Dancing tilings - why this pattern? @MathVisualProofs

Uploaded September 2024 | Updated September 2026, 2 weeks ago

This short shows the enumeration of all the domino tilings of the (2 x n)-grid for n=1 to n=8. Can you tell the pattern? Can you prove why or how the Fibonacci numbers (perhaps more aptly called the Virahanka numbers) appear?

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If you are looking for more information about this, I recommend this fantastic video by ⁠ : youtu.be/Ct7oltmdJrM or the wonderful textbook Proofs that Really Count: The Art of Combinatorial Proof from Arthur Benjamin and Jennifer Quinn: bookstore.ams.org/dol-27

#dominotilings #fibonacci #counting #count #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #discretemath #combinatorics #enumeration #synthwave

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Leibniz Formula for Pi/4 - A Pi Day Visualization/Dissection

$Wallis Sieve Area! In this short, we show how to build the Wallis Sieve using an iterative procedure of cutting remaining square lengths into the next odd and removing the created central square in the corresponding square grid. Along the way, we discuss how to compute the area of the resulting limiting shape as an infinite product. This infinite product is related to the famous Wallis product and so the shaded area is amazingly Pi/4. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Wallis Sieve, check out this wonderful short article by Evelyn Lamb: https://www.scientificamerican.com/blog/roots-of-unity/a-few-of-my-favorite-spaces-the-wallis-sieve/ #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #dynamicalsystems #fractal #fractals #wallissieve #wallis #wallisproduct #infiniteproduct To learn more about animating with manim, check out: https://manim.community$

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$Chaos in a Heptagon! In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Chaos game, see the following links: https://en.wikipedia.org/wiki/Chaos_game https://mathworld.wolfram.com/ChaosGa... https://math.bu.edu/DYSYS/chaos-game/... https://youtu.be/kbKtFN71Lfs https://youtu.be/IGlGvSXkRGI https://youtube.com/shorts/yDHkNDrHfIw #chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals To learn more about animating with manim, check out: https://manim.community$