AM-GM Inequality via negative space
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.
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For other visual proofs of this fact see:
• AM-GM Inequality II (visual proof)
• Visual Proof of AM-GM Inequality I
• Mean Inequalities (visual proof of AM...
For a nearly identical visual proof of another inequality (Cauchy-Schwarz) see
• Cauchy Bunyakovsky Schwarz Inequality...
This animation is based on a visual proof that appears in Icons of Mathematics by Claudi Alsina and Roger B. Nelsen (MAA, 2011):
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