Geometric Representations of Mathematical Inequalities
By
nomemory
Slow-proofed and worth the wait. Worth its weight in flour.
Summary
This article explores the geometric representation of mathematical inequalities, inspired by a 1985 image from Roland H. Eddy. The author examines how classic inequalities like HM-AM-GM-QM (harmonic, arithmetic, geometric, and quadratic means) and others can be visualized using geometric shapes including circles, semicircles, containers, and 3D containers. The content demonstrates mathematical concepts through geometric interpretations, showing how symmetry in shapes relates to mathematical inequalities rather than just aesthetic preferences.
Key quotes
· 5 pulled...symmetry isn't just a preference for 'pretty' shapes.
I wanted to see if I could find ways to represent inequalities in a geometrical way (you know, classic circles, triangles, squares, cubes, rectangular prisms...)
And it tickled my imagination a little, just enough to write this short post.
The HM-AM-GM-QM Inequality
The two circles, The Semicircle, The Container, The 3D container
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