Uploaded November 2025 | Updated September 2026, 2 weeks ago

---

Try everything Brilliant has to offer by visiting brilliant.org/wrathofmath and you'll also get 20% off an annual premium subscription!

In school we learn all about quadratic equations and their parabolic graphs. Importantly we learn how to 'solve' them by factoring, graphing, completing the square and using the quadratic formula. But there's one method they never taught you that involves and UNTOLD number of fractions. Today we discover this secret! #brilliant #algebra #mathtricks

🛍 Check out my math fashion brand! mathshion.com
❤️ Join Wrath of Math to get exclusive videos, lecture notes, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join

More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Business Inquiries: wrathofmathlessons@gmail.com

Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● TikTok: tiktok.com/@wrathofmathedu
● X: https://x.com/wrathofmathedu

SOURCES
Continued Fractions by C. D. Olds
Continued Fractions: Notes for a short course at the Ithaca High School Senior Math Seminar by Gautam Gopal Krishnan
Continued Fractions and Pell's Equation by Seung Hyun Yang
allresearchjournal.com/archives/2020/vol6issue1/PartD/6-10-428-385.pdf

0:00 Intro
1:46 Bombelli's Approximation
3:44 Constructing the Beast
7:51 Solving x^2=2
10:57 The Ultimate Weapon
14:45 Potential Disasters
19:29 Rate of Convergence
21:49 Conclusion