Root 3 is Irrational @MathVisualProofs

Uploaded October 2025 | Updated September 2026, 2 weeks ago

In this video, we use the "Carpets Theorem" to prove that the square root of three is irrational by a visual infinite descent argument.

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This animation is based on an argument from Stanley Tennebaum. If you are interested, I recommend this article from John Conway and Joseph Shipman about the irrationality of square root of two (and others):

http://dev.mccme.ru/~merzon/mirror/mathtabletalks/files/irrational-conway.pdf

For a longer version with root two, see:
youtu.be/-dbzvN4jnfY?si=6uT5EFkUCp8D8eh7

And for a short about root two:
youtu.be/s4pdePg_m3w?si=yzG-h2YJUmuYJ9Sy

Here is an alternate irrational visual argument:
youtube.com/watch?v=uWZsVx7wqeA

#irrationalnumbers #realnumbers #manim #math #mtbos #animation #theorem #visualproof #proof #iteachmath #mathematics #irrational #carpetstheorem #proofbycontradiction #root2 #algebra #infinitedescent

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Pythagorean theorem from a (semi) circle!

$Chaos Game finds the Mandelbrot Quintet In this video, we show how to use a random process of iteratively applying five affine transformations in the real plane to generate a 5-rep-tile known as the Mandelbrot Quintet. What happens if you do something similar with different affine transformations? Here is a bit longer version (without words): https://youtu.be/rLxx6b-oJGo Check out these videos for related constructions: https://youtube.com/shorts/dklWNdM9WSg https://youtu.be/rLxx6b-oJGo https://youtu.be/NBI_5GdvqUo If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! This animation was inspired by an article written by Lorelei Koss that appeared in the Proceedings of Bridges 2015: https://archive.bridgesmathart.org/2015/bridges2015-423.pdf . For more information, you should also check out the related article Fractal Tilings in the Plane by Richard Darst, Judith Palagallo and Thomas Price from the February 1998 Mathematics Magazine: https://www.jstor.org/stable/2691339 #chaos #chaosgame #quintet #mandelbrot #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals To learn more about animating with manim, check out: https://manim.community$

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