A triplet tree forms one of the most beautiful structures in math
2023-12-13•Hacker News•Share on Twitter•Share on Linkedin•Copy link
Summary:
The Markov equation, discovered by Andrey Markov in 1879, connects tough-to-approximate irrational numbers to integer solutions.
The equation has a simple rule that generates a tree of solutions, with branches containing sequences like the Fibonacci and Pell sequences.
The uniqueness conjecture, which states that the largest number in each triplet uniquely determines the two smaller numbers, remains unproven but progress has been made in recent years.