def side_project(self, morty):
rect = PictureInPictureFrame()
rect.next_to(morty, UP+LEFT)
side_project = TextMobject("Side project")
side_project.next_to(rect, UP)
dollar_sign = TexMobject("\\$")
cross = VGroup(*[
Line(vect, -vect, color = RED)
for vect in UP+RIGHT, UP+LEFT
])
cross.scale_to_fit_height(dollar_sign.get_height())
no_money = VGroup(dollar_sign, cross)
no_money.next_to(rect, DOWN)
self.play(
morty.change_mode, "raise_right_hand",
morty.look_at, rect
)
self.play(
Write(side_project),
ShowCreation(rect)
)
self.dither()
self.play(Blink(morty))
self.dither()
self.play(Write(dollar_sign))
self.play(ShowCreation(cross))
self.screen_title = side_project
self.cross = cross
def generate_points(self):
self.cell_height = self.height / self.nrows
self.cell_width = self.width / self.nrows
self.bottom_left = (self.cell_width * self.nrows / 2.0)*LEFT + \
(self.cell_height * self.nrows / 2.0)*DOWN
num_to_num_mob = {}
self.coords_to_mobs = {}
self.coords = [
(n, k)
for n in range(self.nrows)
for k in range(n+1)
]
for n, k in self.coords:
num = choose(n, k)
center = self.coords_to_center(n, k)
num_mob = TexMobject(str(num))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / num_mob.get_height(),
self.portion_to_fill * self.cell_width / num_mob.get_width(),
)
num_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_mobs:
self.coords_to_mobs[n] = {}
self.coords_to_mobs[n][k] = num_mob
self.add(*[
self.coords_to_mobs[n][k]
for n, k in self.coords
])
return self
def side_project(self, morty):
rect = PictureInPictureFrame()
rect.next_to(morty, UP+LEFT)
side_project = TextMobject("Side project")
side_project.next_to(rect, UP)
dollar_sign = TexMobject("\\$")
cross = VGroup(*[
Line(vect, -vect, color = RED)
for vect in UP+RIGHT, UP+LEFT
])
cross.scale_to_fit_height(dollar_sign.get_height())
no_money = VGroup(dollar_sign, cross)
no_money.next_to(rect, DOWN)
self.play(
morty.change_mode, "raise_right_hand",
morty.look_at, rect
)
self.play(
Write(side_project),
ShowCreation(rect)
)
self.wait()
self.play(Blink(morty))
self.wait()
self.play(Write(dollar_sign))
self.play(ShowCreation(cross))
self.screen_title = side_project
self.cross = cross
def get_number_mobjects(self, *numbers):
# TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = []
for number in numbers:
mob = TexMobject(str(int(number)))
vert_scale = 2 * self.tick_size / mob.get_height()
hori_scale = self.tick_frequency * self.unit_length_to_spatial_width / mob.get_width()
mob.scale(min(vert_scale, hori_scale))
mob.shift(self.number_to_point(number))
mob.shift(self.get_vertical_number_offset())
result.append(mob)
return result
def generate_n_choose_k_mobs(self):
self.coords_to_n_choose_k = {}
for n, k in self.coords:
nck_mob = TexMobject(r"{%d \choose %d}" % (n, k))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / nck_mob.get_height(),
self.portion_to_fill * self.cell_width / nck_mob.get_width(),
)
center = self.coords_to_mobs[n][k].get_center()
nck_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_n_choose_k:
self.coords_to_n_choose_k[n] = {}
self.coords_to_n_choose_k[n][k] = nck_mob
return self
def generate_n_choose_k_mobs(self):
self.coords_to_n_choose_k = {}
for n, k in self.coords:
nck_mob = TexMobject(r"{%d \choose %d}"%(n, k))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / nck_mob.get_height(),
