_matrix).transpose())
matrix.highlight_columns(X_COLOR, Y_COLOR)
matrix.next_to(ORIGIN, LEFT).to_edge(UP)
matrix_background = BackgroundRectangle(matrix)
self.play(ShowCreation(matrix_background), Write(matrix))
if self.show_square:
self.add_unit_square(animate = True)
self.add_foreground_mobject(matrix_background, matrix)
self.dither()
self.apply_transposed_matrix([self.transposed_matrix[0], [0, 1]])
self.apply_transposed_matrix([[1, 0], self.transposed_matrix[1]])
self.dither()
if self.show_square:
bottom_brace = Brace(self.i_hat, DOWN)
right_brace = Brace(self.square, RIGHT)
width = TexMobject(str(self.transposed_matrix[0][0]))
height = TexMobject(str(self.transposed_matrix[1][1]))
width.next_to(bottom_brace, DOWN)
height.next_to(right_brace, RIGHT)
for mob in bottom_brace, width, right_brace, height:
mob.add_background_rectangle()
self.play(Write(mob, run_time = 0.5))
self.dither()
width_target, height_target = width.copy(), height.copy()
det = np.linalg.det(self.transposed_matrix)
times, eq_det = map(TexMobject, ["\\times", "=%d"%det])
words = TextMobject("New area $=$")
equation = VMobject(
words, width_target, times, height_target, eq_det
)
equation.arrange_submobjects(RIGHT, buff = 0.2)
equation.next_to(self.square, UP, aligned_edge = LEFT)
equation.shift(0.5*RIGHT)
background_rect = BackgroundRectangle(equation)
self.play(
ShowCreation(background_rect),
Transform(width.copy(), width_target),
Transform(height.copy(), height_target),
*map(Write, [words, times, eq_det])
)
self.dither()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to,
i_array,
TexMobject("=").highlight(BLACK),
j_to,
j_array,
TexMobject("=").highlight(BLACK),
k_to,
k_array,
TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff=0.1)
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(
reduce(lambda a1, a2: np.append(a1, a2, axis=1),
[m.copy().get_mob_matrix() for m in arrays]))
matrix.to_edge(DOWN)
start_entries = reduce(op.add,
map(lambda a: a.get_entries().split(), arrays))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time=1))
self.wait()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes))
self.wait()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to, i_array, TexMobject("=").highlight(BLACK),
j_to, j_array, TexMobject("=").highlight(BLACK),
k_to, k_array, TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff = 0.1)
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(reduce(
lambda a1, a2 : np.append(a1, a2, axis = 1),
[m.copy().get_mob_matrix() for m in arrays]
))
matrix.to_edge(DOWN)
start_entries = reduce(op.add, map(
lambda a : a.get_entries().split(),
arrays
))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time = 1))
self.dither()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes)
)
self.dither()
def construct(self):
morty = Mortimer()
morty.to_corner(DOWN+RIGHT)
morty.look(DOWN+LEFT)
new_morty = morty.copy().change_mode("speaking")
new_morty.look(DOWN+LEFT)
randys = VMobject(*[
Randolph(color = color).scale(0.8)
for color in BLUE_D, BLUE_C, BLUE_E
])
randys.arrange_submobjects(RIGHT)
randys.to_corner(DOWN+LEFT)
randy = randys.split()[1]
speech_bubble = morty.get_bubble(SpeechBubble)
words = TextMobject("Think of some vector...")
speech_bubble.position_mobject_inside(words)
thought_bubble = randy.get_bubble()
arrow = Vector([2, 1]).scale(0.7)
or_word = TextMobject("or")
array = Matrix([2, 1]).scale(0.5)
q_mark = TextMobject("?")
thought = VMobject(arrow, or_word, array, q_mark)
thought.arrange_submobjects(RIGHT, buff = 0.2)
thought_bubble.position_mobject_inside(thought)
thought_bubble.set_fill(BLACK, opacity = 1)
self.add(morty, randys)
self.play(
ShowCreation(speech_bubble),
Transform(morty, new_morty),
Write(words)
)
self.wait(2)
self.play(
FadeOut(speech_bubble),
FadeOut(words),
ApplyMethod(randy.change_mode, "pondering"),
ShowCreation(thought_bubble),
Write(thought)
)
self.wait(2)
def construct(self):
morty = Mortimer()
morty.to_corner(DOWN+RIGHT)
morty.look(DOWN+LEFT)
new_morty = morty.copy().change_mode("speaking")
new_morty.look(DOWN+LEFT)
randys = VMobject(*[
Randolph(color = color).scale(0.8)
for color in BLUE_D, BLUE_C, BLUE_E
])
randys.arrange_submobjects(RIGHT)
randys.to_corner(DOWN+LEFT)
randy = randys.split()[1]
speech_bubble = morty.get_bubble("speech")
words = TextMobject("Think of some vector...")
