Rethinking the real line #SoME3

We take a geometric approach to rational numbers, to rethink how to organize the real line. Along the way, we visualize Diophantine approximation and continued fractions. And your favourite number, pi. Much of the mathematics here is based on the following article: Series, C. The geometry of markoff numbers. The Mathematical Intelligencer 7, 20–29 (1985). https://doi.org/10.1007/BF03025802 A big thanks to the Summer of Math Exposition competition for the motivation to make this happen, and a big thanks to my audience for forgiving my video-editing non-skills. Some of the software used in creating this: Sage Mathematics Software, Manim, VPython, p5.js, Krita, Audacity, Kdenlive. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Music used in the video: Walk Through the Park -- TrackTribe George Street Shuffle -- Kevin MacLeod Quarter Mix -- Freedom Trail Studio Love Struck -- E's Jammy Jams George Street Shuffle by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/ Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1300035 Artist: http://incompetech.com/