self.portion_to_fill * self.cell_width / nck_mob.get_width(),
)
center = self.coords_to_mobs[n][k].get_center()
nck_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_n_choose_k:
self.coords_to_n_choose_k[n] = {}
self.coords_to_n_choose_k[n][k] = nck_mob
return self
def get_number_mobjects(self, *numbers):
#TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = []
for number in numbers:
mob = TexMobject(str(int(number)))
vert_scale = 2 * self.tick_size / mob.get_height()
hori_scale = self.tick_frequency * self.unit_length_to_spatial_width / mob.get_width(
)
mob.scale(min(vert_scale, hori_scale))
mob.shift(self.number_to_point(number))
mob.shift(self.get_vertical_number_offset())
result.append(mob)
return result
def scale_vector(self, v, factor, v_label,
v_name = "v", factor_tex = None):
starting_mobjects = list(self.mobjects)
if factor_tex is None:
factor_tex = str(factor)
scaled_vector = self.add_vector(
factor*v.get_end(), animate = False
)
self.remove(scaled_vector)
label_tex = "%s\\vec{\\textbf{%s}}"%(factor_tex, v_name)
label = self.label_vector(
scaled_vector, label_tex, animate = False,
add_to_vector = False
)
self.remove(label)
factor_mob = TexMobject(factor_tex)
if factor_mob.get_height() > 1:
factor_mob.scale_to_fit_height(0.9)
if factor_mob.get_width() > 1:
factor_mob.scale_to_fit_width(0.9)
factor_mob.shift(1.5*RIGHT+2.5*UP)
num_factor_parts = len(factor_mob.split())
factor_mob_parts_in_label = label.split()[:num_factor_parts]
label_remainder_parts = label.split()[num_factor_parts:]
factor_in_label = VMobject(*factor_mob_parts_in_label)
label_remainder = VMobject(*label_remainder_parts)
self.play(Write(factor_mob, run_time = 1))
self.dither()
self.play(
ApplyMethod(v.copy().highlight, DARK_GREY),
ApplyMethod(v_label.copy().highlight, DARK_GREY),
Transform(factor_mob, factor_in_label),
Transform(v.copy(), scaled_vector),
Transform(v_label.copy(), label_remainder),
)
self.dither(2)
self.clear()
self.add(*starting_mobjects)
def scale_vector(self, v, factor, v_label,
v_name = "v", factor_tex = None):
starting_mobjects = list(self.mobjects)
if factor_tex is None:
factor_tex = str(factor)
scaled_vector = self.add_vector(
factor*v.get_end(), animate = False
)
self.remove(scaled_vector)
label_tex = "%s\\vec{\\textbf{%s}}"%(factor_tex, v_name)
label = self.label_vector(
scaled_vector, label_tex, animate = False,
add_to_vector = False
)
self.remove(label)
factor_mob = TexMobject(factor_tex)
if factor_mob.get_height() > 1:
factor_mob.scale_to_fit_height(0.9)
if factor_mob.get_width() > 1:
factor_mob.scale_to_fit_width(0.9)
factor_mob.shift(1.5*RIGHT+2.5*UP)
num_factor_parts = len(factor_mob.split())
factor_mob_parts_in_label = label.split()[:num_factor_parts]
label_remainder_parts = label.split()[num_factor_parts:]
factor_in_label = VMobject(*factor_mob_parts_in_label)
label_remainder = VMobject(*label_remainder_parts)
self.play(Write(factor_mob, run_time = 1))
self.wait()
self.play(
ApplyMethod(v.copy().highlight, DARK_GREY),
ApplyMethod(v_label.copy().highlight, DARK_GREY),
Transform(factor_mob, factor_in_label),
Transform(v.copy(), scaled_vector),
Transform(v_label.copy(), label_remainder),
)
self.wait(2)
self.clear()
self.add(*starting_mobjects)
def construct(self):
MAX_OPACITY = 0.4
INDICATOR_RADIUS = 0.6
OPACITY_FOR_UNIT_INTENSITY = 0.5
A = np.array([5., -3., 0.])
B = np.array([-5., 3., 0.])
