Uploaded September 2025 | Updated September 2026, 2 weeks ago
This is a short, animated visual proof demonstrating the sum of the infinite series with first term 3/4 and ratio 1/4 using a famous rep-tile shape known as the Sphinx. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are some other visual proofs of the same fact:
youtu.be/8i1xj5ORwUw
youtube.com/shorts/qk1IPvvWfr0?si=_pWQ_YbQpig_xpLn
youtube.com/shorts/7K1IV-mRDho?si=y-75V2NZoBIhlG7E
Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw
This animation is based on the fact that any rep-tile leads to a geometric series sum visualization and the Sphinx is a famous rep-tile, which you can learn more about at en.wikipedia.org/wiki/Sphinx_tiling
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #equilateraltriangle #sphinx #sphinxtile #rep-tile #reptile
To learn more about animating with manim, check out:
https://manim.community
______________________________
Music in this video:
Blockbuster by Alex-Productions | https://onsound.eu/
Music promoted by free-stock-music.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
creativecommons.org/licenses/by/3.0/deed.en_US
This is a short, animated visual proof demonstrating the sum of the infinite series with first term 3/4 and ratio 1/4 using a famous rep-tile shape known as the Sphinx. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are some other visual proofs of the same fact:
youtu.be/8i1xj5ORwUw
youtube.com/shorts/qk1IPvvWfr0?si=_pWQ_YbQpig_xpLn
youtube.com/shorts/7K1IV-mRDho?si=y-75V2NZoBIhlG7E
Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw
This animation is based on the fact that any rep-tile leads to a geometric series sum visualization and the Sphinx is a famous rep-tile, which you can learn more about at en.wikipedia.org/wiki/Sphinx_tiling
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #equilateraltriangle #sphinx #sphinxtile #rep-tile #reptile
To learn more about animating with manim, check out:
https://manim.community
______________________________
Music in this video:
Blockbuster by Alex-Productions | https://onsound.eu/
Music promoted by free-stock-music.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
creativecommons.org/licenses/by/3.0/deed.en_US