speech_bubble.position_mobject_inside(words)
thought_bubble = randy.get_bubble()
arrow = Vector([2, 1]).scale(0.7)
or_word = TextMobject("or")
array = Matrix([2, 1]).scale(0.5)
q_mark = TextMobject("?")
thought = VMobject(arrow, or_word, array, q_mark)
thought.arrange_submobjects(RIGHT, buff = 0.2)
thought_bubble.position_mobject_inside(thought)
thought_bubble.set_fill(BLACK, opacity = 1)
self.add(morty, randys)
self.play(
ShowCreation(speech_bubble),
Transform(morty, new_morty),
Write(words)
)
self.dither(2)
self.play(
FadeOut(speech_bubble),
FadeOut(words),
ApplyMethod(randy.change_mode, "pondering"),
ShowCreation(thought_bubble),
Write(thought)
)
self.dither(2)
def construct(self):
icons = [VideoIcon() for x in range(10)]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity=1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
icons = icons.split()
def rate_func_creator(offset):
return lambda a: min(max(2 * (a - offset), 0), 1)
self.play(*[
FadeIn(icon, run_time=5, rate_func=rate_func_creator(offset))
for icon, offset in zip(icons, np.linspace(0, 0.5, len(icons)))
])
self.wait()
def construct(self):
self.setup()
matrix = Matrix(np.array(self.transposed_matrix).transpose())
matrix.highlight_columns(X_COLOR, Y_COLOR)
matrix.next_to(ORIGIN, LEFT).to_edge(UP)
matrix_background = BackgroundRectangle(matrix)
self.play(ShowCreation(matrix_background), Write(matrix))
if self.show_square:
self.add_unit_square(animate=True)
self.add_foreground_mobject(matrix_background, matrix)
self.wait()
self.apply_transposed_matrix([self.transposed_matrix[0], [0, 1]])
self.apply_transposed_matrix([[1, 0], self.transposed_matrix[1]])
self.wait()
if self.show_square:
bottom_brace = Brace(self.i_hat, DOWN)
right_brace = Brace(self.square, RIGHT)
width = TexMobject(str(self.transposed_matrix[0][0]))
height = TexMobject(str(self.transposed_matrix[1][1]))
width.next_to(bottom_brace, DOWN)
height.next_to(right_brace, RIGHT)
for mob in bottom_brace, width, right_brace, height:
mob.add_background_rectangle()
self.play(Write(mob, run_time=0.5))
self.wait()
width_target, height_target = width.copy(), height.copy()
det = np.linalg.det(self.transposed_matrix)
times, eq_det = map(TexMobject, ["\\times", "=%d" % det])
words = TextMobject("New area $=$")
equation = VMobject(words, width_target, times, height_target,
eq_det)
equation.arrange_submobjects(RIGHT, buff=0.2)
equation.next_to(self.square, UP, aligned_edge=LEFT)
equation.shift(0.5 * RIGHT)
background_rect = BackgroundRectangle(equation)
self.play(ShowCreation(background_rect),
Transform(width.copy(), width_target),
Transform(height.copy(), height_target),
*map(Write, [words, times, eq_det]))
self.wait()
def construct(self):
morty = Mortimer(mode = "speaking")
morty.to_corner(DOWN + RIGHT)
bubble = morty.get_bubble(SpeechBubble)
bubble.write("I'm assuming you \\\\ know linear algebra\\dots")
words = bubble.content
bubble.clear()
randys = VMobject(*[
Randolph(color = c)
for c in BLUE_D, BLUE_C, BLUE_E
])
randys.arrange_submobjects(RIGHT)
randys.scale(0.8)
randys.to_corner(DOWN+LEFT)
self.add(randys, morty)
self.play(FadeIn(bubble), Write(words), run_time = 3)
for randy in np.array(randys.split())[[2,0,1]]:
self.play(Blink(randy))
self.dither()
def scale_basis_vectors(self, new_array):
i_hat, j_hat = self.get_basis_vectors()
self.add_vector(i_hat)
i_hat_label = self.label_vector(
i_hat, "\\hat{\\imath}",
color = X_COLOR,
label_scale_factor = 1
)
self.add_vector(j_hat)
j_hat_label = self.label_vector(
j_hat, "\\hat{\\jmath}",
color = Y_COLOR,
label_scale_factor = 1
)
self.dither()
x, y = new_array.get_mob_matrix().flatten()
for coord, v, label, factor, shift_right in [
(x, i_hat, i_hat_label, self.vector_coords[0], False),
(y, j_hat, j_hat_label, self.vector_coords[1], True)
]:
faded_v = v.copy().fade(0.7)
scaled_v = Vector(factor*v.get_end(), color = v.get_color())
scaled_label = VMobject(coord.copy(), label.copy())
scaled_label.arrange_submobjects(RIGHT, buff = 0.1)
scaled_label.move_to(label, DOWN+RIGHT)
scaled_label.shift((scaled_v.get_end()-v.get_end())/2)
coord_copy = coord.copy()
