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Curated by: Mathematical Visual Proofs (650 videos)
e^ Pi vs Pi^e: which is bigger? III Visual proof via tangent and secant lines In this video, we present an animated visual proof demonstrating that if e is less than A, then e^A is greater than A^e, where we focus primarily on the case with A=pi. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! This animation is based on a visual proof by Charles D. Gallant from the February 1991 issue of Mathematics Magazine (https://doi.org/10.2307/2690451 ). If you like this video, check out this more general video: https://youtu.be/4SxslxoYwgU If you are interested in the general question about A^B vs. B^A, check out this article from Bikash Chakraborty and Nazrul Haque: https://link.springer.com/article/10.1007/s00283-024-10342-5 If you like this video, check out my playlists on inequalities and calculus: https://youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=J-BdpxhqAUsf2_85 https://youtube.com/playlist?list=PLZh9gzIvXQUutzxgeJemfN2DrUGt3ccVg&si=HLzczjg8dIT-nKNZ #math #manim #theorem #visualproof #calculus To learn more about animating with manim, check out: https://manim.community