C = np.array([-5., -3., 0.])
morty = self.get_primary_pi_creature()
morty.scale(0.3).flip()
right_pupil = morty.pupils[1]
morty.next_to(C, LEFT, buff=0, submobject_to_align=right_pupil)
horizontal = VMobject(stroke_width=1)
horizontal.set_points_as_corners([C, A])
vertical = VMobject(stroke_width=1)
vertical.set_points_as_corners([C, B])
self.play(ShowCreation(horizontal), ShowCreation(vertical))
indicator = LightIndicator(
color=LIGHT_COLOR,
radius=INDICATOR_RADIUS,
opacity_for_unit_intensity=OPACITY_FOR_UNIT_INTENSITY,
show_reading=True,
precision=2)
indicator.next_to(morty, LEFT)
self.play(Write(indicator))
ls1 = LightSource(radius=20, num_levels=50)
ls2 = ls1.deepcopy()
#print "==="
#print ls1.get_source_point()
ls1.move_source_to(A)
#print ls1.get_source_point()
#print "==="
#print ls2.get_source_point()
ls2.move_source_to(B)
#print ls2.get_source_point()
self.play(FadeIn(ls1.lighthouse), FadeIn(ls2.lighthouse),
SwitchOn(ls1.ambient_light), SwitchOn(ls2.ambient_light))
distance1 = np.linalg.norm(C - ls1.get_source_point())
intensity = ls1.ambient_light.opacity_function(
distance1) / indicator.opacity_for_unit_intensity
distance2 = np.linalg.norm(C - ls2.get_source_point())
intensity += ls2.ambient_light.opacity_function(
distance2) / indicator.opacity_for_unit_intensity
self.play(UpdateLightIndicator(indicator, intensity))
self.wait()
ls3 = ls1.deepcopy()
ls3.move_to(np.array([6, 3.5, 0]))
new_indicator = indicator.copy()
new_indicator.light_source = ls3
new_indicator.measurement_point = C
self.add(new_indicator)
self.play(indicator.shift, 2 * UP)
#intensity = intensity_for_light_source(ls3)
self.play(
SwitchOff(ls1.ambient_light),
#FadeOut(ls1.lighthouse),
SwitchOff(ls2.ambient_light),
#FadeOut(ls2.lighthouse),
UpdateLightIndicator(new_indicator, 0.0))
# create a *continual* animation for the replacement source
updater = ContinualLightIndicatorUpdate(new_indicator)
self.add(updater)
self.play(
SwitchOn(ls3.ambient_light),
FadeIn(ls3.lighthouse),
)
self.wait()
# move the light source around
# TODO: moving along a path arc
location = np.array([-3, -2., 0.])
self.play(ls3.move_source_to, location)
location = np.array([6., 1., 0.])
self.play(ls3.move_source_to, location)
location = np.array([5., 2., 0.])
self.play(ls3.move_source_to, location)
closer_location = interpolate(location, C, 0.5)
self.play(ls3.move_source_to, closer_location)
self.play(ls3.move_source_to, location)
# maybe move in a circle around C using a loop?
# find the coords of the altitude point H
# as the solution of a certain LSE
xA = A[0]
yA = A[1]
xB = B[0]
yB = B[1]
xC = C[0]
yC = C[1]
matrix = np.array([[yA - yB, xB - xA], [xA - xB, yA - yB]]) # sic
vector = np.array([xB * yA - xA * yB, xC * (xA - xB) + yC * (yA - yB)])
H2 = np.linalg.solve(matrix, vector)
H = np.append(H2, 0.)
self.play(ls3.move_source_to, H)
# draw lines to complete the geometric picture
# and label the lengths
line_a = VMobject()
line_a.set_points_as_corners([B, C])
line_b = VMobject()
line_b.set_points_as_corners([A, C])
line_c = VMobject()
line_c.set_points_as_corners([A, B])
line_h = VMobject()
line_h.set_points_as_corners([H, C])
label_a = TexMobject("a")
label_a.next_to(line_a, LEFT, buff=0.5)
label_b = TexMobject("b")
label_b.next_to(line_b, DOWN, buff=0.5)
label_h = TexMobject("h")
label_h.next_to(line_h.get_center(), RIGHT, buff=0.5)
self.play(ShowCreation(line_a), Write(label_a))
self.play(ShowCreation(line_b), Write(label_b))
self.play(ShowCreation(line_c), )
self.play(ShowCreation(line_h), Write(label_h))
# state the IPT
theorem_location = np.array([3., 2., 0.])
