Listing the Rationals Using Continued Fractions, Part 2

This video provides rigor to the ideas from the first video. We verify the essential properties of the Calkin-Wilf tree, as well as its correspondence with continued fractions. Applications to irrational numbers are explored, including the golden ratio and the square root of 2, which become running examples in the series. Finally, we revisit an important case of the Euclidean algorithm relating to certain paths in the tree.

Chapters:
00:00 - Welcome
00:14 - Calkin-Wilf tree
02:43 - Golden ratio
05:08 - Square root of 2
06:33 - Left and right rules
07:24 - Continued fractions
08:00 - Ending left
08:35 - Euclidean algorithm
09:20 - Outro

[compasstech]

Great work Ben - thank you! Looking forward to more.

[ARC-]

Great video! Lots of cool properties of the Calkin-Wilf tree and great animations for them :)

[wyattstevens]

Let's say you know the value of l(n) to be L and just want to know l(n+1). There's a way to do this, surprisingly! Here it is: 1/l(n+1)= 2int(l(n))-l(n)+1