self.play(
Transform(v.copy(), faded_v),
Transform(v, scaled_v),
Transform(VMobject(coord_copy, label), scaled_label),
)
self.dither()
if shift_right:
group = VMobject(v, coord_copy, label)
self.play(ApplyMethod(
group.shift, self.vector_coords[0]*RIGHT
))
self.dither()
def show_matrix(self):
for vect, char in zip([self.i_hat, self.j_hat], ["i", "j"]):
vect.words = TextMobject("$\\hat\\%smath$ lands on" % char,
str(int(vect.get_end()[0])))
direction = UP if vect is self.i_hat else DOWN
vect.words.next_to(vect.get_end(), direction, buff=LARGE_BUFF)
vect.words.highlight(vect.get_color())
matrix = Matrix([[1, 2]])
matrix_words = TextMobject("Transformation matrix: ")
matrix_group = VMobject(matrix_words, matrix)
matrix_group.arrange_submobjects(buff=MED_SMALL_BUFF)
matrix_group.to_edge(UP)
entries = matrix.get_entries()
self.play(Write(matrix_words), Write(matrix.get_brackets()))
for i, vect in enumerate([self.i_hat, self.j_hat]):
self.play(vect.rotate, np.pi / 12, rate_func=wiggle)
self.play(Write(vect.words))
self.dither()
self.play(vect.words[1].copy().move_to, entries[i])
self.dither()
def construct(self):
self.setup()
self.plane.fade(0.3)
self.add_unit_square(color = YELLOW_E, opacity = 0.5)
self.add_title(
["The", "``determinant''", "of a transformation"],
scale_factor = 1
)
self.title.split()[1].split()[1].highlight(YELLOW)
matrix_background, matrix, det_text = self.get_matrix()
self.add_foreground_mobject(matrix_background, matrix)
A = TexMobject("A")
area_label = VMobject(A.copy(), A.copy(), A)
area_label.move_to(self.square)
det = np.linalg.det(self.t_matrix)
if np.round(det) == det:
det = int(det)
area_label_target = VMobject(
TexMobject(str(det)), TexMobject("\\cdot"), A.copy()
)
if det < 1 and det > 0:
area_label_target.scale(det)
area_label_target.arrange_submobjects(RIGHT, buff = 0.1)
self.add_moving_mobject(area_label, area_label_target)
self.dither()
self.apply_transposed_matrix(self.t_matrix)
self.dither()
det_mob_copy = area_label.split()[0].copy()
new_det_mob = det_mob_copy.copy().scale_to_fit_height(
det_text.split()[0].get_height()
)
new_det_mob.next_to(det_text, RIGHT, buff = 0.2)
new_det_mob.add_background_rectangle()
det_mob_copy.add_background_rectangle(opacity = 0)
self.play(Write(det_text))
self.play(Transform(det_mob_copy, new_det_mob))
self.dither()
def construct(self):
physy = Physicist()
mathy = Mathematician(mode="pondering")
compy = ComputerScientist()
creatures = [physy, compy, mathy]
physy.title = TextMobject("Physics student").to_corner(DOWN + LEFT)
compy.title = TextMobject("CS student").to_corner(DOWN + RIGHT)
mathy.title = TextMobject("Mathematician").to_edge(DOWN)
names = VMobject(physy.title, mathy.title, compy.title)
names.arrange_submobjects(RIGHT, buff=1)
names.to_corner(DOWN + LEFT)
for pi in creatures:
pi.next_to(pi.title, UP)
vector, symbol, coordinates = self.intro_vector()
for pi in creatures:
self.play(Write(pi.title), FadeIn(pi), run_time=1)
self.dither(2)
self.remove(symbol, coordinates)
self.physics_conception(creatures, vector)
self.cs_conception(creatures)
self.handle_mathy(creatures)
def cs_conception(self, creatures):
self.fade_all_but(creatures, 1)
physy, compy, mathy = creatures
title = TextMobject("Vectors $\\Leftrightarrow$ lists of numbers")
title.to_edge(UP)
vectors = VMobject(*map(matrix_to_mobject, [
[2, 1],
[5, 0, 0, -3],
[2.3, -7.1, 0.1],
]))
vectors.arrange_submobjects(RIGHT, buff=1)
vectors.to_edge(LEFT)
self.play(ApplyMethod(compy.change_mode, "sassy"),
Write(title, run_time=1))
self.play(Write(vectors))
self.dither()
self.play(ApplyMethod(compy.change_mode, "pondering"))
self.house_example(vectors, title)
self.restore_creatures(creatures)
def construct(self):
icons = [VideoIcon() for x in range(10)]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
icons = icons.split()
def rate_func_creator(offset):
return lambda a : min(max(2*(a-offset), 0), 1)
self.play(*[
FadeIn(
icon,
run_time = 5,
rate_func = rate_func_creator(offset)
)
for icon, offset in zip(icons, np.linspace(0, 0.5, len(icons)))
])
self.dither()
def add_scaling(self, arrows, syms, arrays):
