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Elteoremadebeethoven/sqrt_2.py

Created October 9, 2024 01:08
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Code from my Short "Sqrt(2) is irrational".
Raw
sqrt_2.py
from manim import *
config.disable_caching = True
# Change default font size
DEFAULT_FONT_SIZE = 28
MathTex.set_default(font_size=DEFAULT_FONT_SIZE)
Tex.set_default(font_size=DEFAULT_FONT_SIZE)
SCALE_FACTOR = 1
tmp_pixel_height = config.pixel_height
config.pixel_height = config.pixel_width
config.pixel_width = tmp_pixel_height
config.frame_height = config.frame_height / SCALE_FACTOR
config.frame_width = config.frame_height * 9 / 16
class MainScene(Scene):
def align_tex_with_symbol(self, t1, t2):
"""
Align t2 with one symbol of t1
"""
tex1, index1 = t1
tex2, index2 = t2
ref1 = tex1[index1].get_center()
ref2 = tex2[index2].get_center()
vector = ref1 - ref2
tex2_y = tex2.get_y()
tex2.shift(vector).set_y(tex2_y)
def construct(self):
title = Tex("Suppose ",
"$\\displaystyle\\sqrt{2} = \\frac{p}{q}$",
"is an irreducible", "fraction")
title[-2:].arrange(DOWN, aligned_edge=LEFT, buff=0.1)
title[-2:].next_to(title[1], RIGHT, buff=0.2)
title.set_x(0).to_edge(UP)
equations = [
# 0 1 2 3
MathTex("\\sqrt{2}","q","=","p"),
# 0 1 2 3 4 5 6
MathTex("\\Rightarrow","(","\\sqrt{2}q",")^2","=","p","^2"),
# 0 1 2 3 4 5 6
MathTex("\\Rightarrow","2","q","^2","=","p","^2"),
]
eq_grp1 = VGroup(*equations)\
.arrange(DOWN, aligned_edge=LEFT, buff=0.1)\
.next_to(title, DOWN)
conc1 = Tex("If $p^2$ is even then $p$ is even")\
.next_to(eq_grp1, DOWN)
_because = Tex("Because:").next_to(conc1, DOWN)
odd_proof = VGroup(
# 0 1 2 3 4 5 6 7 8, 9 10
MathTex("(2k-1)^2","=","4","k","^","2","-","4","k","+1"),
# 0 1 2 3 4 5 6 7 8
MathTex("=","4","k","(","k","-","1",")","+1"),
).arrange(DOWN, aligned_edge=LEFT).next_to(_because, DOWN)
odd_proof[1].align_to(odd_proof[0][1], LEFT)
generic_odd_brace = Brace(odd_proof[0][0], DOWN, buff=0.05)
generic_odd_tex = generic_odd_brace.get_text(r"generic\\odd\\number", buff=0.05)
generic_odd_tex.scale(0.7, about_point=generic_odd_tex.get_top())
_4kp1_brace = Brace(odd_proof[1][1:8], DOWN, buff=0)\
.scale([1.1,1,1])
_4kp1_tex = _4kp1_brace.get_text("even", buff=0.05)
# _4kp1_tex.scale(0.8, about_point=_4kp1_tex.get_top())
_1 = odd_proof[1][-1].copy().next_to(_4kp1_tex, RIGHT)
_1.align_to(odd_proof[1][-1], LEFT)
_1.align_to(_4kp1_tex, DOWN)
odd_brace = Brace(VGroup(_4kp1_tex, _1), DOWN, buff=0)\
.scale([1.1,1,1])
odd_tex = odd_brace.get_text("odd", buff=0.05)
logic_proof = VGroup(
# 0 1 2 3
MathTex("{\\rm odd}(n)","\\to","{\\rm odd}(n^2)"),
# 0 1 2 3
MathTex("\\Leftrightarrow","\\neg","{\\rm odd}(n^2)","\\to","\\neg","{\\rm odd}(n)"),
# 0 1 2 3
MathTex("\\Leftrightarrow","{\\rm even}(n^2)","\\to","{\\rm even}(n)"),
Tex("$\\therefore p$ is even"),
).arrange(DOWN, aligned_edge=LEFT, buff=0.1)\
.next_to(odd_proof, DOWN, buff=1.2)
q_contradiction = VGroup(
# 0 1 2 3 4 5 6 7 8
MathTex("\\Rightarrow", "2", "q^2", "=", "(", "2", "k" ,")", "^2"),
MathTex("\\Rightarrow", "2", "q^2", "=", "4", "k", "^2"),
# 0 1 2 3 4 5
MathTex("\\Rightarrow","q^2", "=", "2", "k", "^2"),
MathTex("\\therefore\\,\\text{even}(q^2)\\to\\text{even}(q)"),
MathTex("\\Rightarrow \\sqrt{2} = \\frac{2k}{2m}"),
).arrange(DOWN, aligned_edge=LEFT, buff=0.1)\
.next_to(logic_proof, DOWN, buff=0.1)
adm_sign = MathTex("!", stroke_width=3, stroke_opacity=1).scale(2)\
