GoKawiil... beneath a 🌘 Waning Crescent
…symmetry isn’t just a preference for “pretty” shapes.
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.
After writing my previous handout article regarding inequalities, 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 the like). So I’ve been digging and improvising, and I’ve come up with some animations to help people get a geometrical intuition of things that are mostly studied in algebra and analysis.
Some of the animations are standard and are taught in the right kind of schools, but others have some originality. For those, I actually developed the ideas using pen, paper, and my own imagination. If somebody else already did that, it’s fine; I am not a fool to claim “real” originality when it comes to basic mathematics. The roads were already very circulated in the last 2000 years.
The HM-AM-GM-QM Inequality
This is the most popular inequality chain we encounter during our school years. To remind you of it, in case you’ve forgotten, the simple version for three numbers $a, b, c > 0$ is:
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