s_arrows = VMobject(TexMobject("2"),
Vector([1, 1]).highlight(YELLOW), TexMobject("="),
Vector([2, 2]).highlight(WHITE))
s_arrows.arrange_submobjects(RIGHT)
s_arrows.scale(0.75)
s_arrows.next_to(arrows, DOWN)
s_arrays = VMobject(TexMobject("2"),
matrix_to_mobject([3, -5]).highlight(YELLOW),
TextMobject("="),
matrix_to_mobject(["2(3)", "2(-5)"]))
s_arrays.arrange_submobjects(RIGHT)
s_arrays.scale(0.75)
s_arrays.next_to(arrays, DOWN)
s_syms = TexMobject(["2", "\\vec{\\textbf{v}}"])
s_syms.split()[-1].highlight(YELLOW)
s_syms.next_to(syms, DOWN)
self.play(Write(s_arrows), Write(s_arrays), Write(s_syms), run_time=2)
self.dither()
def scale_basis_vectors(self, new_array):
i_hat, j_hat = self.get_basis_vectors()
self.add_vector(i_hat)
i_hat_label = self.label_vector(i_hat,
"\\hat{\\imath}",
color=X_COLOR,
label_scale_factor=1)
self.add_vector(j_hat)
j_hat_label = self.label_vector(j_hat,
"\\hat{\\jmath}",
color=Y_COLOR,
label_scale_factor=1)
self.wait()
x, y = new_array.get_mob_matrix().flatten()
for coord, v, label, factor, shift_right in [
(x, i_hat, i_hat_label, self.vector_coords[0], False),
(y, j_hat, j_hat_label, self.vector_coords[1], True)
]:
faded_v = v.copy().fade(0.7)
scaled_v = Vector(factor * v.get_end(), color=v.get_color())
scaled_label = VMobject(coord.copy(), label.copy())
scaled_label.arrange_submobjects(RIGHT, buff=0.1)
scaled_label.move_to(label, DOWN + RIGHT)
scaled_label.shift((scaled_v.get_end() - v.get_end()) / 2)
coord_copy = coord.copy()
self.play(
Transform(v.copy(), faded_v),
Transform(v, scaled_v),
Transform(VMobject(coord_copy, label), scaled_label),
)
self.wait()
if shift_right:
group = VMobject(v, coord_copy, label)
self.play(
ApplyMethod(group.shift, self.vector_coords[0] * RIGHT))
self.wait()
def describe_scalars(self, v, plane):
axes = plane.get_axes()
long_v = Vector(2 * v.get_end())
long_minus_v = Vector(-2 * v.get_end())
original_v = v.copy()
scaling_word = TextMobject("``Scaling''").to_corner(UP + LEFT)
scaling_word.shift(2 * RIGHT)
scalars = VMobject(
*map(TexMobject, ["2,", "\\dfrac{1}{3},", "-1.8,", "\\dots"]))
scalars.arrange_submobjects(RIGHT, buff=0.4)
scalars.next_to(scaling_word, DOWN, aligned_edge=LEFT)
scalars_word = TextMobject("``Scalars''")
scalars_word.next_to(scalars, DOWN, aligned_edge=LEFT)
self.remove(plane)
self.add(axes)
self.play(Write(scaling_word), Transform(v, long_v), run_time=1.5)
self.play(Transform(v, long_minus_v, run_time=3))
self.play(Write(scalars))
self.dither()
self.play(Write(scalars_word))
self.play(Transform(v, original_v), run_time=3)
self.dither(2)
def show_matrix(self):
for vect, char in zip([self.i_hat, self.j_hat], ["i", "j"]):
vect.words = TextMobject(
"$\\hat\\%smath$ lands on"%char,
str(int(vect.get_end()[0]))
)
direction = UP if vect is self.i_hat else DOWN
vect.words.next_to(vect.get_end(), direction, buff = LARGE_BUFF)
vect.words.highlight(vect.get_color())
matrix = Matrix([[1, 2]])
matrix_words = TextMobject("Transformation matrix: ")
matrix_group = VMobject(matrix_words, matrix)
matrix_group.arrange_submobjects(buff = MED_SMALL_BUFF)
matrix_group.to_edge(UP)
entries = matrix.get_entries()
self.play(Write(matrix_words), Write(matrix.get_brackets()))
for i, vect in enumerate([self.i_hat, self.j_hat]):
self.play(vect.rotate, np.pi/12, rate_func = wiggle)
self.play(Write(vect.words))
self.dither()
self.play(vect.words[1].copy().move_to, entries[i])
self.dither()
def construct(self):
matrix = Matrix([
[2, 0],
[-1, 1],
[-2, 1],
])
matrix.highlight_columns(X_COLOR, Y_COLOR)
brace = Brace(matrix)
words = VMobject(TextMobject("Span", "of columns"),
TexMobject("\\Updownarrow"),
TextMobject("``Column space''"))
words.arrange_submobjects(DOWN, buff=0.1)
words.next_to(brace, DOWN)
words[0][0].highlight(PINK)
words[2].highlight(TEAL)
words[0].add_background_rectangle()
words[2].add_background_rectangle()
VMobject(matrix, brace, words).center()
self.add(matrix)
self.play(GrowFromCenter(brace), Write(words, run_time=2))
self.dither()
def series_of_videos(self, chapters):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2*SPACE_WIDTH/12.)
