Uploaded June 2024 | Updated September 2026, 2 weeks ago
This video is a compilation of seven shorter videos that I have created showing various visual proofs without words of the famous AM-GM inequality, which states that the arithmetic mean of two numbers (a+b)/2 is greater than or equal to the geometric mean of the two numbers square root of a times b.
To see the original videos (in shorter form and sometimes with words/explanations), check the links below. Of course there are many other visual proofs of this amazing fact, but these are my favorite seven.
Let me know your favorite in the comments!
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
0:00 Introduction
0:05 Folding Proof : youtu.be/IJGwvvQdfgg and youtube.com/shorts/YAGjrfpHq-Q (attribution: Yukio Kobayashi)
0:40 Circle with Triangles : youtu.be/HFGSsPbYc-s (attribution: Roger B. Nelsen)
1:07 Sliding Triangles: youtu.be/SEPkdPWKdO0 (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles : youtu.be/jNx05gXSblE (attribution : Roland H. Eddy)
2:38 Eight Kites : youtu.be/02yM5LqMWUs (attribution: Ayoub B. Ayoub)
3:27 Tatami : youtu.be/62G9fak1vyk and youtube.com/shorts/if800mpoJaY(attribution: Doris Schattschneider)
4:05 Semicircle : youtu.be/Pt8IX_Q5U1A and youtube.com/shorts/jB0OZYA_EI0 (attribution: Charles D. Gallant)
4:49 Ending citation
If you like this inequality or others, you can check out my playlists of inequalities and AM-GM inequality:
Inequalities: youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=_cVhtnlrrAIQg9f6
AM-GM : youtube.com/playlist?list=PLZh9gzIvXQUuoRR4kTd628cWdFQ1BDyS6&si=zZYGTtPAsp0jXr42
#math #amgminequality #area #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #inequality #inequalities
To learn more about animating with manim, check out:
https://manim.community
This video is a compilation of seven shorter videos that I have created showing various visual proofs without words of the famous AM-GM inequality, which states that the arithmetic mean of two numbers (a+b)/2 is greater than or equal to the geometric mean of the two numbers square root of a times b.
To see the original videos (in shorter form and sometimes with words/explanations), check the links below. Of course there are many other visual proofs of this amazing fact, but these are my favorite seven.
Let me know your favorite in the comments!
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):
0:00 Introduction
0:05 Folding Proof : youtu.be/IJGwvvQdfgg and youtube.com/shorts/YAGjrfpHq-Q (attribution: Yukio Kobayashi)
0:40 Circle with Triangles : youtu.be/HFGSsPbYc-s (attribution: Roger B. Nelsen)
1:07 Sliding Triangles: youtu.be/SEPkdPWKdO0 (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles : youtu.be/jNx05gXSblE (attribution : Roland H. Eddy)
2:38 Eight Kites : youtu.be/02yM5LqMWUs (attribution: Ayoub B. Ayoub)
3:27 Tatami : youtu.be/62G9fak1vyk and youtube.com/shorts/if800mpoJaY(attribution: Doris Schattschneider)
4:05 Semicircle : youtu.be/Pt8IX_Q5U1A and youtube.com/shorts/jB0OZYA_EI0 (attribution: Charles D. Gallant)
4:49 Ending citation
If you like this inequality or others, you can check out my playlists of inequalities and AM-GM inequality:
Inequalities: youtube.com/playlist?list=PLZh9gzIvXQUuKcFHdtjFkwAVELDxu9nH4&si=_cVhtnlrrAIQg9f6
AM-GM : youtube.com/playlist?list=PLZh9gzIvXQUuoRR4kTd628cWdFQ1BDyS6&si=zZYGTtPAsp0jXr42
#math #amgminequality #area #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #inequality #inequalities
To learn more about animating with manim, check out:
https://manim.community
