Uploaded March 2026 | Updated September 2026, 2 weeks ago
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: buymeacoffee.com/VisualProofs. Thanks!
This animation is based on a visual proof by Charles D. Gallant from the February 1991 issue of Mathematics Magazine (doi.org/10.2307/2690451 ).
If you like this video, check out this more general video:
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: link.springer.com/article/10.1007/s00283-024-10342-5
If you like this video, check out my playlists on inequalities and calculus:
youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=J-BdpxhqAUsf2_85
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
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: buymeacoffee.com/VisualProofs. Thanks!
This animation is based on a visual proof by Charles D. Gallant from the February 1991 issue of Mathematics Magazine (doi.org/10.2307/2690451 ).
If you like this video, check out this more general video:
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: link.springer.com/article/10.1007/s00283-024-10342-5
If you like this video, check out my playlists on inequalities and calculus:
youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=J-BdpxhqAUsf2_85
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
