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Preliminary end to leibniz project
This commit is contained in:
Grant Sanderson
parent
1d953b5616
commit
ea8b03f07a
3 changed files with 349 additions and 42 deletions
384
leibniz.py
384
leibniz.py
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@ -2966,6 +2966,40 @@ class RecipeFor1125(IntroduceRecipe):
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self.play(Write(words))
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self.dither()
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class Show1125Circle(LatticePointScene):
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CONFIG = {
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"y_radius" : 35,
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"max_lattice_point_radius" : 35,
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}
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def construct(self):
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self.plane.set_stroke(width = 1)
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radius = np.sqrt(1125)
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circle = self.get_circle(radius)
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radial_line, root_label = self.get_radial_line_with_label(radius)
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dots = self.get_lattice_points_on_r_squared_circle(1125)
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self.play(
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ShowCreation(radial_line),
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Write(root_label, run_time = 1)
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)
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self.add_foreground_mobject(root_label)
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self.play(
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Rotating(
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radial_line,
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rate_func = smooth,
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about_point = self.plane_center
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),
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ShowCreation(circle),
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LaggedStart(
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DrawBorderThenFill,
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dots,
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stroke_width = 4,
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stroke_color = PINK,
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),
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run_time = 2,
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)
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self.dither(2)
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class SummarizeCountingRule(Show125Circle):
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CONFIG = {
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"dot_radius" : 0.075,
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@ -4044,8 +4078,6 @@ class CountLatticePointsInBigCircle(LatticePointScene):
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class AddUpGrid(Scene):
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def construct(self):
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self.force_skipping()
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self.add_radicals()
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self.add_row_lines()
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self.add_chi_sums()
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@ -4057,6 +4089,7 @@ class AddUpGrid(Scene):
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self.factor_out_R()
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self.show_chi_sum_values()
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self.compare_to_pi_R_squared()
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self.celebrate()
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def add_radicals(self):
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self.radicals = CountLatticePointsInBigCircle.get_radicals()
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@ -4167,14 +4200,24 @@ class AddUpGrid(Scene):
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]
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prime_rects.highlight(GREEN)
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self.play(FadeIn(composite_rects))
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randy = Randolph().flip()
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randy.next_to(self.chi_mobs, RIGHT)
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self.play(FadeIn(randy))
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self.play(randy.change_mode, "pleading")
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self.play(
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FadeIn(composite_rects),
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randy.look_at, composite_rects.get_bottom()
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)
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self.dither(2)
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self.play(
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FadeOut(composite_rects),
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FadeIn(prime_rects)
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FadeIn(prime_rects),
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randy.look_at, prime_rects.get_top(),
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)
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self.dither(2)
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self.play(FadeOut(prime_rects))
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self.play(Blink(randy))
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self.dither()
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self.play(*map(FadeOut, [prime_rects, randy]))
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def organize_into_columns(self):
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left_x = self.arrows.get_right()[0] + SMALL_BUFF
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@ -4201,17 +4244,13 @@ class AddUpGrid(Scene):
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rect = Rectangle(
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stroke_color = WHITE,
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stroke_width = 2,
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fill_color = BLACK,
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fill_color = average_color(BLUE_E, BLACK),
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fill_opacity = 1,
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height = 1.2,
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height = 1.15,
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width = 2*SPACE_WIDTH - 2*MED_SMALL_BUFF,
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)
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rect.move_to(3*LEFT, LEFT)
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rect.to_edge(UP, buff = SMALL_BUFF)
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# words = TextMobject(
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# "\\# Lattice points \\\\ within radius $R$"
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# )
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# words.scale(0.7)
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words = TextMobject("Total")
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words.scale(0.8)
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words.next_to(rect.get_left(), RIGHT, SMALL_BUFF)
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@ -4231,34 +4270,30 @@ class AddUpGrid(Scene):
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for chi_mob in self.chi_mobs:
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chi_mob_columns[chi_mob.d - 1].add(chi_mob)
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terms = VGroup()
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full_sum = VGroup()
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for d in range(1, 7):
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chi_args = ["{\\chi(", str(d), ")"]