icon.set_stroke(color = WHITE, width = 0)
icons = [icon.copy() for chapter in chapters.split()]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
randy = Randolph()
randy.to_corner()
bubble = randy.get_bubble()
new_icons = icons.copy().scale(0.2)
bubble.position_mobject_inside(new_icons)
self.play(Transform(
chapters, icons,
path_arc = np.pi/2,
))
self.clear()
self.add(icons)
self.play(FadeIn(randy))
self.play(Blink(randy))
self.dither()
self.play(
ShowCreation(bubble),
Transform(icons, new_icons)
)
self.remove(icons)
bubble.make_green_screen()
self.dither()
def construct(self):
self.setup()
self.plane.fade(0.3)
self.add_unit_square(color=YELLOW_E, opacity=0.5)
self.add_title(["The", "``determinant''", "of a transformation"],
scale_factor=1)
self.title.split()[1].split()[1].highlight(YELLOW)
matrix_background, matrix, det_text = self.get_matrix()
self.add_foreground_mobject(matrix_background, matrix)
A = TexMobject("A")
area_label = VMobject(A.copy(), A.copy(), A)
area_label.move_to(self.square)
det = np.linalg.det(self.t_matrix)
if np.round(det) == det:
det = int(det)
area_label_target = VMobject(TexMobject(str(det)),
TexMobject("\\cdot"), A.copy())
if det < 1 and det > 0:
area_label_target.scale(det)
area_label_target.arrange_submobjects(RIGHT, buff=0.1)
self.add_moving_mobject(area_label, area_label_target)
self.wait()
self.apply_transposed_matrix(self.t_matrix)
self.wait()
det_mob_copy = area_label.split()[0].copy()
new_det_mob = det_mob_copy.copy().scale_to_fit_height(
det_text.split()[0].get_height())
new_det_mob.next_to(det_text, RIGHT, buff=0.2)
new_det_mob.add_background_rectangle()
det_mob_copy.add_background_rectangle(opacity=0)
self.play(Write(det_text))
self.play(Transform(det_mob_copy, new_det_mob))
self.wait()
def cs_conception(self, creatures):
self.fade_all_but(creatures, 1)
physy, compy, mathy = creatures
title = TextMobject("Vectors $\\Leftrightarrow$ lists of numbers")
title.to_edge(UP)
vectors = VMobject(*map(matrix_to_mobject, [
[2, 1],
[5, 0, 0, -3],
[2.3, -7.1, 0.1],
]))
vectors.arrange_submobjects(RIGHT, buff = 1)
vectors.to_edge(LEFT)
self.play(
ApplyMethod(compy.change_mode, "sassy"),
Write(title, run_time = 1)
)
self.play(Write(vectors))
self.dither()
self.play(ApplyMethod(compy.change_mode, "pondering"))
self.house_example(vectors, title)
self.restore_creatures(creatures)
def construct(self):
matrix = Matrix(np.arange(9).reshape((3, 3)))
vect = Matrix(list("xyz"))
vect.scale_to_fit_height(matrix.get_height())
col1, col2, col3 = columns = [
Matrix(col)
for col in matrix.copy().get_mob_matrix().transpose()
]
coords = x, y, z = [m.copy() for m in vect.get_entries().split()]
eq, plus1, plus2 = map(TexMobject, list("=++"))
everything = VMobject(
matrix, vect, eq,
x, col1, plus1,
y, col2, plus2,
z, col3
)
everything.arrange_submobjects(buff = 0.1)
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
result = VMobject(x, col1, plus1, y, col2, plus2, z, col3)
trips = [
(matrix, DOWN, "Transformation"),
(vect, UP, "Input vector"),
(result, DOWN, "Output vector"),
]
braces = []
for mob, direction, text in trips:
brace = Brace(mob, direction)
words = TextMobject(text)
words.next_to(brace, direction)
brace.add(words)
braces.append(brace)
matrix_brace, vect_brace, result_brace = braces
self.play(*map(Write, [matrix, vect]), run_time = 2)
self.play(Write(matrix_brace, run_time = 1))
self.play(Write(vect_brace, run_time = 1))
sexts = zip(
matrix.get_mob_matrix().transpose(),
columns,
vect.get_entries().split(),
coords,
[eq, plus1, plus2],
[X_COLOR, Y_COLOR, Z_COLOR]
)
for o_col, col, start_coord, coord, sym, color in sexts:
o_col = VMobject(*o_col)
self.play(
start_coord.highlight, YELLOW,
o_col.highlight, color
)
coord.highlight(YELLOW)
col.highlight(color)