.next_to(q_contradiction[-1], RIGHT)\
.set_color(RED)
# --------- Aligns
_because.align_to(title, LEFT)
self.align_tex_with_symbol((eq_grp1[0],2), (eq_grp1[1], 4))
self.align_tex_with_symbol((eq_grp1[0],2), (eq_grp1[2], 4))
eq_grp1[2][0].align_to(eq_grp1[1][0], LEFT)
self.align_tex_with_symbol((logic_proof[0], 2), (logic_proof[1], 3))
self.align_tex_with_symbol((logic_proof[0], 2), (logic_proof[2], 2))
logic_proof[2][0].align_to(logic_proof[1][0], LEFT)
logic_proof.set_x(0)
self.align_tex_with_symbol((q_contradiction[0], 3), (q_contradiction[2], 2))
q_contradiction[2][0].align_to(q_contradiction[1][0], LEFT)
_therefore = MathTex("\\therefore")\
.next_to(logic_proof[0], LEFT, buff=0.1)
_logic_proof_1 = VGroup(_therefore, logic_proof[0]).set_x(0)
logic_proof[-1].align_to(_logic_proof_1, LEFT)
fade_group = VGroup(
_because,
odd_proof,
logic_proof[:-1],
generic_odd_brace,
generic_odd_tex,
_1, odd_brace, odd_tex,
_4kp1_tex, _4kp1_brace,
_therefore
)
shift_grp = VGroup(
# logic_proof,
q_contradiction,
adm_sign
)
shift_grp.shift(UP * fade_group.height)
# ------- Animations
self.play(Write(title))
self.wait()
self.play(
TransformFromCopy(title[1][:3], eq_grp1[0][0][:]), # sqrt(2)
TransformFromCopy(title[1][-1], eq_grp1[0][1]), # q
TransformFromCopy(title[1][3], eq_grp1[0][2]), # =
TransformFromCopy(title[1][4], eq_grp1[0][3]), # p
)
self.play(
TransformMatchingShapes(eq_grp1[0].copy(), eq_grp1[1]),
)
self.play(
TransformMatchingShapes(eq_grp1[1].copy(), eq_grp1[2]),
)
self.play(Write(conc1))
self.wait()
self.play(Write(_because))
self.play(Write(odd_proof[0][0]))
self.play(
GrowFromCenter(generic_odd_brace),
FadeIn(generic_odd_tex),
)
self.wait()
self.play(Write(odd_proof[0][1:]))
self.play(
TransformMatchingShapes(odd_proof[0][1:-1].copy(), odd_proof[1][:-1]),
TransformFromCopy(odd_proof[0][-1], odd_proof[1][-1])
)
self.play(
GrowFromCenter(_4kp1_brace),
FadeIn(_4kp1_tex),
)
self.play(
TransformFromCopy(odd_proof[1][-1], _1)
)
self.play(
GrowFromCenter(odd_brace),
FadeIn(odd_tex),
)
self.play(Write(_logic_proof_1))
self.wait()
self.play(
TransformMatchingTex(logic_proof[0].copy(), logic_proof[1]),
)
self.play(
*[
ReplacementTransform(logic_proof[1][i].copy(), logic_proof[2][j])
for i,j in [
(0, 0),
(2, 1),
(3, 2),
(5, 3),
]
],
run_time=3
)
self.play(
Indicate(conc1),
Indicate(logic_proof[-2]),
run_time=2.5
)
self.play(Write(logic_proof[-1]))
self.wait()
# --- shift group
self.play(
FadeOut(fade_group),
logic_proof[-1].animate.shift(UP * fade_group.height)
)
self.wait()
self.play(Write(q_contradiction[0]))
self.play(
TransformMatchingTex(q_contradiction[0].copy(), q_contradiction[1]),
)
self.play(
TransformFromCopy(q_contradiction[1][0], q_contradiction[2][0]),
TransformFromCopy(q_contradiction[1][2:], q_contradiction[2][1:]),
)
self.play(Write(q_contradiction[3]))
self.wait()
self.play(Write(q_contradiction[4]))
self.wait()
self.play(FadeIn(adm_sign, scale=9))
self.play(
Indicate(title[-2:], color=RED),
Indicate(q_contradiction[4], color=RED),
run_time=2
)
self.wait()
self.play(FadeOut(*self.mobjects))
self.play(
Write(Tex("$\\therefore\\,\\sqrt{2}$ is irrational")),
run_time=1
)
self.wait(2)
# self.add(
# title, *eq_grp1, conc1, _because, odd_proof,
# generic_odd_brace,
# generic_odd_tex,
# _4kp1_brace, _4kp1_tex, _1,
# odd_brace, odd_tex,
# *logic_proof,
# *q_contradiction,
# adm_sign
# )
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