3b1b-manim/scripts/inventing_math_images.py

#!/usr/bin/env python

import numpy as np
import itertools as it
from copy import deepcopy
import sys


from animation import *
from mobject import *
from constants import *
from region import *
from scene import Scene
from script_wrapper import command_line_create_scene
from inventing_math import divergent_sum, draw_you



class SimpleText(Scene):
    args_list = [
         ("Build from the start...",),
         ("What would that feel like?",),
         ("Arbitrary decisions hinder generality",),
         ("Section 1: Discovering and Defining Infinite Sums",),
         ("Section 2: Seeking Generality",),
         ("Section 3: Redefining Distance",),
         ("``Approach''?",),
         ("Rigor would dicate you ignore these",),
         ("dist($A$, $B$) = dist($A+x$, $B+x$) \\quad for all $x$",),
         ("How does a useful distance function differ from a random function?",),
         ("Pause now, if you like, and see if you can invent your own distance function from this.",),
         ("$p$-adic metrics \\\\ ($p$ is any prime number)",),
         ("This does not meant to match the history of discoveries",),
    ]
    @staticmethod
    def args_to_string(text):
        return initials(filter(lambda c : c in string.letters + " ", text))

    def construct(self, text):
        self.add(text_mobject(text))


class SimpleTex(Scene):
    args_list = [
        (
            "\\frac{9}{10}+\\frac{9}{100}+\\frac{9}{1000}+\\cdots = 1",
            "SumOf9s"
        ),
        (
            "0 < p < 1",
            "PBetween0And1"
        ),
    ]
    @staticmethod
    def args_to_string(expression, words):
        return words

    def construct(self, expression, words):
        self.add(tex_mobject(expression))


class OneMinusOnePoem(Scene):
    def construct(self):
        verse1 = text_mobject("""
            \\begin{flushleft}
            When one takes one from one  \\\\
            plus one from one plus one \\\\
            and on and on but ends  \\\\
            anon then starts again, \\\\
            then some sums sum to one, \\\\
            to zero other ones. \\\\
            One wonders who'd have won \\\\
            had stopping not been done; \\\\
            had he summed every bit \\\\
            until the infinite. \\\\
            \\end{flushleft}
        """).scale(0.5).to_corner(UP+LEFT)
        verse2 = text_mobject("""
            \\begin{flushleft}
            Lest you should think that such \\\\
            less well-known sums are much \\\\
            ado about nonsense \\\\
            I do give these two cents: \\\\
            The universe has got \\\\
            an answer which is not \\\\
            what most would first surmise, \\\\
            it is a compromise, \\\\
            and though it seems a laugh \\\\
            the universe gives ``half''. \\\\
            \\end{flushleft}
        """).scale(0.5).to_corner(DOWN+LEFT)
        equation = tex_mobject(
            "1-1+1-1+\\cdots = \\frac{1}{2}"
        )
        self.add(verse1, verse2, equation)
        
class DivergentSum(Scene):
    def construct(self):
        self.add(divergent_sum().scale(0.75))


class PowersOfTwoSmall(Scene):
    def construct(self):
        you, bubble = draw_you(with_bubble=True)
        bubble.write(
            "Is there any way in which apparently \
            large powers of two can be considered small?"
        )
        self.add(you, bubble, bubble.content)