self.play(
Write(col.get_brackets()),
Transform(
o_col.copy(), col.get_entries(),
path_arc = -np.pi
),
Transform(
start_coord.copy(), coord,
path_arc = -np.pi
),
Write(sym)
)
self.dither()
self.play(Write(result_brace, run_time = 1))
self.dither()
class TeacherStudentsScene(Scene):
def setup(self):
self.teacher = Mortimer()
self.teacher.to_corner(DOWN + RIGHT)
self.teacher.look(DOWN+LEFT)
self.students = VMobject(*[
Randolph(color = c)
for c in BLUE_D, BLUE_C, BLUE_E
])
self.students.arrange_submobjects(RIGHT)
self.students.scale(0.8)
self.students.to_corner(DOWN+LEFT)
self.students = self.students.split()
for pi_creature in self.get_everyone():
pi_creature.bubble = None
self.add(*self.get_everyone())
def get_teacher(self):
return self.teacher
def get_students(self):
return self.students
def get_everyone(self):
return [self.get_teacher()] + self.get_students()
def get_bubble_intro_animation(self, content, bubble_type,
pi_creature,
**bubble_kwargs):
bubble = pi_creature.get_bubble(bubble_type, **bubble_kwargs)
bubble.add_content(content)
if pi_creature.bubble:
content_intro_anims = [
Transform(pi_creature.bubble, bubble),
Transform(pi_creature.bubble.content, bubble.content)
]
else:
content_intro_anims = [
FadeIn(bubble),
Write(content),
]
pi_creature.bubble = bubble
return content_intro_anims
def introduce_bubble(self, content, bubble_type, pi_creature,
pi_creature_target_mode = None,
added_anims = [],
**bubble_kwargs):
if all(map(lambda s : isinstance(s, str), content)):
content = TextMobject(*content)
elif len(content) == 1 and isinstance(content[0], TexMobject):
content = content[0]
else:
raise Exception("Invalid content type")
content_intro_anims = self.get_bubble_intro_animation(
content, bubble_type, pi_creature, **bubble_kwargs
)
if not pi_creature_target_mode:
if bubble_type is "speech":
pi_creature_target_mode = "speaking"
else:
pi_creature_target_mode = "pondering"
for p in self.get_everyone():
if p.bubble and p is not pi_creature:
added_anims += [
FadeOut(p.bubble),
FadeOut(p.bubble.content)
]
p.bubble = None
added_anims.append(ApplyMethod(p.change_mode, "plain"))
anims = added_anims + content_intro_anims + [
ApplyMethod(
pi_creature.change_mode,
pi_creature_target_mode,
),
]
self.play(*anims)
return pi_creature.bubble
def teacher_says(self, *content, **kwargs):
return self.introduce_bubble(
content, "speech", self.get_teacher(), **kwargs
)
def student_says(self, *content, **kwargs):
student = self.get_students()[kwargs.get("student_index", 1)]
return self.introduce_bubble(content, "speech", student, **kwargs)
def teacher_thinks(self, *content, **kwargs):
return self.introduce_bubble(
content, "thought", self.get_teacher(), **kwargs
)
def student_thinks(self, *content, **kwargs):
student = self.get_students()[kwargs.get("student_index", 1)]
return self.introduce_bubble(content, "thought", student, **kwargs)
def random_blink(self, num_times = 1):
for x in range(num_times):
pi_creature = random.choice(self.get_everyone())
self.play(Blink(pi_creature))
self.dither()
def change_student_modes(self, *modes):
self.play(*[
ApplyMethod(pi.change_mode, mode)
for pi, mode in zip(self.get_students(), modes)
])
def zoom_in_on_thought_bubble(self, radius = SPACE_HEIGHT+SPACE_WIDTH):
bubble = None
for pi in self.get_everyone():
if hasattr(pi, "bubble") and isinstance(pi.bubble, ThoughtBubble):
bubble = pi.bubble
break
if bubble is None:
raise Exception("No pi creatures have a thought bubble")
vect = -bubble.get_bubble_center()
def func(point):
centered = point+vect
return radius*centered/np.linalg.norm(centered)
self.play(*[
ApplyPointwiseFunction(func, mob)
for mob in self.get_mobjects()
])
class TeacherStudentsScene(Scene):
def setup(self):
self.teacher = Mortimer()
self.teacher.to_corner(DOWN + RIGHT)
