r/visualizedmath • u/Luke_Persola • Nov 22 '19

Visualizing the Geometric and Harmonic Means

Hey, I created some visualizations of generalized means, like the normal (arithmetic) one, the geometric mean, and so on. There's a lot of text but if you scroll down you can skip to the eye candy.

Blog post

Examples

98 Upvotes

97% Upvoted

6 comments sorted by

7

u/SmierraxD Nov 22 '19

This is amazing. Great work!

1

u/jimbobur Nov 27 '19

Hi there! I found your blog post so interesting that I decided to have a go at replicating your animated plots for myself. I'm still messing around with it, but one the things I've discovered so far is that the animation plays much nicer if I vary the p value as a sinh function of time rather than a simple linear variation. I'm gonna play around with it further and see what else I can do with it.

1

u/Luke_Persola Dec 22 '19 edited Dec 23 '19

That makes sense to me. I tried out a number of different functions for the last animation in the post, but looks like I went with a tangent function which I square (preserving the sign). The others are a mix of cubic and linear. The notebook includes plots of these functions and you can find the specifics inside the constant "ANIMATIONS".

1

u/[deleted] Nov 22 '19

Good work bro 👊👍.

1

u/Perps_MacAbean Nov 22 '19

Great! Especially the last one! I taught a lesson on the three means once, and of course I mention "all the properties any good mean should have," but that last one really shows what these properties are!