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R_args = ["{R^2"]
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if d != 1:
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chi_args.append("\\over %d}"%d)
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R_args.append("\\over %d}"%d)
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term = VGroup(
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TexMobject("R^2"),
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TexMobject(*chi_args),
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TexMobject(*R_args),
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TexMobject("\\chi(", str(d), ")"),
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TexMobject("+")
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)
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term.arrange_submobjects(RIGHT, SMALL_BUFF)
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term[2].next_to(term[1][-1][0], RIGHT, SMALL_BUFF)
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if d != 1:
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term[2].add(term[1][-1])
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term[1].remove(term[1][-1])
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term[1][1].highlight(YELLOW)
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terms.add(term)
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terms.arrange_submobjects(RIGHT, SMALL_BUFF)
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terms.scale(0.7)
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terms.next_to(self.count_words, RIGHT, SMALL_BUFF)
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full_sum.add(term)
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full_sum.arrange_submobjects(RIGHT, SMALL_BUFF)
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full_sum.scale(0.7)
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full_sum.next_to(self.count_words, RIGHT, SMALL_BUFF)
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self.revert_to_original_skipping_status()
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for column, term in zip(chi_mob_columns, terms):
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for column, term in zip(chi_mob_columns, full_sum):
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rect = SurroundingRectangle(column)
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rect.stretch_to_fit_height(2*SPACE_HEIGHT)
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rect.move_to(column, UP)
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rect.set_stroke(width = 0)
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rect.set_fill(YELLOW, 0.3)
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self.play(FadeIn(rect))
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self.dither()
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self.play(
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@ -4271,7 +4306,7 @@ class AddUpGrid(Scene):
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Write(term[2]),
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)
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self.dither()
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if term is terms[2]:
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if term is full_sum[2]:
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vect = sum([
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self.count_rect.get_left()[0],
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SPACE_WIDTH,
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@ -4282,26 +4317,295 @@ class AddUpGrid(Scene):
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for m in [
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self.count_rect,
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self.count_words,
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]+list(terms[:3])
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]+list(full_sum[:3])
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])
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VGroup(*terms[3:]).shift(vect)
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VGroup(*full_sum[3:]).shift(vect)
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self.play(FadeOut(rect))
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self.full_sum = full_sum
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def factor_out_R(self):
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pass
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self.corner_four.generate_target()
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R_squared = TexMobject("R^2")
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dots = TexMobject("\\cdots")
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lp, rp = map(TexMobject, ["\\big(", "\\big)"])
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new_sum = VGroup(
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self.corner_four.target, R_squared, lp
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)
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R_fracs, chi_terms, plusses = full_sum_parts = [
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VGroup(*[term[i] for term in self.full_sum])
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for i in range(3)
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]
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targets = []
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for part in full_sum_parts:
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part.generate_target()
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targets.append(part.target)
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for R_frac, chi_term, plus in zip(*targets):
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chi_term.scale(0.9)
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chi_term.move_to(R_frac[0], DOWN)
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if R_frac is R_fracs.target[0]:
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new_sum.add(chi_term)
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else:
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new_sum.add(VGroup(chi_term, R_frac[1]))
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new_sum.add(plus)
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new_sum.add(dots)
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new_sum.add(rp)
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new_sum.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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new_sum.next_to(self.count_words, RIGHT, SMALL_BUFF)
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R_squared.shift(0.5*SMALL_BUFF*UP)
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R_movers = VGroup()
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for R_frac in R_fracs.target:
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if R_frac is R_fracs.target[0]:
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mover = R_frac
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else:
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mover = R_frac[0]
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Transform(mover, R_squared).update(1)
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R_movers.add(mover)
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self.play(*it.chain(
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map(Write, [lp, rp, dots]),
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map(MoveToTarget, full_sum_parts),
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), run_time = 2)
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self.remove(R_movers)
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self.add(R_squared)
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self.dither()
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self.play(
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MoveToTarget(self.corner_four, run_time = 2),
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FadeOut(self.corner_four.rect)
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)
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self.dither(2)
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self.remove(self.full_sum, self.corner_four)
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self.add(new_sum)
