AM-GM Inequality via negative space @MathVisualProofs

Uploaded August 2024 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof demonstrating the arithmetic mean geometric mean inequality using algebraic areas and the Side-Angle-Side formula for a parallelogram.

If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!

For other visual proofs of this fact see:

youtu.be/Pt8IX_Q5U1A
youtu.be/62G9fak1vyk
youtu.be/HFGSsPbYc-s

For a nearly identical visual proof of another inequality (Cauchy-Schwarz) see
youtu.be/mKg_gVagHy8

This animation is based on a visual proof that appears in Icons of Mathematics by Claudi Alsina and Roger B. Nelsen (MAA, 2011):

#mathshorts #mathvideo #math #amgminequality #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #inequality

To learn more about animating with manim, check out:
https://manim.community

Nested Powers of 2 Hypocycloids (synthwave enumeration)

Geometric sum of powers of 1/3 (v. III visual proof in a hexagon)

$Simpson’s Paradox Visually! In this short video, we show how to think about Simpsons paradox visually in terms of vector arithmetic. In particular we show that ratios can be represented by slopes of lines (or slopes of vectors) and then we can have an interesting slope reversal when adding as you would add proportions or statistics (not usual fraction arithmetic). If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! The visual proof in this video is based on a proof without words by Jerzy Kocik from the December 2001 issue of Mathematics Magazine ( https://www.jstor.org/stable/2691038 page 399). #mathshorts #mathvideo #math #statistics #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #paradox #simpsonsparadox #simpson #derekjeter #davidjustice #baseball #proportion #vectors #vectoraddition #battingaverage #data To learn more about animating with manim, check out: https://manim.community$

A Factorial Sum Produces the Factorial Number System (visual proof)