self.teacher.look(DOWN+LEFT)
self.students = VMobject(*[
Randolph(color = c)
for c in BLUE_D, BLUE_C, BLUE_E
])
self.students.arrange_submobjects(RIGHT)
self.students.scale(0.8)
self.students.to_corner(DOWN+LEFT)
for pi_creature in self.get_everyone():
pi_creature.bubble = None
self.add(*self.get_everyone())
def get_teacher(self):
return self.teacher
def get_students(self):
return self.students.split()
def get_everyone(self):
return [self.get_teacher()] + self.get_students()
def get_bubble_intro_animation(self, content, bubble_type,
pi_creature,
**bubble_kwargs):
bubble = pi_creature.get_bubble(bubble_type, **bubble_kwargs)
bubble.add_content(content)
if pi_creature.bubble:
content_intro_anims = [
Transform(pi_creature.bubble, bubble),
Transform(pi_creature.bubble.content, bubble.content)
]
else:
content_intro_anims = [
FadeIn(bubble),
Write(content),
]
pi_creature.bubble = bubble
return content_intro_anims
def introduce_bubble(self, content, bubble_type, pi_creature,
pi_creature_target_mode = None,
added_anims = [],
**bubble_kwargs):
if isinstance(content, str):
content = TextMobject(content)
content_intro_anims = self.get_bubble_intro_animation(
content, bubble_type, pi_creature, **bubble_kwargs
)
if not pi_creature_target_mode:
if bubble_type is "speech":
pi_creature_target_mode = "speaking"
else:
pi_creature_target_mode = "pondering"
for p in self.get_everyone():
if p.bubble and p is not pi_creature:
added_anims += [
FadeOut(p.bubble),
FadeOut(p.bubble.content)
]
p.bubble = None
added_anims.append(ApplyMethod(p.change_mode, "plain"))
anims = added_anims + content_intro_anims + [
ApplyMethod(
pi_creature.change_mode,
pi_creature_target_mode,
),
]
self.play(*anims)
return pi_creature.bubble
def teacher_says(self, content = "", **kwargs):
return self.introduce_bubble(
content, "speech", self.get_teacher(), **kwargs
)
def student_says(self, content = "", student_index = 1, **kwargs):
student = self.get_students()[student_index]
return self.introduce_bubble(content, "speech", student, **kwargs)
def teacher_thinks(self, content = "", **kwargs):
return self.introduce_bubble(
content, "thought", self.get_teacher(), **kwargs
)
def student_thinks(self, content = "", student_index = 1, **kwargs):
student = self.get_students()[student_index]
return self.introduce_bubble(content, "thought", student, **kwargs)
def random_blink(self, num_times = 1):
for x in range(num_times):
pi_creature = random.choice(self.get_everyone())
self.play(Blink(pi_creature))
self.dither()
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VMobject(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
self.add(everything)
def construct(self):
vect = Matrix(["x", "y"])
vect.get_entries().highlight(YELLOW)
rot_matrix = Matrix([[0, -1], [1, 0]])
rot_matrix.highlight(TEAL)
shear_matrix = Matrix([[1, 1], [0, 1]])
shear_matrix.highlight(PINK)
l_paren, r_paren = map(TexMobject, ["\\Big(", "\\Big)"])
for p in l_paren, r_paren:
p.scale_to_fit_height(1.4 * vect.get_height())
long_way = VMobject(shear_matrix, l_paren, rot_matrix, vect, r_paren)
long_way.arrange_submobjects(buff=0.1)
long_way.to_edge(LEFT).shift(UP)
equals = TexMobject("=").next_to(long_way, RIGHT)
comp_matrix = Matrix([[1, -1], [1, 0]])
comp_matrix.highlight_columns(X_COLOR, Y_COLOR)
vect_copy = vect.copy()
short_way = VMobject(comp_matrix, vect_copy)
short_way.arrange_submobjects(buff=0.1)
short_way.next_to(equals, RIGHT)
pairs = [
(rot_matrix, "Rotation"),
(shear_matrix, "Shear"),
(comp_matrix, "Composition"),
]
for matrix, word in pairs:
brace = Brace(matrix)
text = TextMobject(word).next_to(brace, DOWN)
brace.highlight(matrix.get_color())
text.highlight(matrix.get_color())
matrix.add(brace, text)
comp_matrix.split()[-1].submobject_gradient_highlight(TEAL, PINK)
