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/q39...

Credit to mathmasterzach for his help. His website: https://www.mathmasterzach.com/

Additional sources:
https://www.cut-the-knot.org/blue/Med...
https://www.whitman.edu/Documents/Aca...

My Patreon:   / 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