Most of us know about the golden ratio, \(\phi = \frac{1+\sqrt{5}}{2} \) and how it can be considered the most irrational number, but most people never ask the question, “What is the second and third most irrational number?” In this post, I discuss discuss some special irrational numbers, and why they can be considered the 2nd and 3rd most irrational numbers. Finding good rational approximations to reals. In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The problem on how well a real number can be approximated by rational numbers is…

# What is the 3rd most irrational number?