import numpy as np import itertools as it from helpers import * from mobject.tex_mobject import TexMobject, TextMobject, Brace from mobject import Mobject from mobject.image_mobject import ImageMobject from topics.three_dimensions import Stars from animation import Animation from animation.transform import * from animation.simple_animations import * from animation.playground import TurnInsideOut, Vibrate from topics.geometry import * from topics.characters import * from topics.functions import ParametricFunction, FunctionGraph from topics.number_line import * from mobject.region import Region, region_from_polygon_vertices from scene import Scene class PhysicalIntuition(Scene): def construct(self): n_terms = 4 def func((x, y, ignore)): z = complex(x, y) if (np.abs(x%1 - 0.5)<0.01 and y < 0.01) or np.abs(z)<0.01: return ORIGIN out_z = 1./(2*np.tan(np.pi*z)*(z**2)) return out_z.real*RIGHT - out_z.imag*UP arrows = Mobject(*[ Arrow(ORIGIN, np.sqrt(2)*point) for point in compass_directions(4, RIGHT+UP) ]) arrows.highlight(YELLOW) arrows.ingest_sub_mobjects() all_arrows = Mobject(*[ arrows.copy().scale(0.3/(x)).shift(x*RIGHT) for x in range(1, n_terms+2) ]) terms = TexMobject([ "\\dfrac{1}{%d^2} + "%(x+1) for x in range(n_terms) ]+["\\cdots"]) terms.shift(2*UP) plane = NumberPlane(color = BLUE_E) axes = Mobject(NumberLine(), NumberLine().rotate(np.pi/2)) axes.highlight(WHITE) for term in terms.split(): self.play(ShimmerIn(term, run_time = 0.5)) self.dither() self.play(ShowCreation(plane), ShowCreation(axes)) self.play(*[ Transform(*pair) for pair in zip(terms.split(), all_arrows.split()) ]) self.play(PhaseFlow( func, plane, run_time = 5, virtual_time = 8 )) class TimeLine(Scene): def construct(self): dated_events = [ { "date" : 1696, "text": "Johann Bernoulli poses Brachistochrone problem", "picture" : "Johann_Bernoulli2" }, { "date" : 1662, "text" : "Fermat states his principle of least time", "picture" : "Pierre_de_Fermat" } ] speical_dates = [2016] + [ obj["date"] for obj in dated_events ] centuries = range(1600, 2100, 100) timeline = NumberLine( numerical_radius = 300, number_at_center = 1800, unit_length_to_spatial_width = SPACE_WIDTH/100, tick_frequency = 10, numbers_with_elongated_ticks = centuries ) timeline.add_numbers(*centuries) centers = [ Point(timeline.number_to_point(year)) for year in speical_dates ] timeline.add(*centers) timeline.shift(-centers[0].get_center()) self.add(timeline) self.dither() run_times = iter([3, 1]) for point, event in zip(centers[1:], dated_events): self.play(ApplyMethod( timeline.shift, -point.get_center(), run_time = run_times.next() )) picture = ImageMobject(event["picture"], invert = False) picture.scale_to_fit_width(2) picture.to_corner(UP+RIGHT) event_mob = TextMobject(event["text"]) event_mob.shift(2*LEFT+2*UP) date_mob = TexMobject(str(event["date"])) date_mob.scale(0.5) date_mob.shift(0.6*UP) line = Line(event_mob.get_bottom(), 0.2*UP) self.play( ShimmerIn(event_mob), ShowCreation(line), ShimmerIn(date_mob) ) self.play(FadeIn(picture)) self.dither(3) self.play(*map(FadeOut, [event_mob, date_mob, line, picture])) class StayedUpAllNight(Scene): def construct(self): clock = Circle(radius = 2, color = WHITE) clock.add(Dot(ORIGIN)) ticks = Mobject(*[ Line(1.8*vect, 2*vect, color = GREY) for vect in compass_directions(12) ]) clock.add(ticks) hour_hand = Line(ORIGIN, UP) minute_hand = Line(ORIGIN, 1.5*UP) clock.add(hour_hand, minute_hand) clock.to_corner(UP+RIGHT) hour_hand.get_center = lambda : clock.get_center() minute_hand.get_center = lambda : clock.get_center() solution = ImageMobject( "Newton_brachistochrone_solution2", use_cache = False ) solution.point_thickness = 3 solution.highlight(GREY) solution.scale_to_fit_width(5) solution.to_corner(UP+RIGHT) newton = ImageMobject("Old_Newton", invert = False) newton.scale(0.8) phil_trans = TextMobject("Philosophical Transactions") rect = Rectangle(height = 6, width = 4.5, color = WHITE) rect.to_corner(UP+RIGHT) rect.shift(DOWN) phil_trans.scale_to_fit_width(0.8*rect.get_width()) phil_trans.next_to(Point(rect.get_top()), DOWN) new_solution = solution.copy() new_solution.scale_to_fit_width(phil_trans.get_width()) new_solution.next_to(phil_trans, DOWN, buff = 1) not_newton = TextMobject("-Totally not by Newton") not_newton.scale_to_fit_width(2.5) not_newton.next_to(new_solution, DOWN, aligned_edge = RIGHT) phil_trans.add(rect) newton_complaint = TextMobject([ "``I do not love to be", " \\emph{dunned} ", "and teased by foreigners''" ], size = "\\small") newton_complaint.to_edge(UP, buff = 0.2) dunned = newton_complaint.split()[1] dunned.highlight() dunned_def = TextMobject("(old timey term for making \\\\ demands on someone)") dunned_def.scale(0.7) dunned_def.next_to(phil_trans, LEFT) dunned_def.shift(2*UP) dunned_arrow = Arrow(dunned_def, dunned) johann = ImageMobject("Johann_Bernoulli2", invert = False) johann.scale(0.4) johann.to_edge(LEFT) johann.shift(DOWN) johann_quote = TextMobject("``I recognize the lion by his claw''") johann_quote.next_to(johann, UP, aligned_edge = LEFT) self.play(ApplyMethod(newton.to_edge, LEFT)) self.play(ShowCreation(clock)) kwargs = { "axis" : OUT, "rate_func" : smooth } self.play( Rotating(hour_hand, radians = -2*np.pi, **kwargs), Rotating(minute_hand, radians = -12*2*np.pi, **kwargs), run_time = 5 ) self.dither() self.clear() self.add(newton) clock.ingest_sub_mobjects() self.play(Transform(clock, solution)) self.remove(clock) self.add(solution) self.dither() self.play( FadeIn(phil_trans), Transform(solution, new_solution) ) self.dither() self.play(ShimmerIn(not_newton)) phil_trans.add(solution, not_newton) self.dither() self.play(*map(ShimmerIn, newton_complaint.split())) self.dither() self.play( ShimmerIn(dunned_def), ShowCreation(dunned_arrow) ) self.dither() self.remove(dunned_def, dunned_arrow) self.play(FadeOut(newton_complaint)) self.remove(newton_complaint) self.play( FadeOut(newton), GrowFromCenter(johann) ) self.remove(newton) self.dither() self.play(ShimmerIn(johann_quote)) self.dither() class ThetaTSigmoidGraph(Scene): def construct(self): pass