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finished IntroScene tweaks

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This commit is contained in:
Ben Hambrecht
2018-02-23 19:38:27 +01:00
parent 497961082e
commit f5e545e3dd
1 changed files with 87 additions and 24 deletions
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111
active_projects/basel.py
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@@ -241,8 +241,8 @@ class IntroScene(PiCreatureScene):
CONFIG = {
"rect_height" : 0.2,
"duration" : 1.0,
"eq_spacing" : 3 * MED_LARGE_BUFF
"duration" : 0.5,
"eq_spacing" : 6 * MED_LARGE_BUFF
}
def construct(self):
@@ -328,6 +328,8 @@ class IntroScene(PiCreatureScene):
ReplacementTransform(self.partial_sum_decimal, self.q_marks)
)
self.wait()
def build_up_sum_on_number_line(self):
@@ -342,21 +344,25 @@ class IntroScene(PiCreatureScene):
unit_size = 5,
tick_frequency = 0.2,
line_to_number_buff = MED_LARGE_BUFF
)
).shift(LEFT)
self.number_line_labels = self.number_line.get_number_mobjects()
self.add(self.number_line,self.number_line_labels)
self.play(
FadeIn(self.number_line),
FadeIn(self.number_line_labels)
)
self.wait()
# create slabs for series terms
max_n = 10
max_n1 = 10
max_n2 = 100
terms = [0] + [1./(n**2) for n in range(1, max_n + 1)]
terms = [0] + [1./(n**2) for n in range(1, max_n2 + 1)]
series_terms = np.cumsum(terms)
lines = VGroup()
self.rects = VGroup()
slab_colors = [YELLOW, BLUE] * (max_n / 2)
slab_colors = [YELLOW, BLUE] * (max_n2 / 2)
for t1, t2, color in zip(series_terms, series_terms[1:], slab_colors):
line = Line(*map(self.number_line.number_to_point, [t1, t2]))
@@ -375,52 +381,102 @@ class IntroScene(PiCreatureScene):
#self.rects.radial_gradient_highlight(ORIGIN, 5, YELLOW, BLUE)
self.little_euler_terms = VGroup()
for i in range(1,7):
if i == 1:
term = TexMobject("1", fill_color = slab_colors[i-1])
else:
term = TexMobject("{1\over " + str(i**2) + "}", fill_color = slab_colors[i-1])
term.scale(0.4)
self.little_euler_terms.add(term)
for i in range(5):
self.play(
GrowFromPoint(self.rects[i], self.euler_sum[2*i].get_center(),
run_time = self.duration)
run_time = 1)
)
term = self.little_euler_terms.submobjects[i]
term.next_to(self.rects[i], UP)
self.play(FadeIn(term))
for i in range(5, max_n):
self.ellipsis = TexMobject("\cdots")
self.ellipsis.scale(0.4)
for i in range(5, max_n1):
if i == 5:
self.ellipsis.next_to(self.rects[i+3], UP)
self.play(
FadeIn(self.ellipsis),
GrowFromPoint(self.rects[i], self.euler_sum[10].get_center(),
run_time = 0.5)
)
else:
self.play(
GrowFromPoint(self.rects[i], self.euler_sum[10].get_center(),
run_time = 0.5)
)
for i in range(max_n1, max_n2):
self.play(
GrowFromPoint(self.rects[i], self.euler_sum[10].get_center(),
run_time = self.duration)
)
GrowFromPoint(self.rects[i], self.euler_sum[10].get_center(),
run_time = 0.01)
)
self.wait()
PI = TAU/2
P = self.q_marks.get_center() + 0.5 * DOWN + 0.5 * LEFT
Q = self.rects[-1].get_center() + 0.2 * UP
self.arrow = CurvedArrow(P, Q,
angle = TAU/12,
color = YELLOW
)
self.play(FadeIn(self.arrow))
self.wait()
def show_pi_answer(self):
self.pi_answer = TexMobject("{\\pi^2 \\over 6}").highlight(YELLOW)
self.pi_answer.move_to(self.partial_sum_decimal)
self.pi_answer.next_to(self.euler_sum[-1], RIGHT,
self.pi_answer.next_to(self.euler_sum[-1], RIGHT, buff = 1,
submobject_to_align = self.pi_answer[-2])
self.play(ReplacementTransform(self.q_marks, self.pi_answer))
self.wait()
def other_pi_formulas(self):
self.play(
FadeOut(self.rects),
FadeOut(self.number_line_labels),
FadeOut(self.number_line)
FadeOut(self.number_line),
FadeOut(self.little_euler_terms),
FadeOut(self.ellipsis),
FadeOut(self.arrow)
)
self.leibniz_sum = TexMobject(
"1-{1\\over 3}+{1\\over 5}-{1\\over 7}+{1\\over 9}-\\cdots",
"=", "{\\pi \\over 4}")
"=", "\quad\,\,{\\pi \\over 4}", arg_separator = " \\, ")
self.wallis_product = TexMobject(
"{2\\over 1} \\cdot {2\\over 3} \\cdot {4\\over 3} \\cdot {4\\over 5}" +
"\\cdot {6\\over 5} \\cdot {6\\over 7} \\cdots",
"=", "{\\pi \\over 2}")
"=", "\quad\,\, {\\pi \\over 2}", arg_separator = " \\, ")
self.leibniz_sum.next_to(self.euler_sum.get_part_by_tex("="), DOWN,
buff = self.eq_spacing,
buff = 2,
submobject_to_align = self.leibniz_sum.get_part_by_tex("=")
)
self.wallis_product.next_to(self.leibniz_sum.get_part_by_tex("="), DOWN,
buff = self.eq_spacing,
buff = 2,
submobject_to_align = self.wallis_product.get_part_by_tex("=")
)
@@ -448,7 +504,11 @@ class IntroScene(PiCreatureScene):
# focus on pi squared
pi_squared = self.euler_sum.get_part_by_tex("\\pi")[-3]
self.play(
ScaleInPlace(pi_squared,2,rate_func = wiggle)
WiggleOutThenIn(pi_squared,
scale_value = 4,
angle = 0.003 * TAU,
run_time = 2
)
)
@@ -458,17 +518,20 @@ class IntroScene(PiCreatureScene):
q_circle = Circle(
stroke_color = YELLOW,
fill_color = YELLOW,
fill_opacity = 0.5,
radius = 0.4,
stroke_width = 10.0
fill_opacity = 0.25,
radius = 0.5,
stroke_width = 3.0
)
q_mark = TexMobject("?")
q_mark.next_to(q_circle)
thought = Group(q_circle, q_mark)
q_mark.scale_to_fit_height(0.8 * q_circle.get_height())
q_mark.scale_to_fit_height(0.6 * q_circle.get_height())
self.look_at(pi_squared)
self.pi_creature_thinks(thought,target_mode = "confused",
bubble_kwargs = { "height" : 2, "width" : 3 })
bubble_kwargs = { "height" : 2.5, "width" : 5 })
self.look_at(pi_squared)
self.wait()