A derivation of the curve that is approximated by a common visualization of the bubble sort diagram.

Read the full proof on my site: https://linesthatconnect.github.io/bl...

The viral sorting algorithm video which first sparked my interest:    • 15 Sorting Algorithms in 6 Minutes  

The animations in this video were created using Manim: https://www.manim.community/

Music credits:
Fluidscape by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/...
Night Music by Kevin Macleod
river - Calm and Relaxing Piano Music by HarumachiMusic
... And a couple of my own songs:
The Fog:   / the-fog  
Heavy Head, Light Rain:   / heavy-head-light-rain  
Thanks For Watching:   / thanks-for-watching  


Chapters:
00:00 Intro:
0:37 Laying the Background
3:20 How Bubble Sort Works
6:59 Mathematically Describing Diagrams
9:13 Stretching the Diagrams
11:52 Visual Derivation
14:38 Symbolic Derivation
16:48 Nice!
17:07 A Rigorous Solution