What happens if we add fractions incorrectly? Can we do something with that? This video covers mediants, Simpson's paradox, Farey sequences, the Stern-Brocot tree, Ford circles, rational approximations, and Hurwitz's theorem.
Hurwitz range interactive: https://www.desmos.com/calculator/q39cnrut4m
Free poster of the conclusion flow diagram for download: https://drive.google.com/file/d/1tKWcIdzvF86TxqprY_i9Rhw56wByn2Jg/
Credit to mathmasterzach for his help. His website: https://www.mathmasterzach.com/
Additional sources:
https://www.cut-the-knot.org/blue/Mediant.shtml
https://www.whitman.edu/Documents/Academics/Mathematics/2016/Zukin.pdf
My Patreon: https://www.patreon.com/zhulimath/
0:00 Definition of a mediant
1:52 Simpson's Paradox
6:03 List of all rational numbers
15:41 Visualizations
17:08 Ford circles
18:41 Rational approximations and Hurwitz's Theorem
25:20 Outro: Why did we do all of this?
Intro riff taken from: Nikolai Kapustin - 8 Concert Etudes, Op. 40: III. Toccatina
Music Credit:
Elegance / Megan Wofford
Technicolor Dreamscape / Franz Gordon
Joy in the Little Things / Sayuri Hayashi Egnell
Reve d'enfant / Magnus Ludvigsson
Lovely Dinner / Franz Gordon
When Sun Meets Moon / Gavin Luke
courtesy of www.epidemicsound.com