Рет қаралды 36,121
In this video, we present two animated visual proofs demonstrating that if e is less than or equal to A and A is less than B then A^B is greater than B^A . Moreover, we include a bonus proof that is sometimes referred to as the standard way to get this result.
Correction : at 0:57 I had misspoken, so I cut 1 second, which is why the tangent line appears so fast and the audio has a break.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
This animation is based on two visual proofs, one by Charles D. Gallant from the February 1991 issue of Mathematics Magazine (doi.org/10.2307/2690451 ) and the other by Nazrul Haque from the January 2021 issue of Resonance (doi.org/10.1007/s12045-020-11... ). Notice that plugging in A = e and B = Pi, we get Pi^e is less than e^Pi.
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....
If you like this video, check out my playlists on inequalities and calculus:
• Inequalities
• Calculus
#mathshorts #mathvideo #math #inequality #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #inequality #logarithm #naturallog #exponential
To learn more about animating with manim, check out:
manim.community