He points out that the YouTube video "uses mediants" to compute rational approximations to real numbers. He then says that the continued fraction expansion is better. However, the mediant-based method is totally identical to the continued fraction expansion method. The two are related via the Stern-Brocot tree (https://en.m.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree).
The fractions that one gets from iterating the mediant process are exactly the "semiconvergents" one gets from the continued fraction process. Truncating the continued fraction gives the "convergents"; these are special mediants which are right before switching direction as one zig zags on the tree.
The fractions that one gets from iterating the mediant process are exactly the "semiconvergents" one gets from the continued fraction process. Truncating the continued fraction gives the "convergents"; these are special mediants which are right before switching direction as one zig zags on the tree.