Visualization of Pi being Irrational (the animation could go on forever)

Prepare for a visually striking journey through the mathematical concept of Pi! Ever wondered what it means for Pi to be irrational? This mesmerizing animation offers a unique perspective on the relationship between the continued fractions and Pi's never-ending, non-repeating decimal expansion.

Note: I do not know who made the original, if someone could please comment with the link to the original upload I will be happy to add it here!

Coupled with the beautiful sounds of Vivaldi's Four Seasons, the video captures the almost tantalizing moments where Pi appears to be close to rational approximations, but then veers away, reinforcing its "irrational" nature. Watch as the animated trail narrowly "misses" hitting certain key points—these are the moments Pi eludes its approximations like 22/7 or 333/106. If you find math to be the closest thing to actual magic we have, this video will captivate your imagination.

📐 Equation at the Bottom Explained:

You'll notice an equation at the bottom of the screen; it represents the complex domain of a circle and spiral. For every one rotation the inner circle completes, the outer circle does Pi rotations. In this way, the dot never lines up exactly with its starting point—emphasizing Pi's irrationality.

💡 Fun Fact:

At various timestamps, the animation highlights when the dot 'almost' aligns with its starting point—these are the moments when Pi misses some of its continued fraction approximations. For instance, at timestamp ~342, it narrowly misses the integer "3". At ~2520, it sways away from 22/7, and so on.

🎶 Background Music:

The captivating background music is from Vivaldi’s Four Seasons composition, focusing on "Summer". A perfect accompaniment that adds another layer of beauty to the video.

🔗 Related Links:

Further Reading: Numberphile's in-depth exploration of Pi
Music Credits: Mari Samuelsen performing Vivaldi’s Four Seasons

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Mathematics, Pi, Irrational Numbers, Number Theory, Geometry, Animated Visualization, Mathematical Constants, Complex Numbers, Spirals, Educational Content, Science and Math, STEM, Circle Geometry, Approximations, Continued Fractions, Mathematical Beauty, Trigonometry, Rational vs Irrational, Algebra, Math Education, YouTube Education, High School Math, College Math, Numberphile, Advanced Mathematics, Academic Topics, Math Animation, Math Exploration, Math Curiosity, Math Concepts, Vivaldi, Four Seasons, Classical Music in STEM, Mathematical Art, Math in Nature, Ratio, Infinite Series, Mind-blowing Math, Math Theorems, Math Mysteries, Pi Day, 3.14159, Geometric Progression, Explaining Pi, Math for Adults, Mathematical Models, Ancient Mathematics, Math History, Math Lore, Unresolved Math Problems, Learning Math, Math Puzzles, Math Challenge, Visualization Techniques, Math and Music, Infographics, Mathematical Equations, Golden Ratio, Math and Philosophy, Math Enthusiasts, Interactive Learning, Math in Real Life, Math in Culture, Mathematical Representation, Satisfying Math, r/BeAmazed, Reddit Discussions, User Generated Content, Audience Engagement, Math Discussion, Visual Learning, Cognitive Learning, Modern Mathematics, Math Symbols, Conceptual Understanding, Theoretical Math, Applied Math, Math Lovers, Math Nerds, Academic Research, Math and Technology, Math Software, DIY Math, Virtual Learning, Math Breakthroughs, Mindfulness in Math, Critical Thinking, Problem Solving,

#Pi #IrrationalNumbers #Mathematics #Science #Animation #Vivaldi #FourSeasons #ComplexDomain #Numberphile #ContinuedFractions #Mesmerizing #Educational #MusicInMath #InfiniteLoop #rBeAmazed

Hope you enjoy the journey through the endless landscape of Pi!

[OyeAlguien]

I love when pi just says "f**k this sh*t imma be irrational" and proceeds to be irrational all over the place

[carumsarene]

The video is a good way to showcase chaos fatalism too.

[ChEeSeWaLeK]

I like how you took this from the actual creator, and trying to play it off as your own work.

[ossianwestermark]

Pov: my 37 brain cell after somehow working together for once

[dcterr]

This is really just an illustration of the first 5 continued fraction coefficients of pi. The fact that the curve is nearly closed after the third and fifth near completions is related to the fact that the third and fifth coefficients are so large, namely 15 and 292, respectively. Unfortunately, we could never prove in a finite amount of time with this video that pi is irrational any more than we could by computing its continued fraction term by term, which is infinite, due to the fact that pi is irrational. Nice video in any case!

[ares.arctic]

With metric math, irrationality is not a longshot as it’s not that surprising, but it says a lot when it isn’t even rational on a circle

[jotablog]

Al acabar la primera vuelta se me dispara el TOC.

[antifurrydiplomat]

average calamity weapon attack: The Book of Pi
infinite range. TBoP causes this animation to play. after the animation is done, the ball goes to the surface and rolls in whatever direction the use if facing. the ball can also bounch, but each bounce is 50% the height of the last bounce. the stronger the title (damaged to godly) of the weapon is, the faster the animation

[NguyênNguyễnĐình-ml]

Can you explain more about it: examples of functions in mathematics?

[Bacon]

Those parts where the lines don't quite touch are so infuriating

[ayanjawaid]

this video is taken from Instagram.. i follow the creator who made this video on insta

[bentibbly]

When you have ocd and you hate yourself

[joelchristophr]

both the arms dont have same angular speed ig...

[leonardoeneria]

Oppenheimer theme on this was better IMO

[Lws-]

This is not your video, credit the one who made this

[maciejkozowski]

Quit boring. Any irrational number can do that... I'm wrong? What so special about pi? Better would be visualization illustrating the fact that π is a transcendental number.

[LucidLiuxx]

stolen video.
credit the creator, or better yet stop being lazy and make your own content.

[MalluG]

I just realized that up actually could theoretically end instead of being infinite this only theoretical of course🍍🍱🥟🦪🥟🥟🥟🥟🥟🥟🦪🥟🥟🥟🥟🥟🥟🥟🍘🥟🥟