Uploads from Mathematical Visual Proofs

Currently Playing: The Sphinx Sums a Series!

The Sphinx Sums a Series! 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: https://www.buymeacoffee.com/VisualProofs. Thanks! For a wordless version of this animation see : https://youtu.be/KUaO5dnjGvI Here are some other visual proofs of the same fact: https://youtu.be/8i1xj5ORwUw https://youtube.com/shorts/qk1IPvvWfr0?si=_pWQ_YbQpig_xpLn https://youtube.com/shorts/7K1IV-mRDho?si=y-75V2NZoBIhlG7E Also, check out my playlist on geometric sums/series: https://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 https://en.wikipedia.org/wiki/Sphinx_tiling ​​ #math​ #calculus​ #manim​ #infiniteseries #proofwithoutwords #mathematics To learn more about animating with manim, check out: https://manim.community