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self.new_sum = new_sum
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def show_chi_sum_values(self):
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pass
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alt_rhs = TexMobject(
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"\\approx", "4", "R^2",
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"\\left(1 - \\frac{1}{3} + \\frac{1}{5}" + \
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"-\\frac{1}{7} + \\frac{1}{9} - \\frac{1}{11}" + \
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"+ \\cdots \\right)",
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)
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alt_rhs.scale(0.9)
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alt_rhs.next_to(
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self.count_words[-1], DOWN,
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buff = LARGE_BUFF,
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aligned_edge = LEFT
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)
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self.play(
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*map(FadeOut, [
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self.chi_mobs, self.plusses, self.arrows,
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self.radicals, self.row_lines
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]) + [
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FadeOut(self.count_rect),
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Animation(self.new_sum),
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Animation(self.count_words),
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]
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)
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self.play(Write(alt_rhs))
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self.dither(2)
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self.alt_rhs = alt_rhs
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def compare_to_pi_R_squared(self):
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pass
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approx, pi, R_squared = area_rhs = TexMobject(
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"\\approx", "\\pi", "R^2"
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)
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area_rhs.next_to(self.alt_rhs, RIGHT)
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brace = Brace(
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VGroup(self.alt_rhs, area_rhs), DOWN
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)
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brace.add(brace.get_text(
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"Arbitrarily good as $R \\to \\infty$"
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))
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pi_sum = TexMobject(
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"4", self.alt_rhs[-1].get_tex_string(),
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"=", "\\pi"
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)
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pi_sum.scale(0.9)
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pi = pi_sum.get_part_by_tex("pi")
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pi.scale(2, about_point = pi.get_left())
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pi.highlight(YELLOW)
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pi_sum.shift(
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self.alt_rhs[-1].get_bottom(),
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MED_SMALL_BUFF*DOWN,
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-pi_sum[1].get_top()
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)
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self.play(Write(area_rhs))
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self.dither()
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self.play(FadeIn(brace))
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self.dither(2)
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self.play(FadeOut(brace))
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self.play(*[
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ReplacementTransform(m.copy(), pi_sum_part)
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for pi_sum_part, m in zip(pi_sum, [
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self.alt_rhs.get_part_by_tex("4"),
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self.alt_rhs[-1],
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area_rhs[0],
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area_rhs[1],
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])
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])
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def celebrate(self):
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creatures = TeacherStudentsScene().get_pi_creatures()
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self.play(FadeIn(creatures))
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self.play(*[
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ApplyMethod(pi.change, "hooray", self.alt_rhs)
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for pi in creatures
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])
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self.dither()
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for i in 0, 2, 3:
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self.play(Blink(creatures[i]))
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self.dither()
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class IntersectionOfTwoFields(TeacherStudentsScene):
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def construct(self):
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circles = VGroup()
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for vect, color, adj in (LEFT, BLUE, "Algebraic"), (RIGHT, YELLOW, "Analytic"):
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circle = Circle(color = WHITE)
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circle.set_fill(color, opacity = 0.3)
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circle.stretch_to_fit_width(7)
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circle.stretch_to_fit_height(4)
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circle.shift(SPACE_WIDTH*vect/3.0 + LEFT)
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title = TextMobject("%s \\\\ number theory"%adj)
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title.scale(0.7)
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title.move_to(circle)
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title.to_edge(UP, buff = SMALL_BUFF)
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circle.next_to(title, DOWN, SMALL_BUFF)
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title.highlight(color)
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circle.title = title
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circles.add(circle)
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new_number_systems = TextMobject(
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"New \\\\ number systems"
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)
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gaussian_integers = TextMobject(
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"e.g. Gaussian \\\\ integers"
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)
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new_number_systems.next_to(circles[0].get_top(), DOWN, MED_SMALL_BUFF)
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new_number_systems.shift(MED_LARGE_BUFF*(DOWN+2*LEFT))
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gaussian_integers.next_to(new_number_systems, DOWN)
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gaussian_integers.highlight(BLUE)
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circles[0].words = VGroup(new_number_systems, gaussian_integers)
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zeta = TexMobject("\\zeta(s) = \\sum_{n=1}^\\infty \\frac{1}{n^2}")
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L_function = TexMobject(
