def get_paths(self):
sharp_corner = Mobject(
Line(3*UP+LEFT, LEFT),
Arc(angle = np.pi/2, start_angle = np.pi),
Line(DOWN, DOWN+3*RIGHT)
).ingest_submobjects().highlight(GREEN)
paths = [
Arc(
angle = np.pi/2,
radius = 3,
start_angle = 4
),
LoopTheLoop(),
Line(7*LEFT, 7*RIGHT, color = RED_D),
sharp_corner,
FunctionGraph(
lambda x : 0.05*(x**2)+0.1*np.sin(2*x)
),
FunctionGraph(
lambda x : x**2,
x_min = -3,
x_max = 2,
density = 3*DEFAULT_POINT_DENSITY_1D
)
]
cycloid = Cycloid()
self.align_paths(paths, cycloid)
return paths + [cycloid]
def get_path(self):
result = FunctionGraph(lambda x: 0.05 * (x**2) + 0.1 * np.sin(2 * x))
result.rotate(-np.pi / 20)
result.scale(0.7)
result.shift(DOWN)
return result
def get_path(self):
result = FunctionGraph(
lambda x : 0.05*(x**2)+0.1*np.sin(2*x)
)
result.rotate(-np.pi/20)
result.scale(0.7)
result.shift(DOWN)
return result
def construct(self):
horiz_radius = 5
vert_radius = 3
vert_axis = NumberLine(numerical_radius=vert_radius)
vert_axis.rotate(np.pi / 2)
vert_axis.shift(horiz_radius * LEFT)
horiz_axis = NumberLine(numerical_radius=5,
numbers_with_elongated_ticks=[])
axes = Mobject(horiz_axis, vert_axis)
graph = FunctionGraph(lambda x: 0.4 * (x - 2) * (x + 2) + 3,
x_min=-2,
x_max=2,
density=3 * DEFAULT_POINT_DENSITY_1D)
graph.stretch_to_fit_width(2 * horiz_radius)
graph.highlight(YELLOW)
min_point = Dot(graph.get_bottom())
nature_finds = TextMobject("Nature finds this point")
nature_finds.scale(0.5)
nature_finds.highlight(GREEN)
nature_finds.shift(2 * RIGHT + 3 * UP)
arrow = Arrow(nature_finds.get_bottom(), min_point, color=GREEN)
side_words_start = TextMobject("Parameter describing")
top_words, last_side_words = [
map(TextMobject, pair)
for pair in [("Light's travel time",
"Potential energy"), ("path", "mechanical state")]
]
for word in top_words + last_side_words + [side_words_start]:
word.scale(0.7)
side_words_start.next_to(horiz_axis, DOWN)
side_words_start.to_edge(RIGHT)
for words in top_words:
words.next_to(vert_axis, UP)
words.to_edge(LEFT)
for words in last_side_words:
words.next_to(side_words_start, DOWN)
for words in top_words[1], last_side_words[1]:
words.highlight(RED)
self.add(axes, top_words[0], side_words_start, last_side_words[0])
self.play(ShowCreation(graph))
self.play(ShimmerIn(nature_finds), ShowCreation(arrow),
ShowCreation(min_point))
self.dither()
self.play(FadeOut(top_words[0]), FadeOut(last_side_words[0]),
GrowFromCenter(top_words[1]),
GrowFromCenter(last_side_words[1]))
self.dither(3)
def construct(self):
horiz_radius = 5
vert_radius = 3
vert_axis = NumberLine(numerical_radius = vert_radius)
vert_axis.rotate(np.pi/2)
vert_axis.shift(horiz_radius*LEFT)
horiz_axis = NumberLine(
numerical_radius = 5,
numbers_with_elongated_ticks = []
)
axes = Mobject(horiz_axis, vert_axis)
graph = FunctionGraph(
lambda x : 0.4*(x-2)*(x+2)+3,
x_min = -2,
x_max = 2,
density = 3*DEFAULT_POINT_DENSITY_1D
)
graph.stretch_to_fit_width(2*horiz_radius)
graph.highlight(YELLOW)
min_point = Dot(graph.get_bottom())
nature_finds = TextMobject("Nature finds this point")
nature_finds.scale(0.5)
nature_finds.highlight(GREEN)
nature_finds.shift(2*RIGHT+3*UP)
arrow = Arrow(
nature_finds.get_bottom(), min_point,
color = GREEN
)
side_words_start = TextMobject("Parameter describing")
top_words, last_side_words = [
map(TextMobject, pair)
for pair in [
("Light's travel time", "Potential energy"),
("path", "mechanical state")
]
]
for word in top_words + last_side_words + [side_words_start]:
word.scale(0.7)
side_words_start.next_to(horiz_axis, DOWN)
side_words_start.to_edge(RIGHT)
for words in top_words:
words.next_to(vert_axis, UP)
words.to_edge(LEFT)
for words in last_side_words:
words.next_to(side_words_start, DOWN)
for words in top_words[1], last_side_words[1]:
words.highlight(RED)
self.add(
axes, top_words[0], side_words_start,
last_side_words[0]
)
self.play(ShowCreation(graph))
self.play(
ShimmerIn(nature_finds),
ShowCreation(arrow),
ShowCreation(min_point)
)
self.dither()
self.play(
FadeOut(top_words[0]),
FadeOut(last_side_words[0]),
GrowFromCenter(top_words[1]),
GrowFromCenter(last_side_words[1])
)
self.dither(3)