The Shape of Inequalities

…symmetry isn't just a preference for "pretty" shapes.

Contents


Introduction
The HM-AM-GM-QM Inequality

The two circles
The Semicircle
The Container
The 3D container


The Sum of Squares Inequality
Nesbitt's Inequality
Conclusion



Introduction
While I was randomly browsing the web, I came across this nice picture:




Roland H. Eddy, Memorial University of Newfoundland, Canada, 1985



And it tickled my imagination a little, just enough to write this short post.