#!/usr/bin/env python from helpers import * from mobject.tex_mobject import TexMobject from mobject import Mobject from mobject.image_mobject import ImageMobject from mobject.vectorized_mobject import * from animation.animation import Animation from animation.transform import * from animation.simple_animations import * from animation.playground import * from topics.geometry import * from topics.characters import * from topics.functions import * from topics.number_line import * from topics.numerals import * from topics.combinatorics import * from scene import Scene from camera import Camera from mobject.svg_mobject import * from mobject.tex_mobject import * from mobject.vectorized_mobject import * ## To watch one of these scenes, run the following: ## python extract_scene.py -p file_name class LightCone(Circle): pass class IntroScene(PiCreatureScene): CONFIG = { "rect_height" : 0.2, "duration" : 1.0, "eq_spacing" : 3 * MED_LARGE_BUFF } def construct(self): morty = self.get_primary_pi_creature() morty.scale(0.7).to_corner(DOWN+RIGHT) self.build_up_euler_sum() self.force_skipping() self.build_up_sum_on_number_line() self.show_pi_answer() self.other_pi_formulas() self.refocus_on_euler_sum() self.revert_to_original_skipping_status() def build_up_euler_sum(self): self.euler_sum = TexMobject( "1", "+", "{1 \\over 4}", "+", "{1 \\over 9}", "+", "{1 \\over 16}", "+", "{1 \\over 25}", "+", "\\cdots", "=", arg_separator = " \\, " ) self.euler_sum.to_edge(UP) self.euler_sum.shift(2*LEFT) terms = [1./n**2 for n in range(1,6)] partial_results_values = np.cumsum(terms) self.play( FadeIn(self.euler_sum[0], run_time = self.duration) ) equals_sign = self.euler_sum.get_part_by_tex("=") self.partial_sum_decimal = DecimalNumber(partial_results_values[1], num_decimal_points = 2) self.partial_sum_decimal.next_to(equals_sign, RIGHT) for i in range(4): FadeIn(self.partial_sum_decimal, run_time = self.duration) if i == 0: self.play( FadeIn(self.euler_sum[1], run_time = self.duration), FadeIn(self.euler_sum[2], run_time = self.duration), FadeIn(equals_sign, run_time = self.duration), FadeIn(self.partial_sum_decimal, run_time = self.duration) ) else: self.play( FadeIn(self.euler_sum[2*i+1], run_time = self.duration), FadeIn(self.euler_sum[2*i+2], run_time = self.duration), ChangeDecimalToValue( self.partial_sum_decimal, partial_results_values[i+1], run_time = self.duration, num_decimal_points = 6, show_ellipsis = True, position_update_func = lambda m: m.next_to(equals_sign, RIGHT) ) ) self.wait() self.q_marks = TextMobject("???").highlight(YELLOW) self.q_marks.move_to(self.partial_sum_decimal) self.play( FadeIn(self.euler_sum[-3], run_time = self.duration), # + FadeIn(self.euler_sum[-2], run_time = self.duration), # ... ReplacementTransform(self.partial_sum_decimal, self.q_marks) ) def build_up_sum_on_number_line(self): self.number_line = NumberLine( x_min = 0, color = WHITE, number_at_center = 1, stroke_width = 1, numbers_with_elongated_ticks = [0,1,2,3], numbers_to_show = np.arange(0,5), unit_size = 5, tick_frequency = 0.2, line_to_number_buff = MED_LARGE_BUFF ) self.number_line_labels = self.number_line.get_number_mobjects() self.add(self.number_line,self.number_line_labels) self.wait() # create slabs for series terms max_n = 10 terms = [0] + [1./(n**2) for n in range(1, max_n + 1)] series_terms = np.cumsum(terms) lines = VGroup() self.rects = VGroup() slab_colors = [YELLOW, BLUE] * (max_n / 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])) rect = Rectangle() rect.stroke_width = 0 rect.fill_opacity = 1 rect.highlight(color) rect.stretch_to_fit_height( self.rect_height, ) rect.stretch_to_fit_width(line.get_width()) rect.move_to(line) self.rects.add(rect) lines.add(line) #self.rects.radial_gradient_highlight(ORIGIN, 5, RED, BLUE) for i in range(5): self.play( GrowFromPoint(self.rects[i], self.euler_sum[2*i].get_center(), run_time = self.duration) ) for i in range(5, max_n): self.play( GrowFromPoint(self.rects[i], self.euler_sum[10].get_center(), run_time = self.duration) ) 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, submobject_to_align = self.pi_answer[-2]) self.play(ReplacementTransform(self.q_marks, self.pi_answer)) def other_pi_formulas(self): self.play( FadeOut(self.rects), FadeOut(self.number_line_labels), FadeOut(self.number_line) ) self.leibniz_sum = TexMobject( "1-{1\\over 3}+{1\\over 5}-{1\\over 7}+{1\\over 9}-\\cdots", "=", "{\\pi \\over 4}") 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}") self.leibniz_sum.next_to(self.euler_sum.get_part_by_tex("="), DOWN, buff = self.eq_spacing, 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, submobject_to_align = self.wallis_product.get_part_by_tex("=") ) self.play( Write(self.leibniz_sum) ) self.play( Write(self.wallis_product) ) def refocus_on_euler_sum(self): self.euler_sum.add(self.pi_answer) self.play( FadeOut(self.leibniz_sum), FadeOut(self.wallis_product), ApplyMethod(self.euler_sum.shift, ORIGIN + 2*UP - self.euler_sum.get_center()) ) # focus on pi squared pi_squared = self.euler_sum.get_part_by_tex("\\pi")[-3] self.play( ScaleInPlace(pi_squared,2,rate_func = wiggle) ) morty = self.get_primary_pi_creature() bubble = ThoughtBubble(height = 2, width = 5) bubble.pin_to(morty) thought = Circle() thought.add(TexMobject("?")) thought.next_to(morty,LEFT, LARGE_BUFF, UP) thought.generate_target() bubble.add_content(thought.target) self.play( morty.change_mode, "confused", FadeIn(bubble) ) self.wait() class FirstLightHouseScene(Scene): def construct(self): self.show_lighthouses_on_number_line() def show_lighthouses_on_number_line(self): self.number_line = NumberLine( x_min = 0, color = WHITE, number_at_center = 1, stroke_width = 1, numbers_with_elongated_ticks = [0,1,2,3], numbers_to_show = np.arange(0,5), unit_size = 5, tick_frequency = 0.2, line_to_number_buff = MED_LARGE_BUFF ) self.number_line_labels = self.number_line.get_number_mobjects() self.add(self.number_line,self.number_line_labels) self.wait() first_lighthouse_indicator = Circle( stroke_width = 1, stroke_color = WHITE, fill_color = RED, fill_opacity = 1, radius = 0.3 ) origin_point = self.number_line.number_to_point(0) first_lighthouse_indicator.move_to(origin_point) self.add(first_lighthouse_indicator) lighthouse1 = SVGMobject(file_name = "lighthouse") self.add(lighthouse1) self.wait()