theorem = TexMobject("{1\over a^2} + {1\over b^2} = {1\over h^2}")
theorem_name = TextMobject("Inverse Pythagorean Theorem")
buffer = 1.2
theorem_box = Rectangle(width=buffer * theorem.get_width(),
height=buffer * theorem.get_height())
theorem.move_to(theorem_location)
theorem_box.move_to(theorem_location)
theorem_name.next_to(theorem_box, UP)
self.play(Write(theorem), )
self.play(
ShowCreation(theorem_box),
Write(theorem_name),
)
def construct(self):
base_str = self.base_str
func_def = TexMobject("M(", "t", ")", "= ", "%s^" % base_str, "t")
func_def.to_corner(UP + LEFT)
self.add(func_def)
ratio = TexMobject("{ {%s^" % base_str, "{t", "+", "dt}", "-",
"%s^" % base_str, "t}", "\\over \\,", "dt}")
ratio.shift(UP + LEFT)
lhs = TexMobject("{dM", "\\over \\,", "dt}", "(", "t", ")", "=")
lhs.next_to(ratio, LEFT)
two_to_t_plus_dt = VGroup(*ratio[:4])
two_to_t = VGroup(*ratio[5:7])
two_to_t_two_to_dt = TexMobject("%s^" % base_str, "t",
"%s^" % base_str, "{dt}")
two_to_t_two_to_dt.move_to(two_to_t_plus_dt, DOWN + LEFT)
exp_prop_brace = Brace(two_to_t_two_to_dt, UP)
one = TexMobject("1")
one.move_to(ratio[5], DOWN)
lp, rp = parens = TexMobject("()")
parens.stretch(1.3, 1)
parens.scale_to_fit_height(ratio.get_height())
lp.next_to(ratio, LEFT, buff=0)
rp.next_to(ratio, RIGHT, buff=0)
extracted_two_to_t = TexMobject("%s^" % base_str, "t")
extracted_two_to_t.next_to(lp, LEFT, buff=SMALL_BUFF)
expressions = [
ratio, two_to_t_two_to_dt, extracted_two_to_t, lhs, func_def
]
for expression in expressions:
expression.highlight_by_tex("t", YELLOW)
expression.highlight_by_tex("dt", GREEN)
#Apply exponential property
self.play(Write(ratio), Write(lhs), self.pi_creature.change_mode,
"raise_right_hand")
self.dither(2)
self.play(two_to_t_plus_dt.next_to, exp_prop_brace, UP,
self.pi_creature.change_mode, "pondering")
self.play(
ReplacementTransform(
two_to_t_plus_dt.copy(),
two_to_t_two_to_dt,
run_time=2,
path_arc=np.pi,
), FadeIn(exp_prop_brace))
self.dither(2)
#Talk about exponential property
add_exp_rect, mult_rect = rects = [
Rectangle(
stroke_color=BLUE,
stroke_width=2,
).replace(mob).scale_in_place(1.1)
for mob in [VGroup(*two_to_t_plus_dt[1:]), two_to_t_two_to_dt]
]
words = VGroup(
*[TextMobject(s, " ideas") for s in "Additive", "Multiplicative"])
words[0].move_to(words[1], LEFT)
words.highlight(BLUE)
words.next_to(two_to_t_plus_dt, RIGHT, buff=1.5 * LARGE_BUFF)
arrows = VGroup(*[
Arrow(word.get_left(), rect, color=words.get_color())
for word, rect in zip(words, rects)
])
self.play(ShowCreation(add_exp_rect))
self.dither()
self.play(ReplacementTransform(add_exp_rect.copy(), mult_rect))
self.dither()
self.change_mode("happy")
self.play(Write(words[0], run_time=2))
self.play(ShowCreation(arrows[0]))
self.dither()
self.play(
Transform(*words),
Transform(*arrows),
)
self.dither(2)
self.play(*map(FadeOut, [
words[0],
arrows[0],
add_exp_rect,
mult_rect,
two_to_t_plus_dt,
exp_prop_brace,
]))
#Factor out 2^t
self.play(*[
FadeIn(mob, run_time=2, rate_func=squish_rate_func(smooth, 0.5, 1))
for mob in one, lp, rp
] + [
ReplacementTransform(
mob,
extracted_two_to_t,
path_arc=np.pi / 2,
run_time=2,
) for mob in two_to_t,
VGroup(*two_to_t_two_to_dt[:2])
] + [lhs.next_to, extracted_two_to_t, LEFT])
self.change_mode("pondering")
shifter = VGroup(ratio[4], one, *two_to_t_two_to_dt[2:])
stretcher = VGroup(lp, ratio[7], rp)
self.play(shifter.next_to, ratio[7], UP, stretcher.stretch_in_place,
0.9, 0)
self.dither(2)
#Ask about dt -> 0
brace = Brace(VGroup(extracted_two_to_t, ratio), DOWN)
alt_brace = Brace(parens, DOWN)
dt_to_zero = TexMobject("dt", "\\to 0")
dt_to_zero.highlight_by_tex("dt", GREEN)
dt_to_zero.next_to(brace, DOWN)
self.play(GrowFromCenter(brace))
self.play(Write(dt_to_zero))
self.dither(2)
#Who cares
randy = Randolph()
randy.scale(0.7)
randy.to_edge(DOWN)
self.play(
FadeIn(randy),
self.pi_creature.change_mode,
"plain",
)
self.play(
PiCreatureSays(
randy,
"Who cares?",
bubble_kwargs={"direction": LEFT},
target_mode="angry",
))
self.dither(2)
self.play(RemovePiCreatureBubble(randy), FadeOut(randy),
self.pi_creature.change_mode, "hooray",
self.pi_creature.look_at, parens)
self.play(Transform(brace, alt_brace), dt_to_zero.next_to, alt_brace,
DOWN)
self.dither()
#Highlight separation
rects = [
Rectangle(
stroke_color=color,
stroke_width=2,
).replace(mob, stretch=True).scale_in_place(1.1)
for mob, color in [
(VGroup(parens, dt_to_zero), GREEN),
(extracted_two_to_t, YELLOW),
]
]
self.play(ShowCreation(rects[0]))
self.dither(2)
self.play(ReplacementTransform(rects[0].copy(), rects[1]))
self.change_mode("happy")
self.dither()
self.play(*map(FadeOut, rects))
#Plug in specific values
static_constant = self.try_specific_dt_values()
constant = static_constant.copy()
#Replace with actual constant
limit_term = VGroup(brace, dt_to_zero, ratio[4], one, rects[0],
*ratio[7:] + two_to_t_two_to_dt[2:])
self.play(FadeIn(rects[0]))
self.play(limit_term.to_corner, DOWN + LEFT)
self.play(lp.stretch, 0.5, 1, lp.stretch, 0.8, 0, lp.next_to,
extracted_two_to_t[0], RIGHT, rp.stretch, 0.5, 1, rp.stretch,
0.8, 0, rp.next_to, lp, RIGHT, SMALL_BUFF, rp.shift,
constant.get_width() * RIGHT, constant.next_to,
extracted_two_to_t[0], RIGHT, MED_LARGE_BUFF)
self.dither()
self.change_mode("confused")
self.dither()
#Indicate distinction between dt group and t group again
for mob in limit_term, extracted_two_to_t:
self.play(FocusOn(mob))
self.play(Indicate(mob))
self.dither()
#hold_final_value
derivative = VGroup(lhs, extracted_two_to_t, parens, constant)
func_def_rhs = VGroup(*func_def[-2:]).copy()
func_lp, func_rp = func_parens = TexMobject("()")
func_parens.set_fill(opacity=0)
func_lp.next_to(func_def_rhs[0], LEFT, buff=0)
func_rp.next_to(func_lp, RIGHT, buff=func_def_rhs.get_width())
func_def_rhs.add(func_parens)
M = lhs[0][1]
self.play(
FadeOut(M),
func_def_rhs.move_to,
M,
LEFT,
func_def_rhs.set_fill,
None,
1,
)
lhs[0].submobjects[1] = func_def_rhs
self.dither()
self.play(derivative.next_to, self.pi_creature, UP, derivative.to_edge,
RIGHT, self.pi_creature.change_mode, "raise_right_hand")
self.dither(2)
for mob in extracted_two_to_t, constant:
self.play(Indicate(mob))
self.dither()
self.dither(2)
def construct(self):
base_str = self.base_str
func_def = TexMobject("M(", "t", ")", "= ", "%s^"%base_str, "t")
func_def.to_corner(UP+LEFT)
self.add(func_def)
ratio = TexMobject(
"{ {%s^"%base_str, "{t", "+", "dt}", "-",
"%s^"%base_str, "t}",
"\\over \\,", "dt}"
)
ratio.shift(UP+LEFT)
lhs = TexMobject("{dM", "\\over \\,", "dt}", "(", "t", ")", "=")
lhs.next_to(ratio, LEFT)
two_to_t_plus_dt = VGroup(*ratio[:4])
two_to_t = VGroup(*ratio[5:7])
two_to_t_two_to_dt = TexMobject(
"%s^"%base_str, "t",
"%s^"%base_str, "{dt}"
)
two_to_t_two_to_dt.move_to(two_to_t_plus_dt, DOWN+LEFT)
exp_prop_brace = Brace(two_to_t_two_to_dt, UP)
one = TexMobject("1")
one.move_to(ratio[5], DOWN)
lp, rp = parens = TexMobject("()")
parens.stretch(1.3, 1)
parens.scale_to_fit_height(ratio.get_height())
lp.next_to(ratio, LEFT, buff = 0)
rp.next_to(ratio, RIGHT, buff = 0)
extracted_two_to_t = TexMobject("%s^"%base_str, "t")
extracted_two_to_t.next_to(lp, LEFT, buff = SMALL_BUFF)
expressions = [
ratio, two_to_t_two_to_dt,
extracted_two_to_t, lhs, func_def
]
for expression in expressions:
expression.highlight_by_tex("t", YELLOW)
expression.highlight_by_tex("dt", GREEN)
#Apply exponential property
self.play(
Write(ratio), Write(lhs),
self.pi_creature.change_mode, "raise_right_hand"
)
self.dither(2)
self.play(
two_to_t_plus_dt.next_to, exp_prop_brace, UP,
self.pi_creature.change_mode, "pondering"
)
self.play(
ReplacementTransform(
two_to_t_plus_dt.copy(), two_to_t_two_to_dt,
run_time = 2,
path_arc = np.pi,
),
FadeIn(exp_prop_brace)
)
self.dither(2)
#Talk about exponential property
add_exp_rect, mult_rect = rects = [
Rectangle(
stroke_color = BLUE,
stroke_width = 2,
).replace(mob).scale_in_place(1.1)
for mob in [
VGroup(*two_to_t_plus_dt[1:]),
two_to_t_two_to_dt
]
]
words = VGroup(*[
TextMobject(s, " ideas")
for s in "Additive", "Multiplicative"
])
words[0].move_to(words[1], LEFT)
words.highlight(BLUE)
words.next_to(two_to_t_plus_dt, RIGHT, buff = 1.5*LARGE_BUFF)
arrows = VGroup(*[
Arrow(word.get_left(), rect, color = words.get_color())
for word, rect in zip(words, rects)
])
self.play(ShowCreation(add_exp_rect))
self.dither()
self.play(ReplacementTransform(
add_exp_rect.copy(), mult_rect
))
self.dither()
self.change_mode("happy")
self.play(Write(words[0], run_time = 2))
self.play(ShowCreation(arrows[0]))
self.dither()
self.play(
Transform(*words),
Transform(*arrows),
)
self.dither(2)
self.play(*map(FadeOut, [
words[0], arrows[0], add_exp_rect, mult_rect,
two_to_t_plus_dt, exp_prop_brace,
]))
#Factor out 2^t
self.play(*[
FadeIn(
mob,
run_time = 2,
rate_func = squish_rate_func(smooth, 0.5, 1)
)
for mob in one, lp, rp
] + [
ReplacementTransform(
mob, extracted_two_to_t,
path_arc = np.pi/2,
run_time = 2,
)
for mob in two_to_t, VGroup(*two_to_t_two_to_dt[:2])
] + [
lhs.next_to, extracted_two_to_t, LEFT
])
self.change_mode("pondering")
shifter = VGroup(ratio[4], one, *two_to_t_two_to_dt[2:])
stretcher = VGroup(lp, ratio[7], rp)
self.play(
shifter.next_to, ratio[7], UP,
stretcher.stretch_in_place, 0.9, 0
)
self.dither(2)
#Ask about dt -> 0
brace = Brace(VGroup(extracted_two_to_t, ratio), DOWN)
alt_brace = Brace(parens, DOWN)
dt_to_zero = TexMobject("dt", "\\to 0")
dt_to_zero.highlight_by_tex("dt", GREEN)
dt_to_zero.next_to(brace, DOWN)
self.play(GrowFromCenter(brace))
self.play(Write(dt_to_zero))
self.dither(2)
#Who cares
randy = Randolph()
randy.scale(0.7)
randy.to_edge(DOWN)
self.play(
FadeIn(randy),
self.pi_creature.change_mode, "plain",
)
self.play(PiCreatureSays(
randy, "Who cares?",
bubble_kwargs = {"direction" : LEFT},
target_mode = "angry",
))
self.dither(2)
self.play(
RemovePiCreatureBubble(randy),
FadeOut(randy),
self.pi_creature.change_mode, "hooray",
self.pi_creature.look_at, parens
)
self.play(
Transform(brace, alt_brace),
dt_to_zero.next_to, alt_brace, DOWN
)
self.dither()
#Highlight separation
rects = [
Rectangle(
stroke_color = color,
stroke_width = 2,
).replace(mob, stretch = True).scale_in_place(1.1)
for mob, color in [
(VGroup(parens, dt_to_zero), GREEN),
(extracted_two_to_t, YELLOW),
]
]
self.play(ShowCreation(rects[0]))
self.dither(2)
self.play(ReplacementTransform(rects[0].copy(), rects[1]))
self.change_mode("happy")
self.dither()
self.play(*map(FadeOut, rects))
#Plug in specific values
static_constant = self.try_specific_dt_values()
constant = static_constant.copy()
#Replace with actual constant
limit_term = VGroup(
brace, dt_to_zero, ratio[4], one, rects[0],
*ratio[7:]+two_to_t_two_to_dt[2:]
)
self.play(FadeIn(rects[0]))
self.play(limit_term.to_corner, DOWN+LEFT)
self.play(
lp.stretch, 0.5, 1,
lp.stretch, 0.8, 0,
lp.next_to, extracted_two_to_t[0], RIGHT,
rp.stretch, 0.5, 1,
rp.stretch, 0.8, 0,
rp.next_to, lp, RIGHT, SMALL_BUFF,
rp.shift, constant.get_width()*RIGHT,
constant.next_to, extracted_two_to_t[0], RIGHT, MED_LARGE_BUFF
)
self.dither()
self.change_mode("confused")
self.dither()
#Indicate distinction between dt group and t group again
for mob in limit_term, extracted_two_to_t:
self.play(FocusOn(mob))
self.play(Indicate(mob))
self.dither()
#hold_final_value
derivative = VGroup(
lhs, extracted_two_to_t, parens, constant
)
func_def_rhs = VGroup(*func_def[-2:]).copy()
func_lp, func_rp = func_parens = TexMobject("()")
func_parens.set_fill(opacity = 0)
func_lp.next_to(func_def_rhs[0], LEFT, buff = 0)
func_rp.next_to(func_lp, RIGHT, buff = func_def_rhs.get_width())
func_def_rhs.add(func_parens)
M = lhs[0][1]
self.play(
FadeOut(M),
func_def_rhs.move_to, M, LEFT,
func_def_rhs.set_fill, None, 1,
)
lhs[0].submobjects[1] = func_def_rhs
self.dither()
self.play(
derivative.next_to, self.pi_creature, UP,
derivative.to_edge, RIGHT,
self.pi_creature.change_mode, "raise_right_hand"
)
self.dither(2)
for mob in extracted_two_to_t, constant:
self.play(Indicate(mob))
self.dither()
self.dither(2)
