Arithmetic Mean-Geometric Mean Visual Proof Compilation
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: https://www.buymeacoffee.com/VisualPr.... 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 : • Folding the AM-GM Inequality V (quick... and • Fold the AM-GM inequality (attribution: Yukio Kobayashi)
0:40 Circle with Triangles : • Mean Inequalities (visual proof of AM... (attribution: Roger B. Nelsen)
1:07 Sliding Triangles: • AM-GM Inequality III (visual proof) (attribution: Claudi Alsina and Roger B. Nelsen)
1:52 Tangent Circles : • AM-GM Inequality IV (visual proof) (attribution : Roland H. Eddy)
2:38 Eight Kites : • AM-GM Inequality VI (visual proof) (attribution: Ayoub B. Ayoub)
3:27 Tatami : • Visual Proof of AM-GM Inequality I and • AM-GM inequality visually (attribution: Doris Schattschneider)
4:05 Semicircle : • AM-GM Inequality II (visual proof) and • AM-GM Inequality II (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: • Inequalities
AM-GM : • AMGM Inequality
#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
Watch video Arithmetic Mean-Geometric Mean Visual Proof Compilation online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 30 June 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 7,758 once and liked it 418 people.