self.add(vect)
groups = [
[rot_matrix],
[l_paren, r_paren, shear_matrix],
[equals, comp_matrix, vect_copy],
]
for group in groups:
self.play(*map(Write, group))
self.wait()
self.play(*map(FadeOut, [l_paren, r_paren, vect, vect_copy]))
comp_matrix.add(equals)
matrices = VMobject(shear_matrix, rot_matrix, comp_matrix)
self.play(
ApplyMethod(matrices.arrange_submobjects,
buff=0.1,
aligned_edge=UP))
self.wait()
arrow = Arrow(rot_matrix.get_right(), shear_matrix.get_left())
arrow.shift((rot_matrix.get_top()[1] + 0.2) * UP)
words = TextMobject("Read right to left")
words.submobjects.reverse()
words.next_to(arrow, UP)
functions = TexMobject("f(g(x))")
functions.next_to(words, UP)
self.play(ShowCreation(arrow))
self.play(Write(words))
self.wait()
self.play(Write(functions))
self.wait()
def construct(self):
m1_mob, m2_mob, comp_matrix = self.get_matrices()
self.add(m1_mob, m2_mob, m1_mob.label, m2_mob.label, comp_matrix)
result = self.get_result()
col1, col2 = [
VMobject(*m1_mob.split()[1].get_mob_matrix()[:, i]) for i in 0, 1
]
col1.target_color = X_COLOR
col2.target_color = Y_COLOR
for col in col1, col2:
circle = Circle()
circle.stretch_to_fit_height(m1_mob.get_height())
circle.stretch_to_fit_width(m1_mob.get_width() / 2.5)
circle.highlight(col.target_color)
circle.move_to(col)
col.circle = circle
triplets = [
(col1, "i", X_COLOR),
(col2, "j", Y_COLOR),
]
for i, (col, char, color) in enumerate(triplets):
self.add(col)
start_state = self.get_mobjects()
question = TextMobject("Where does $\\hat{\\%smath}$ go?" % char)
question.split()[-4].highlight(color)
question.split()[-5].highlight(color)
question.scale(1.2)
question.shift(DOWN)
first = TextMobject("First here")
first.highlight(color)
first.shift(DOWN + LEFT)
first_arrow = Arrow(first, col.circle.get_bottom(), color=color)
second = TextMobject("Then to whatever this is")
second.highlight(color)
second.to_edge(RIGHT).shift(DOWN)
m2_copy = m2_mob.copy()
m2_target = m2_mob.copy()
m2_target.next_to(m2_mob, DOWN, buff=1)
col_vect = Matrix(col.copy().split())
col_vect.highlight(color)
col_vect.next_to(m2_target, RIGHT, buff=0.1)
second_arrow = Arrow(second, col_vect, color=color)
new_m2_copy = m2_mob.copy().split()[1]
intermediate = VMobject(TexMobject("="),
col_vect.copy().get_entries().split()[0],
Matrix(new_m2_copy.get_mob_matrix()[:, 0]),
TexMobject("+"),
col_vect.copy().get_entries().split()[1],
Matrix(new_m2_copy.get_mob_matrix()[:, 1]),
TexMobject("="))
intermediate.arrange_submobjects(buff=0.1)
intermediate.next_to(col_vect, RIGHT)
product = Matrix(result[:, i])
product.next_to(intermediate, RIGHT)
comp_col = VMobject(*comp_matrix.split()[1].get_mob_matrix()[:, i])
self.play(Write(question, run_time=1))
self.wait()
self.play(Transform(question, first), ShowCreation(first_arrow),
ShowCreation(col.circle),
ApplyMethod(col.highlight, col.target_color))
self.wait()
self.play(
Transform(m2_copy, m2_target, run_time=2),
ApplyMethod(col.copy().move_to, col_vect, run_time=2),
Write(col_vect.get_brackets()),
Transform(first_arrow, second_arrow),
Transform(question, second),
)
self.wait()
self.play(*map(FadeOut, [question, first_arrow]))
self.play(Write(intermediate))
self.wait()
self.play(Write(product))
self.wait()
product_entries = product.get_entries()
self.play(ApplyMethod(comp_col.highlight, BLACK),
ApplyMethod(product_entries.move_to, comp_col))
self.wait()
start_state.append(product_entries)
self.play(*[
FadeOut(mob)
for mob in self.get_mobjects() if mob not in start_state
] + [Animation(product_entries)])
self.wait()
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VMobject(left, right, equals, result)
everything.arrange_submobjects()
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
self.add(everything)
