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What Happens If We Add Fractions Incorrectly?

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