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"L(s, \\chi) = \\sum_{n=1}^\\infty \\frac{\\chi(n)}{n^s}"
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)
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for mob in zeta, L_function:
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mob.scale(0.8)
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zeta.next_to(circles[1].get_top(), DOWN, MED_LARGE_BUFF)
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zeta.shift(MED_LARGE_BUFF*RIGHT)
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L_function.next_to(zeta, DOWN, MED_LARGE_BUFF)
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L_function.highlight(YELLOW)
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circles[1].words = VGroup(zeta, L_function)
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mid_words = TextMobject("Where\\\\ we \\\\ were")
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mid_words.scale(0.7)
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mid_words.move_to(circles)
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for circle in circles:
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self.play(
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Write(circle.title, run_time = 2),
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DrawBorderThenFill(circle, run_time = 2),
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self.teacher.change_mode, "raise_right_hand"
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)
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self.dither()
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for circle in circles:
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for word in circle.words:
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self.play(
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Write(word, run_time = 2),
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self.teacher.change, "speaking",
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*[
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ApplyMethod(pi.change, "pondering")
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for pi in self.get_students()
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]
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)
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self.dither()
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self.play(
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Write(mid_words),
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self.teacher.change, "raise_right_hand"
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)
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self.change_student_modes(
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*["thinking"]*3,
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look_at_arg = mid_words
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)
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self.dither(3)
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class Sponsorship(PiCreatureScene):
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def construct(self):
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morty = self.pi_creature
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logo = SVGMobject(
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file_name = "remix_logo",
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)
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logo.scale_to_fit_height(1)
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logo.center()
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logo.set_stroke(width = 0)
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logo.set_fill(BLUE_D, 1)
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VGroup(*logo[6:]).gradient_highlight(BLUE_B, BLUE_E)
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logo.next_to(morty.get_corner(UP+LEFT), UP)
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url = TextMobject("www.remix.com")
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url.to_corner(UP+LEFT)
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rect = ScreenRectangle(height = 5)
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rect.next_to(url, DOWN, aligned_edge = LEFT)
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self.play(
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morty.change_mode, "raise_right_hand",
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LaggedStart(DrawBorderThenFill, logo, run_time = 3)
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)
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self.dither()
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self.play(
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ShowCreation(rect),
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logo.scale, 0.8,
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logo.to_corner, UP+RIGHT,
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morty.change, "happy"
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)
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self.dither()
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self.play(Write(url))
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self.dither(3)
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for mode in "confused", "pondering", "happy":
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self.play(morty.change_mode, mode)
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self.dither(3)
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class Thumbnail(Scene):
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def construct(self):
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# randy = TexMobject("\\pi").highlight(BLUE_D)
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randy = Randolph()
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randy.scale_to_fit_height(5)
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randy.body.set_stroke(YELLOW, width = 2)
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self.add(randy)
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primes = [
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n for n in range(2, 1000)
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if all(n%k != 0 for k in range(2, n))
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][:140]
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prime_mobs = VGroup()
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x_spacing = LARGE_BUFF
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y_spacing = 0.75
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for i, prime in enumerate(primes):
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prime_mob = Integer(prime)
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prime_mob.scale(0.9)
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x = i%10
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y = i//10
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prime_mob.shift(x*x_spacing*RIGHT + y*y_spacing*DOWN)
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prime_mobs.add(prime_mob)
|
||||
prime_mob.highlight({
|
||||
-1 : YELLOW,
|
||||
0 : RED,
|
||||
1 : BLUE,
|
||||
}[chi_func(prime)])
|
||||
prime_mobs.center().to_edge(UP)
|
||||
for i in range(7):
|
||||
self.add(BackgroundRectangle(
|
||||
VGroup(*prime_mobs[10*i:10*(i+1)]),
|
||||
fill_opacity = 0.5,
|
||||
))
|
||||
self.add(prime_mobs)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -26,7 +26,7 @@ class Scene(object):
|
|||
"frame_duration" : LOW_QUALITY_FRAME_DURATION,
|
||||
"construct_args" : [],
|
||||
"skip_animations" : False,
|
||||
"write_to_movie" : True,
|
||||
"write_to_movie" : False,
|
||||
"save_frames" : False,
|
||||
"output_directory" : MOVIE_DIR,
|
||||
"name" : None,
|
||||
|
|
|
|||
|
|
@ -30,11 +30,14 @@ class DecimalNumber(VMobject):
|
|||
)
|
||||
|
||||
class Integer(VGroup):
|
||||
CONFIG = {
|
||||
"digit_buff" : 0.8*SMALL_BUFF
|
||||
}
|
||||
def __init__(self, integer, **kwargs):
|
||||
num_str = str(integer)
|
||||
VGroup.__init__(self, *map(TexMobject, num_str), **kwargs)
|
||||
self.arrange_submobjects(
|
||||
RIGHT, buff = SMALL_BUFF, aligned_edge = DOWN
|
||||
RIGHT, buff = self.digit_buff, aligned_edge = DOWN
|
||||
)
|
||||
if num_str[0] == "-":
|
||||
self[0].next_to(self[1], LEFT, buff = SMALL_BUFF)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue